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BEGIN:VEVENT
SUMMARY:Pavel Exner (Doppler Institute for Mathematical Physics and Applie
d Mathematics)
DTSTART:20201110T134500Z
DTEND:20201110T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/1
DESCRIPTION:Title: Spiral quantum wavegudies\nby Pavel Exner (Doppler Institute
for Mathematical Physics and Applied Mathematics) as part of Quantum Circ
le\n\n\nAbstract\nThe topic of this talk is a quantum particle confined to
a spiral-shaped region with Dirichlet boundary. As a case study we analyz
e in detail the Archimedean spiral and show that the spectrum above the co
ntinuum threshold is absolutely continuous away from the thresholds. The s
ubtle difference between the radial and perpendicular width implies\, howe
ver\, that in contrast to numerous examples of `less curved' waveguides\,
the discrete spectrum is empty in this case. We also discuss modifications
such a multi-arm Archimedean spirals and spiral waveguides with a central
cavity\; in the latter case bound state already exist if the cavity excee
ds a critical size. For spiral regions of a more general type the spectral
nature depends substantially on whether their coil width is `expanding' o
r `shrinking'. The most interesting situation occurs in the case we call a
symptotically Archimedean\, where the existence of bound states depends on
the direction from which the asymptotics is reached.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dale Frymark (Nuclear Physics Institute CAS)
DTSTART:20201124T134500Z
DTEND:20201124T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/2
DESCRIPTION:Title: Singular boundary conditions for Sturm-Liouville operators via p
erturbation theory\nby Dale Frymark (Nuclear Physics Institute CAS) as
part of Quantum Circle\n\n\nAbstract\nWe show that all self-adjoint exten
sions of semi-bounded Sturm-Liouville operators with general limit-circle
endpoint(s) can be obtained via an additive singular form bounded self-adj
oint perturbation of rank equal to the deficiency indices\, say d=1 or 2.
This characterization generalizes the well-known analog for semi-bounded S
turm-Liouville operators with regular endpoints. Explicitly\, every self-a
djoint extension of the minimal operator can be written as\n$$\n A_{\\T
heta} = A_0 + B \\Theta B*\,\n$$\nwhere $A_0$ is a distinguished self-adjo
int extension and Theta is a self-adjoint linear relation in $\\mathbb{C}^
d$. The perturbation is singular in the sense that it does not belong to t
he underlying Hilbert space but is form bounded with respect to $A_0$\, i.
e. it belongs to $H_{-1}(A_0)$. The construction of a boundary triple and
compatible boundary pair for the symmetric operator ensure that the pertu
rbation is well-defined and self-adjoint extensions are in a one-to-one co
rrespondence with self-adjoint relations $\\Theta$.\n\nAs an example\, sel
f-adjoint extensions of the classical symmetric Jacobi differential equati
on (which has two limit-circle endpoints) are obtained and their spectra i
s analyzed with tools both from the theory of boundary triples and perturb
ation theory.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylwia Kondej (University of Zielona Gora)
DTSTART:20201201T134500Z
DTEND:20201201T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/3
DESCRIPTION:Title: Optimization problem for quantum system with star-shaped potent
ial\nby Sylwia Kondej (University of Zielona Gora) as part of Quantum
Circle\n\n\nAbstract\nWe discuss the spectral properties of singular Schr\
\"odinger operators in three dimensions with the interaction supported by
an equilateral star. Our main result concerns spectral optimization: we sh
ow that the principal eigenvalue is uniquely maximized when the arms are a
rranged in one of the known five sharp configurations.\nThe results disc
ussed in the talk are the joint work with Pavel Exner.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Lotoreichik (Nuclear Physics Institute CAS)
DTSTART:20201208T134500Z
DTEND:20201208T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/4
DESCRIPTION:Title: Szegö-type inequality for the 2-D Dirac operator with infinite
mass boundary conditions\nby Vladimir Lotoreichik (Nuclear Physics Ins
titute CAS) as part of Quantum Circle\n\n\nAbstract\nIn this talk\, we wil
l discuss spectral features of the Dirac operator with infinite mass bound
ary conditions in a smooth bounded domain of $\\mathbb{R}^2$. Motivated by
spectral geometric inequalities\, we derive a non-linear variational form
ulation to characterize its principal eigenvalue. This characterization t
urns out to be very robust and allows for a simple proof of a Szeg\\H{o} t
ype inequality as well as a new reformulation of a Faber-Krahn type inequa
lity for this operator. We will also present strong numerical evidence sup
porting the validity of a Faber-Krahn type inequality.\n\nThis talk is bas
ed on a joint work with Pedro Antunes\, Rafael Benguria\, and Thomas Ourmi
\\`{e}res-Bonafos.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hynek Kovarik (Università degli studi di Brescia)
DTSTART:20201215T134500Z
DTEND:20201215T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/5
DESCRIPTION:Title: Absence of positive eigenvalues of magnetic Schroedinger operato
rs\nby Hynek Kovarik (Università degli studi di Brescia) as part of Q
uantum Circle\n\n\nAbstract\nWe study sufficient conditions for the absenc
e of positive eigenvalues of magnetic Schroedinger operators in R^n. In ou
r main result we prove the absence of eigenvalues above certain threshold
energy which depends explicitly on the magnetic and electric field. A comp
arison with the examples of Miller-Simon shows that our result is sharp as
far as the decay of the magnetic field is concerned.\nThe talk is based o
n a joint work with Silvana Avramska-Lukarska and Dirk Hundertmark.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Denis Borisov (Bashkir State Pedagogical University\, Ufa)
DTSTART:20201222T134500Z
DTEND:20201222T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/6
DESCRIPTION:Title: Accumulation of resonances and eigenvalues for operators with di
stant perturbations\nby Denis Borisov (Bashkir State Pedagogical Unive
rsity\, Ufa) as part of Quantum Circle\n\n\nAbstract\nWe consider a model
one-dimensional problem with distant perturbations\, for which we study a
phenomenon of emerging of infinitely many eigenvalues and resonances near
the bottom of the essential spectrum. We show that they accumulate to a ce
rtain segment of the essential spectrum. Then we discuss possible generali
zation of this result to multi-dimensional models and various situations o
f resonances and eigenvalues distributions.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Pankrashkin (Universitaet Oldenburg)
DTSTART:20210105T134500Z
DTEND:20210105T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/7
DESCRIPTION:Title: On the discrete spectrum of a Schroedinger operator in a half-pl
ane with a potential localized along a line\nby Konstantin Pankrashkin
(Universitaet Oldenburg) as part of Quantum Circle\n\n\nAbstract\nWe disc
uss the the spectral properties of a Schrödinger operator in a half-plane
with Neuman boundary condition and with a (regular or singular) potential
which only depends on the distance to a line. We discuss the cardinality
of the discrete spectrum for the case when the potential is attractive and
the line is not parallel to the boundary. Based in part on a joint work w
ith Sebastian Egger and Joachim Kerner.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aurel Gabris (Czech Technical University)
DTSTART:20210112T134500Z
DTEND:20210112T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/8
DESCRIPTION:Title: Classical and quantum coherences in photonic quantum networks\nby Aurel Gabris (Czech Technical University) as part of Quantum Circle\
n\n\nAbstract\nDiscerning quantum and classical features in a real-world s
cenario is an intriguing task\, especially when the system under scrutiny
has many degrees of freedom. In optics the notion of coherence is of centr
al importance\, and it also comes in two flavours: classical and quantum.
In this talk I will present a simple yet powerful technique to control and
discern classical and quantum coherences in a photonic quantum network\,
an object that may encompass a large number of modes\, all possibly spatia
lly separated. Finally\, I will outline the experimental results from the
application of this technique to photonic networks implemented in the time
-domain. \\\\[.2em]\nReference: Th.~Nitsche\, Syamsundar De\, S.~Barkhofen
\, E.~Meyer-Scott\, J.~Tiedau\, J.~Sperling\, A.~G\\'abris\, I.~Jex\, and
Ch.~Silberhorn\, \\emph{Phys. Rev. Lett.} \\textbf{125}\, 213604 (2020)\n\
nDiscerning quantum and classical features in a real-world scenario is an
intriguing task\, especially when the system under scrutiny has many degre
es of freedom. In optics the notion of coherence is of central importance\
, and it also comes in two flavours: classical and quantum. In this talk I
will present a simple yet powerful technique to control and discern class
ical and quantum coherences in a photonic quantum network\, an object that
may encompass a large number of modes\, all possibly spatially separated.
Finally\, I will outline the experimental results from the application of
this technique to photonic networks implemented in the time-domain. \\\\[
.2em]\nReference: Th.~Nitsche\, Syamsundar De\, S.~Barkhofen\, E.~Meyer-Sc
ott\, J.~Tiedau\, J.~Sperling\, A.~G\\'abris\, I.~Jex\, and Ch.~Silberhorn
\, \\emph{Phys. Rev. Lett.} \\textbf{125}\, 213604 (2020)\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brice Flamencourt (Universite d'Orsay)
DTSTART:20210216T134500Z
DTEND:20210216T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/9
DESCRIPTION:Title: On the convergence of Dirac operators with large masses\nby
Brice Flamencourt (Universite d'Orsay) as part of Quantum Circle\n\n\nAbst
ract\nWe look at a class of Dirac operators with a potential that can be i
nterpreted as masses in separated regions of the space. These operators ar
ise naturally in the study of the MIT bag model in three dimensions\, and
one can generalize their construction to higher dimension. We are interest
ed in the behavior of the operator’s eigenvalues in several asymptotic r
egimes when the masses go to infinity. It can be shown that there is an ef
fective operator on the boundaries of the regions previously considered wh
ich governs the convergence of the spectrum.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Stefanak (Czech Technical University)
DTSTART:20210323T134500Z
DTEND:20210323T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/10
DESCRIPTION:Title: Asymptotic properties of quantum walks on lattices\nby Mart
in Stefanak (Czech Technical University) as part of Quantum Circle\n\n\nAb
stract\nWe provide an overview of results for evolution of discrete time q
uantum walks on lattices. The focus is on homogeneous walks where Fourier
analysis is applicable\, which allows to investigate the spectrum of the e
volution operator in detail. Most of the features of the probability distr
ibution generated by the quantum walk evolution\, e.g. the characteristic
peaks and ballistic spreading\, are captured in the limit density\, which
can be derived from the convergence moments of position rescalled with the
number of steps. The derivation of the limit density is illustrated on th
e example of the quantum walk on a line with the Hadamard coin. We then tu
rn to the examples of quantum walks on a line and a plane with the Grover
coin\, where the evolution operator has a non-empty point spectrum. This r
esults in the trapping effect\, where the walker remains localized in the
vicinity of the starting point with non-vanishing probability.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrii Khrabustovskyi (University of Hradec Kralove)
DTSTART:20210316T134500Z
DTEND:20210316T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/11
DESCRIPTION:Title: Geometric approximation of delta interactions\nby Andrii Kh
rabustovskyi (University of Hradec Kralove) as part of Quantum Circle\n\n\
nAbstract\nIn this talk we demonstrate how to approximate $1d$ Schrodinger
operators with a $\\delta$-potential by the Neumann Laplacian on a narrow
waveguide-like domain. Namely\, we consider the domain consisting of a st
raight narrow strip and a small protuberance with "room-and-passage" geome
try. We show that in the limit when perpendicular size of the strip tends
to zero and the protuberance is appropriated scaled the Neumann Laplacian
on this domain converges in (a kind of) norm resolvent sense to the above
singular Schrodinger operator. The estimates on the rate of this convergen
ce are also derived. As an application we proof the Hausdorff convergence
of spectra. This is a joint work with Olaf Post (Trier).\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiri Lipovsky (University of Hradec Kralove)
DTSTART:20210309T134500Z
DTEND:20210309T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/12
DESCRIPTION:Title: Graphs with preferred-orientation coupling and their spectral p
roperties\nby Jiri Lipovsky (University of Hradec Kralove) as part of
Quantum Circle\n\n\nAbstract\nAbstract: We investigate quantum graphs with
the preferred-orientation coupling conditions suggested by Exner and Tate
r [1]. In particular\, we are interested in the high-energy limit of their
spectra. These coupling conditions violate the time-reversal symmetry\, f
or a particular energy\, the particle approaching the vertex from a given
edge leaves it through the neighbouring edge (for instance\, to the left o
f the incoming edge) and this property is cyclical. It was previously show
n that the vertex scattering matrix depends on the degree of the vertex\;
for an odd-degree vertex\, the scattering matrix converges in the high-ene
rgy limit to the identity matrix\, while even-degree vertices behave diffe
rently. This behaviour affects the transport properties of these graphs.\n
\nWe study two models. The first one is a finite graph consisting of edges
of Platonic solids. We find that the asymptotical distribution of the eig
envalues for the octahedron graph (having even degrees of vertices) is dif
ferent from the other Platonic solids (having odd degrees of vertices)\, f
or which the eigenvalues approach the spectrum of the Neumann Laplacian on
an interval. The second model consists of two types of infinite lattices.
For one of them\, the transport at high energies is possible in the middl
e of the strip and is suppressed at the edges. For the other one\, the tra
nsport is possible at the edge of the strip only.\n\nThe talk will be base
d on two papers in collaboration with P. Exner [2\, 3].\n\nReferences:\n[1
] P. Exner\, M. Tater\, Quantum graphs with vertices of a preferred orient
ation\, Phys. Lett. A 382 (2018) 283–287.\n[2] P. Exner\, J. Lipovs
ky\, Spectral asymptotics of the Laplacian on Platonic solids graphs\, J.
Math. Phys. 60 (2019)\, 122101.\n[3] P. Exner\, J. Lipovsky\, Topological
bulk-edge effects in quantum graph transport\, Phys. Lett. A 384 (2020)\,
126390.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Exner (Czech Academy of Sciences)
DTSTART:20210330T124500Z
DTEND:20210330T134500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/13
DESCRIPTION:Title: Product formulae and Zeno quantum dynamics\nby Pavel Exner
(Czech Academy of Sciences) as part of Quantum Circle\n\n\nAbstract\nWe pr
esent a new product formula which involves a unitary group generated by a
positive self-adjoint operator and a continuous projection-valued function
. The problem is motivated by quantum description of decaying systems\, in
particular\, the Zeno effect coming from frequently repeated measurements
. Applied to it\, the formula expresses the dynamics of such a system. An
example of a permanent position ascertaining leading to the effective Diri
chlet condition is given.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Salzmann (University of Cambridge)
DTSTART:20210406T124500Z
DTEND:20210406T134500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/14
DESCRIPTION:Title: Quantum Zeno effect for open quantum systems\nby Robert Sal
zmann (University of Cambridge) as part of Quantum Circle\n\n\nAbstract\nW
e prove the quantum Zeno effect in open quantum systems whose evolution\,
governed by quantum dynamical semigroups\, is repeatedly and frequently in
terrupted by the action of a quantum operation. For the case of a quantum
dynamical semigroup with a bounded generator\, our analysis leads to a ref
inement of existing results and extends them to a larger class of quantum
operations. We also prove the existence of a novel strong quantum Zeno lim
it for quantum operations for which a certain spectral gap assumption\, wh
ich all previous results relied on\, is lifted. The quantum operations are
instead required to satisfy a weaker property of strong power-convergence
. In addition\, we establish\, for the first time\, the existence of a qua
ntum Zeno limit for the case of unbounded generators in the open system se
tup. We also provide a variety of physically interesting examples of quant
um operations to which our results apply.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Schlosser (TU Graz)
DTSTART:20210413T124500Z
DTEND:20210413T134500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/15
DESCRIPTION:Title: Time evolution of superoscillations\nby Peter Schlosser (TU
Graz) as part of Quantum Circle\n\n\nAbstract\nhttp://gemma.ujf.cas.cz/%7
Eexner/Qcabs/schlosser21a.pdf\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matej Tusek (Czech Technical University)
DTSTART:20210420T124500Z
DTEND:20210420T134500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/16
DESCRIPTION:Title: General delta-shell interactions for the two-dimensional Dirac
operator: self-adjointness and approximation\nby Matej Tusek (Czech Te
chnical University) as part of Quantum Circle\n\n\nAbstract\nIn this talk
the two-dimensional Dirac operator with general local singular interaction
s supported on a closed curve is considered. A systematic study of the int
eraction is performed by decomposing it into a linear combination of four
elementary interactions: electrostatic\, Lorentz scalar\, magnetic\, and a
fourth one which can be absorbed by using unitary transformations. First\
, the self-adjointness and the spectral description of the underlying Dira
c operator will be adressed. This can be considered as a generalization of
a recent work of Behrndt\, Holzmann\, Ourmieres-Bonafos\, and Pankrashkin
. The second part of the talk will be devoted to a construction of approxi
mations of the studied operators by Dirac operators with regular potential
s. The talk is based on a joint work with Cassano\, Lotoreichik\, and Mas.
\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Marletta (Cardiff University)
DTSTART:20210427T124500Z
DTEND:20210427T134500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/17
DESCRIPTION:Title: A Laplace operator with boundary conditions singular at one poi
nt\nby Marco Marletta (Cardiff University) as part of Quantum Circle\n
\n\nAbstract\nIn this talk I will present some work with Rozenblum from 20
09 and some further results with my former student Freddy Symons from 2016
. While it has been known for more than half a century that the Laplace op
erator on a smooth\, bounded domain may have essential spectrum if the bou
ndary conditions are suitably chosen\, typical choices involved non-local
operators. In this talk I will show\, with very elementary arguments\, tha
t even local boundary conditions\, singular even just at a single point\,
can have a huge impact on the spectrum and eigenfunctions. The example we
consider\, first proposed by Berry and Dennis\, still has empty essential
spectrum and compact resolvent. However Weyl’s law fails completely
because the spectrum becomes unbounded below. The positive eigenvalues st
ill obey Weyl asymptotics\, to leading order\; however the (absolute value
s of the) negative eigenvalues do not obey a power law distribution.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noema Nicolussi (Vienna University)
DTSTART:20210504T124500Z
DTEND:20210504T134500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/18
DESCRIPTION:Title: Laplacians on infinite graphs\nby Noema Nicolussi (Vienna U
niversity) as part of Quantum Circle\n\n\nAbstract\nThere are two differen
t notions of a Laplacian operator associated with infinite graphs: discre
te Laplacians and quantum graphs. Both objects have a venerable
history and their spectral theory relates to several diverse bra
nches of mathematics (random walks\, combinatorics\, geometric group theo
ry\, ...). In our talk we explore connections between these two types of o
perators (spectral\, parabolic and geometric properties)\, and exploit the
se relations to prove a number of new results in spectral theory for both
settings. In particular\, we will present applications to the self-adjoin
tness problem on infinite graphs.Based on joint work with Aleksey Ko
stenko (Ljubljana&Vienna) and Mark Malamud (Donetsk).\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Larson (Caltech)
DTSTART:20210504T140000Z
DTEND:20210504T150000Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/19
DESCRIPTION:Title: On the spectrum of the Kronig-Penney model in a constant electr
ic field\nby Simon Larson (Caltech) as part of Quantum Circle\n\n\nAbs
tract\n\\documentclass[12pt\, a4paper]{article} % 11pt for all the article
\n\\usepackage{amsmath\,amsthm\,amsfonts\,amssymb}\n\\usepackage[affil-it]
{authblk}\n\n\\begin{document}\n\n\\title{On the spectrum of the Kronig--P
enney model in a constant electric field}\n\\author{\\large\\sc Simon Lars
on}\n\\affil{\\normalsize Caltech}\n\\date{}\n\\maketitle\n\n\\noindent \\
textbf{Abstract.} We are interested in the nature of the spectrum of the o
ne-dimensional Schr\\"odinger operator\n\\begin{equation*}\n - \\frac{d^2
}{dx^2}-Fx + \\sum_{n \\in \\mathbb{Z}}g_n \\delta(x-n)\n\\end{equation*}\
nwith $F>0$ and two different choices of the coupling constants $\\{g_n\\}
_{n\\in \\mathbb{Z}}$. In the first model $g_n \\equiv \\lambda$ and we pr
ove that if $F\\in \\pi^2 \\mathbb{Q}$ then the spectrum is $\\mathbb{R}$
and is furthermore absolutely continuous away from an explicit discrete se
t of points. In the second model $g_n$ are independent random variables wi
th mean zero and variance $\\lambda^2$. Under certain assumptions on the d
istribution of these random variables we prove that almost surely the spec
trum is dense pure point if $F < \\lambda^2/2$ and purely singular continu
ous if $F> \\lambda^2/2$. Based on joint work with Rupert Frank.\n\\end{do
cument}\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudio Cacciapuoti (Universita degli Studi dell'Insubria)
DTSTART:20210518T124500Z
DTEND:20210518T134500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/20
DESCRIPTION:Title: The nonlinear Schrödinger equation with isolated singularities
\nby Claudio Cacciapuoti (Universita degli Studi dell'Insubria) as par
t of Quantum Circle\n\n\nAbstract\nI will discuss the well posedness of th
e nonlinear Schrödinger equation with power-type nonlinearity and in th
e presence of a delta interaction\, both in dimension two and three. This
is a model of evolution for some singular solutions that are well known in
the analysis of semilinear elliptic equations. I will consider local exis
tence\, uniqueness and continuous dependence from the initial data of stro
ng (operator domain) solutions of the associated Cauchy problem. In dimens
ion two well posedness holds for any power nonlinearity and global existen
ce is proved for powers below the cubic. In dimension three local and glob
al well posedness are restricted to low powers.\nThe talk is based on a jo
int work with Domenico Finco and Diego Noja.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vit Jakubsky (Nuclear Physics Institute CAS)
DTSTART:20210525T124500Z
DTEND:20210525T134500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/21
DESCRIPTION:Title: Reduction scheme for coupled Dirac systems\nby Vit Jakubsky
(Nuclear Physics Institute CAS) as part of Quantum Circle\n\n\nAbstract\n
We analyze a class of coupled quantum systems whose dynamics can be unders
tood via two uncoupled\, lower-dimensional quantum settings with auxiliary
interactions. The general reduction scheme\, based on algebraic propertie
s of the potential term\, is discussed in detail for two-dimensional Dirac
Hamiltonian. We discuss its possible application in description of Dirac
fermions in graphene or bilayer graphene in presence of distortion scatter
ing or spin-orbit interaction. The framework is illustrated on the explici
t examples where the interaction depends on two spatial coordinates or it
is time-dependent.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kyle Scarbrough (Czech Technical University)
DTSTART:20211005T124500Z
DTEND:20211005T134500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/22
DESCRIPTION:Title: Oscillation theory for canonical systems\nby Kyle Scarbroug
h (Czech Technical University) as part of Quantum Circle\n\n\nAbstract\nTh
is talk will be about the spectral theory of canonical systems. After an i
ntroduction to canonical systems\, a version of oscillation theory for the
m will be discussed. Some applications of oscillation theory to semibounde
d systems\, relations between diagonal and nondiagonal systems\, and the e
ssential spectrum will be highlighted.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dale Frymark (Czech Academy od Sciences)
DTSTART:20211019T124500Z
DTEND:20211019T134500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/23
DESCRIPTION:Title: Self-adjointness of the 2-D Dirac operator with singular intera
ctions supported on star-graphs\nby Dale Frymark (Czech Academy od Sci
ences) as part of Quantum Circle\n\n\nAbstract\nWe present an analysis of
the deficiency indices of the 2-D Dirac Operator with Lorentz-scalar inter
actions supported on a star-graph\, with different interaction strengths a
llowed on different leads. In the general case\, we separate variables\, d
ecompose the Dirac operator into an orthogonal sum and find that the defic
iency indices depend on the number of eigenvalues of the so-called spin-or
bit operator within an interval. For the simpler cases when there are two
or three leads much more can be said. Examples when the deficiency indices
are (2\,2) and when the spin-orbit operator has eigenvalues of multiplici
ty two are included. It is also shown that there is a distinguished self-a
djoint extension whose domain lies in H^{1/2}.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michal Jex (Ceremade Paris)
DTSTART:20211026T124500Z
DTEND:20211026T134500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/24
DESCRIPTION:Title: Quantum Systems at The Brink: Critical Potentials and dimension
ality\nby Michal Jex (Ceremade Paris) as part of Quantum Circle\n\n\nA
bstract\nThe existence of eigenfunctions for Schr\\"odinger operators are
of utmost importance in quantum mechanics and its appllications. It is wel
l known that for eigenvalues below the threshold of the essential spectrum
\, eigenvectors exist and decay exponentially. However\, the situation at
the threshold is much more subtle. We present necessary and sufficient con
dition for the Schrödinger operator to have zero energy ground state. We
show that it critically depends on the asymptotic behaviour of the potenti
al. We derive necessary and sufficient conditions for the existence and ab
sence of zero eigenvalue with respect to the dimension $d$. We show that t
he leading order term has a strong dependence on the dimension\, namely $\
\frac{d(4-d)}{|x^2|}$ for $|x|\\rightarrow\\infty$. Furthermore our result
s are in the mathematical sense sharp.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Holzmann (TU Graz)
DTSTART:20211123T134500Z
DTEND:20211123T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/25
DESCRIPTION:Title: Approximation problems for Dirac operators with singular potent
ials\nby Markus Holzmann (TU Graz) as part of Quantum Circle\n\n\nAbst
ract\nIn this talk two approximation problems for three dimensional Dirac
operators with singular $\\delta$-shell potentials supported on compact su
rfaces are discussed. The first one is a generalization of a result by Ges
ztesy and \\v{S}eba\, saying that a family of one dimensional Dirac operat
ors with a special combination of electrostatic and Lorentz scalar $\\delt
a$-interactions converges in the nonrelativistic limit to a Schr\\"odinger
operator with a $\\delta'$-interaction. In the higher dimensional setting
a similar convergence is obtained\, but the limit operator is a Schr\\"od
inger operator with oblique jump conditions which is - for attractive inte
raction strengths - not semibounded from below.\n\nThe second part of the
talk is devoted to the approximation of Dirac operators with $\\delta$-she
ll interactions by Dirac operators with scaled regular potentials in the n
orm resolvent sense. It will be explained how this can be achieved for spe
cial interaction strengths.\n\nThis talk is based on joint works with J.~B
ehrndt\, C. Stelzer\, and G. Stenzel.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frantisek Štampach (Czech Technical University)
DTSTART:20211102T134500Z
DTEND:20211102T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/26
DESCRIPTION:Title: Spectral bounds and stability for 1D discrete Schrödinger oper
ators with complex potentials\nby Frantisek Štampach (Czech Technical
University) as part of Quantum Circle\n\n\nAbstract\nFirst\, we present o
ptimal spectral enclosures for discrete Laplacians on $\\mathbb{Z}$ and $\
\mathbb{N}$ with the Robin boundary condition perturbed by $\\ell^{1}$-com
plex potentials. Second\, we discuss results on a spectral stability of di
screte Schrödinger operators on $\\mathbb{N}$ with small complex potentia
ls and related discrete Hardy inequalities. The talk is based on joint pro
jects with O. O. Ibrogimov\, D. Krejčiřı́k\, and A. Laptev.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miloš Tater (Czech Academy of Sciences)
DTSTART:20211130T134500Z
DTEND:20211130T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/27
DESCRIPTION:Title: Spectral asymptotic of quasi-exactly solvable quartic potential
\nby Miloš Tater (Czech Academy of Sciences) as part of Quantum Circl
e\n\n\nAbstract\nWe discuss the asymptotics and the spectral monodromy of
the quasi-exactly solvable part of the spectrum of the quasi-exactly solva
ble quartic. We formulate a conjecture on the coincidence of the asymptoti
c shape of the level crossings of the latter oscillator with the asymptoti
c shape of zeros of the Yablonskii-Vorob'ev polynomials. Jointly with B. S
hapiro.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artem Kandaurov (Czech Technical University)
DTSTART:20211214T134500Z
DTEND:20211214T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/28
DESCRIPTION:Title: Incremental learning of quantum generative adversarial network<
/a>\nby Artem Kandaurov (Czech Technical University) as part of Quantum Ci
rcle\n\n\nAbstract\nMachine learning field has shown incredible impact on
many kinds of optimization problems. Recently the power of machine learnin
g was applied to speed up the quantum states preparation. Although approxi
mation with quantum generative adversarial networks is one of the fastest
ways to prepare a generic quantum state\, training time for such models is
still significant and can easily impair quantum advantage. This thesis ex
plores incremental learning of quantum generative adversarial networks for
the quantum states preparation problem and introduces learning use cases
reducing the training time.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Malachov (Czech Technical University)
DTSTART:20211221T134500Z
DTEND:20211221T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/29
DESCRIPTION:Title: Chaotic features of purification protocol\nby Martin Malach
ov (Czech Technical University) as part of Quantum Circle\n\n\nAbstract\nQ
uantum information and communication has recently boomed into a promising
discipline offering secure communication and exponential speedup of certai
n algorithms. The basic elements of the quantum version of information/com
munication theory are qubits. A qubit is realised by a two-level quantum s
ystem and two or more qubits can be entangled together to create a collect
ive state with information shared among its parts. Entanglement is a valua
ble resource used even in completely new algorithms like quantum teleporta
tion. As a physical object\, qubit is subject to environment which makes i
ts state decay and disturb the entanglement. Purification protocols and er
ror correction codes aim on repairing the qubit states and retaining their
entanglement. One of proposed protocols use a copy of the qubit to act as
a specific environment but such action has been shown to induce chaotic b
ehavior\, particularly there are states undergoing deterministic chaos whe
n the protocol is iterated on them. Mathematically\, the protocol manifest
s as rational polynomial functions of degree two. We propose a series of m
ore general algorithms with polynomials of higher degree and investigate t
heir properties compared to the original algorithm whose features are also
described in detail. We focus on fractal structures of chaotic states\, s
ymmetries and other general properties of the protocols.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Zelaya (Nuclear Physics Institute CAS)
DTSTART:20220125T134500Z
DTEND:20220125T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/31
DESCRIPTION:Title: Fourth Painlevé and Ermakov equations: quantum invariants and
new exactly solvable time-dependent Hamiltonians\nby Kevin Zelaya (Nuc
lear Physics Institute CAS) as part of Quantum Circle\n\n\nAbstract\nAbstr
act: In this talk\, I discuss a new realization of exactly solvable time-d
ependent Hamiltonians based on the solutions of the fourth Painlev\\'{e} a
nd the Ermakov equations. The latter is achieved by introducing a shape-in
variant condition between an unknown quantum invariant and a set of third-
order intertwining operators with time-dependent coefficients. The new qua
ntum invariant is constructed by adding a deformation term to the well-kno
wn parametric oscillator invariant. Such a deformation depends explicitly
on time through the solutions of the Ermakov equation\, which ensures the
regularity of the new time-dependent potential of the Hamiltonian at each
time. The fourth Painlev\\'{e} equation appears naturally with the aid of
the proper reparametrization\, whose parameters dictate the form of the di
screte spectrum of the quantum invariant. Some particular examples are pre
sented to illustrate the results.\nJoint work with Ian Marquete and V\\'{e
}ronique Hussin.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Lotoreichik (Nuclear Physics Institute)
DTSTART:20220301T134500Z
DTEND:20220301T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/32
DESCRIPTION:Title: Isoperimetric inequality for the two-dimensional magnetic Robin
Laplacian\nby Vladimir Lotoreichik (Nuclear Physics Institute) as par
t of Quantum Circle\n\n\nAbstract\nIn this talk\, we consider the two-dime
nsional magnetic Robin Laplacian with a negative boundary parameter on a b
ounded and sufficiently smooth domain. The respective magnetic field is ch
osen to be homogeneous. Among a certain class of domains\, we prove that t
he disk maximizes the ground state energy under the fixed perimeter constr
aint provided that the magnetic field is of moderate strength. This class
of domains includes\, in particular\, all domains that are contained upon
translations in the disk of the same perimeter and all centrally symmetric
domains. Our result generalizes the isoperimetric inequality for the Robi
n Laplacian without magnetic field due to Antunes\, Freitas\, and Krej\\v{
c}i\\v{r}\\'{i}k. \nThis talk is based on a joint work with Ayman Kachmar.
\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diana Barseghyan (University of Ostrava)
DTSTART:20220208T134500Z
DTEND:20220208T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/33
DESCRIPTION:Title: Spectral geometry in a rotating frame: properties of the ground
state\nby Diana Barseghyan (University of Ostrava) as part of Quantum
Circle\n\n\nAbstract\nWe investigate spectral properties of the operator
describing a quantum particle confined to a planar domain rotating around
a fixed point with certain angular velocity and demonstrate several proper
ties of its principal eigenvalue.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukas Heriban (Czech Technical University)
DTSTART:20220222T134500Z
DTEND:20220222T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/34
DESCRIPTION:by Lukas Heriban (Czech Technical University) as part of Quant
um Circle\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Md Fazlul Hoque (Czech Technical University)
DTSTART:20220503T124500Z
DTEND:20220503T134500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/35
DESCRIPTION:Title: Higher rank quadratic algebra of the $N$-dimensional quantum Sm
orodinsky-Winternitz system\nby Md Fazlul Hoque (Czech Technical Unive
rsity) as part of Quantum Circle\n\n\nAbstract\nAlgebraic methods are powe
rful tools in classical and quantum mechanics. Superintegrable systems are
an important class of classical and quantum systems which can be solved u
sing algebraic approaches. In this talk\, I present higher rank quadratic
algebra of the $N$-dimensional quantum Smorodinsky-Winternitz system\, whi
ch is a maximally superintegrable and exactly solvable model. It is shown
that the model is multiseparable and the wave function can be expressed in
terms of Laguerre and Jacobi polynomials. We present a complete symmetry
algebra ${\\cal SW}(N)$ of the system\, which it is a higher-rank quadrati
c one containing Racah algebra ${\\cal R}(N)$ as subalgebra. The substruct
ures of distinct quadratic Q(3) algebras and their related Casimirs are al
so studied. The energy spectrum of the $N$-dimensional Smorodinsky-Wintern
itz system is obtained algebraically via the different set of subalgebras
based on the Racah algebra ${\\cal R}(N)$. Joint work with Francisco Corre
a\, Ian Marquette\, and Yao-Zhong Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiri Lipovsky (University of Hradec Kralove)
DTSTART:20220510T124500Z
DTEND:20220510T134500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/36
DESCRIPTION:Title: A Gelfand-Levitan Trace Formula for Generic Quantum Graphs\
nby Jiri Lipovsky (University of Hradec Kralove) as part of Quantum Circle
\n\n\nAbstract\nWe generalize the result given by Gelfand and Levitan for
the Schroedinger operator on a segment with Neumann coupling condition. We
give a trace formula for the quantum graph with arbitrary edge lengths an
d generic coupling conditions. The formula is reminiscent of the original
Gelfand-Levitan result on the segment with Neumann boundary conditions. Th
e only case of coupling conditions which is excluded is the condition with
the unitary coupling matrix having eigenvalue -1 (hence it is a set of me
asure zero in the set of all self-adjoint couplings). However\, the consid
ered set does not include Dirichlet\, standard or delta-conditions.\n\nThi
s is joint work with prof. Pedro Freitas.\n\n[1] P. Freitas\, J. Lipovský
\, A Gelfand-Levitan trace formula for generic quantum graphs\, Anal. Math
. Phys. 11 (2021)\, 56 [mp_arc 19-4\; arXiv: 1901.07790 [math-ph]]\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrii Khrabustovskyi (University of Hradec Kralove)
DTSTART:20221101T134500Z
DTEND:20221101T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/37
DESCRIPTION:Title: Domains with small resonators and what one can do with them
\nby Andrii Khrabustovskyi (University of Hradec Kralove) as part of Quant
um Circle\n\n\nAbstract\nhttp://gemma.ujf.cas.cz/%7Eexner/Qcabs/khrabustov
skyi22a.pdf\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Md Fazlul Hoque (Czech Technical University)
DTSTART:20221108T134500Z
DTEND:20221108T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/38
DESCRIPTION:Title: Families of three-dimensional integrable and superintegrable cl
assical Hamiltonian systems in magnetic fields\nby Md Fazlul Hoque (Cz
ech Technical University) as part of Quantum Circle\n\n\nAbstract\nThe tal
k presents families of integrable and superintegrable classical Hamiltonia
n systems in magnetic fields. We consider more general structure of their
quadratic commuting integrals of motion whose leading order terms are elem
ents of the universal enveloping algebra of the three--dimensional Euclide
an algebra. We show how these pairs of commuting elements lead to distinct
independent integrals of motion in several nonvanishing magnetic fields.
We also search for additional first-- and second--order integrals of motio
n of these systems to arrive at superintegrable systems. We construct the
corresponding Poisson algebras of integrals of motion.\nThe talk is based
on joint work with Libor \\v{S}nobl.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylwia Kondej (University of Zielona Gora)
DTSTART:20221115T134500Z
DTEND:20221115T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/39
DESCRIPTION:Title: Quantum system with concentric circles and Aharonov-Bohm flux\nby Sylwia Kondej (University of Zielona Gora) as part of Quantum Circl
e\n\n\nAbstract\nIn this talk we discuss a class of two-dimensional SchrĂ
¶dinger operator with a singular interaction of the $\\delta$ type and a
fixed strength supported by an infinite family of concentric\, equidistant
ly spaced circles. We analyze what happens below the essential spectrum af
ter implementing an Aharonov-Bohm flux $\\alpha \\in [0\,1/2]$ in the cent
er. We prove that there exists a critical value $\\alpha_{\\mathrm{cr}} \\
in (0\, 1/2)$ such that the discrete spectrum has an accumulation point wh
en $\\alpha < \\alpha_{\\mathrm{cr}}$\, while for $\\alpha \\geq \\alpha_{
\\mathrm{crit}}$ the number of eigenvalues is finite. The talk is based on
a common work with P. Exner.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davron Matrasulov (Turin Polytechnic University of Tashkent)
DTSTART:20221122T134500Z
DTEND:20221122T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/40
DESCRIPTION:Title: Dynamical confinement in low-dimensional quantum systems: Recen
t achievements and open problems\nby Davron Matrasulov (Turin Polytech
nic University of Tashkent) as part of Quantum Circle\n\n\nAbstract\nIn th
is talk\, I will discuss the problem of dynamical quantum confinement\, de
scribed in terms of Schrodinger and Dirac equations with time-dependent bo
undary conditions. Practical applications in quantum optics\, atom optics
and condensed matter physics will be discussed. Open problems\, to be atat
cked from mathematicsal viewpoint will be also presented.\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olena Atlasiuk (Mathematical Institute CAS)
DTSTART:20221129T134500Z
DTEND:20221129T144500Z
DTSTAMP:20260404T094938Z
UID:qc_seminar/41
DESCRIPTION:Title: Linear ordinary differential systems with generic boundary cond
itions in Sobolev spaces\nby Olena Atlasiuk (Mathematical Institute CA
S) as part of Quantum Circle\n\n\nAbstract\nhttp://gemma.ujf.cas.cz/%7Eexn
er/Qcabs/atlasiuk22a.pdf\n
LOCATION:https://stable.researchseminars.org/talk/qc_seminar/41/
END:VEVENT
END:VCALENDAR