BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Serena Cenatiempo (GSSI L'Aquila) DTSTART:20210420T133000Z DTEND:20210420T143000Z DTSTAMP:20260404T110829Z UID:UnibaMathPhys/1 DESCRIPTION:Title: Bogoliubov theory for weakly interacting bosons\nby Seren a Cenatiempo (GSSI L'Aquila) as part of UniBA Mathematical Physics Seminar \n\n\nAbstract\nNon relativistic bosons at sufficiently low temperature ex hibit a celebrated critical phase – known as Bose-Einstein condensation (BEC) - effectively corresponding to a macroscopic occupation of a one par ticle state. While the prediction of BEC for non-interacting bosons dates back to one century ago\, there are few\, quite special\, models where we are able to prove that condensation survives in presence of interaction. I n this talk I will review the state of art on the problem and discuss a cl osely related question\, namely the characterization of the low energy spe ctrum of weakly interacting bosons\, a problem that was first addressed in a pioneering work by Bogoliubov in ‘47. I will then present recent resu lts obtained in different regimes\, in two and three dimensions.\nBased on joint works with G. Basti\, C. Boccato\, C.Brennecke\, C. Caraci and B.Sc hlein.\n LOCATION:https://stable.researchseminars.org/talk/UnibaMathPhys/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcello Porta (SISSA Trieste) DTSTART:20210518T133000Z DTEND:20210518T143000Z DTSTAMP:20260404T110829Z UID:UnibaMathPhys/2 DESCRIPTION:Title: Correlation energy of a weakly interacting Fermi gas\nby Marcello Porta (SISSA Trieste) as part of UniBA Mathematical Physics Semin ar\n\n\nAbstract\nIn this talk I will discuss the ground state properties of homogeneous\, interacting Fermi gases\, in the mean-field regime. In th is regime\, Hartree-Fock theory provides a good approximation for the grou nd state energy of the system\; this approximation is based on the replace ment of the space of fermionic wave functions with the smaller set of Slat er determinants\, where the only correlations among the particles are thos e induced by the Pauli principle. I will discuss a rigorous approach that allows to go beyond the Hartree-Fock approximation\, and that in particula r allows to compute the leading order of the correlation energy\, defined as the difference between the many-body ground state energy and the Hartre e-Fock ground state energy. The expression we obtain reproduces the ground state energy of a non-interacting Bose gas\, suggesting that the low ener gy excitations of high density Fermi gases are effectively described by a quasi-free Bose gas. The method of proof consists in a rigorous formulatio n of the bosonization technique\, developed in the condensed matter physic s in the 80s. Joint work with N. Benedikter\, P. T. Nam\, B. Schlein and R . Seiringer.\n LOCATION:https://stable.researchseminars.org/talk/UnibaMathPhys/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Tomaž Prosen (Ljubljana) DTSTART:20210608T133000Z DTEND:20210608T143000Z DTSTAMP:20260404T110829Z UID:UnibaMathPhys/3 DESCRIPTION:Title: Exactly solved models of chaotic many-body dynamics\nby T omaž Prosen (Ljubljana) as part of UniBA Mathematical Physics Seminar\n\n \nAbstract\nOne should be amazed with an unreasonable effectiveness of ran dom matrix theory to describe spectral fluctuations in simple non-integrab le many-body systems\, say one dimensional spin 1/2 chains with local inte ractions. I will discuss a class of Floquet (periodically driven) quantum spin chains - specifically\, dual unitary Floquet circuits - where the ran dom matrix result for the spectral form factor can be derived or even rigo rously proven. Several other nontrivial exactly solvable features of the p resented models\, such as dynamical correlations or entanglement dynamics\ , will be discussed.\n LOCATION:https://stable.researchseminars.org/talk/UnibaMathPhys/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Alessandro Michelangeli (Bonn) DTSTART:20210525T133000Z DTEND:20210525T143000Z DTSTAMP:20260404T110829Z UID:UnibaMathPhys/4 DESCRIPTION:Title: Effective quantum dynamics of composite Bose-Einstein condens ates\nby Alessandro Michelangeli (Bonn) as part of UniBA Mathematical Physics Seminar\n\n\nAbstract\nAmong the most sophisticated\, recent exper iments with Bose-Einstein condensates\, a primary role is played by compos ite condensation. This is like ordinary condensation\, with some kind of i nternal structure: condensate samples consisting of two or more population s of different particle species (condensate mixtures)\, condensates of par ticles whose spin is coupled with external radiation fields (pseudo-spinor condensates)\, condensates with interaction between different hyperfine s tates (spinor condensates)\, or condensates with macroscopic occupation of different one-body orbitals (fragmented condensates). Their observed dyna mics obey multiple coupled non-linear Schrödinger equations\, and in this talk I shall discuss recent rigorous derivations of such effective dynami cs from from the first-principle many-body (linear) Schrödinger equation. A special focus will be given to condensate mixtures\, for which the grou nd state and the correctness of Bogolyubov's theory will be also shown.\n LOCATION:https://stable.researchseminars.org/talk/UnibaMathPhys/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Eva-Maria Graefe (London) DTSTART:20210615T133000Z DTEND:20210615T143000Z DTSTAMP:20260404T110829Z UID:UnibaMathPhys/5 DESCRIPTION:Title: A non-Hermitian PT-symmetric kicked top\nby Eva-Maria Gra efe (London) as part of UniBA Mathematical Physics Seminar\n\n\nAbstract\n A non-Hermitian PT-symmetric version of the kicked top is introduced to st udy the interplay of quantum chaos with balanced loss and gain. The classi cal dynamics arising from the quantum dynamics of the angular momentum exp ectation values are derived. It is demonstrated that the presence of PT-sy mmetry can lead to ''stable'' mixed regular chaotic behaviour without sink s or sources for subcritical values of the gain-loss parameter. For large values of the kicking strength a strange attractor is observed that also p ersists if PT-symmetry is broken. Classical structures are also identified in the quantum dynamics. Finally\, some of the statistics of the eigenval ues of the quantum system are analysed.\n LOCATION:https://stable.researchseminars.org/talk/UnibaMathPhys/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Karol Życzkowski (Cracow\, Warsaw) DTSTART:20210622T133000Z DTEND:20210622T143000Z DTSTAMP:20260404T110829Z UID:UnibaMathPhys/6 DESCRIPTION:Title: The spectra of random operations and random Lindblad operator s\nby Karol Życzkowski (Cracow\, Warsaw) as part of UniBA Mathematica l Physics Seminar\n\n\nAbstract\nWe analyze spectral properties of generic quantum operations\,\nwhich describe open systems under assumption of a s trong\ndecoherence and a strong coupling with an environment.\nIn the case of discrete maps the spectrum of a quantum stochastic\nmap displays a uni versal behaviour: it contains the leading eigenvalue \n\\lambda_1 = 1\, w hile all other eigenvalues are restricted to the disk of radius R<1. \nSim ilar properties are exhibited by spectra of their classical counterparts - random stochastic matrices.\n\nIn the case of a generic dynamics in cont inuous time\, we introduce an ensemble of \nrandom Lindblad operators\, wh ich generate Markov evolution in the space of density \nmatrices of a fixe d size. Universal spectral features of such operators\, \nincluding the le mon-like shape of the spectrum in the complex plane\, are explained\nwith a non-hermitian random matrix model. The structure of the spectrum determi nes\nthe transient behaviour of the quantum system and the convergence of the dynamics\ntowards the generically unique invariant state. The quantum -to-classical transition\nfor this model is also studied and the spectra o f random Kolmogorov operators \nare investigated.\n LOCATION:https://stable.researchseminars.org/talk/UnibaMathPhys/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Cécilia Lancien (Toulouse) DTSTART:20210629T133000Z DTEND:20210629T143000Z DTSTAMP:20260404T110829Z UID:UnibaMathPhys/7 DESCRIPTION:Title: Typical correlations and entanglement in random MPS and PEPS< /a>\nby Cécilia Lancien (Toulouse) as part of UniBA Mathematical Physics Seminar\n\n\nAbstract\nTensor network states are used extensively as a mat hematically convenient description of physically relevant states of many-b ody quantum systems. Those built on regular lattices\, i.e. matrix product states (MPS) in dimension 1 and projected entangled pair states (PEPS) in dimension 2 or higher\, are of particular interest in condensed matter ph ysics. In this talk\, I will try to answer the following general question: which features of MPS and PEPS are generic and which are\, on the contrar y\, exceptional? Or to rephrase it: given an MPS or PEPS sampled at random \, what are the features that it displays with either high or low probabil ity? One property which we will focus on is that of having either rapidly decaying or long-range correlations. In a nutshell\, the main result I wil l state is that translation-invariant MPS and PEPS typically exhibit expon ential decay of correlations at a high rate. I will show two distinct ways of getting to this conclusion\, depending on the dimensional regime under consideration. Both yield intermediate results which are of independent i nterest\, namely: the parent Hamiltonian and the transfer operator of such MPS and PEPS typically have a large spectral gap. If time allows\, I will also present on-going attempts at quantifying the amount of genuinely mul tipartite entanglement in such random MPS and PEPS.\nThe talk will be base d mainly on a joint work with David Perez-Garcia\, available at arXiv:1906 .11682\, and on some work in progress with Ion Nechita.\n LOCATION:https://stable.researchseminars.org/talk/UnibaMathPhys/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Seiringer (IST Austria) DTSTART:20211103T143000Z DTEND:20211103T153000Z DTSTAMP:20260404T110829Z UID:UnibaMathPhys/8 DESCRIPTION:Title: Quantum fluctuations and dynamics of a strongly coupled polar on\nby Robert Seiringer (IST Austria) as part of UniBA Mathematical Ph ysics Seminar\n\n\nAbstract\nWe review old and new results on the Fröhlic h polaron model. The discussion includes the validity of the (classical) L andau--Pekar equations for the dynamics in the strong coupling limit\, qua ntum corrections to this limit\, as well as the divergence of the effectiv e polaron mass.\n LOCATION:https://stable.researchseminars.org/talk/UnibaMathPhys/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Pavel Exner (Prague) DTSTART:20211124T143000Z DTEND:20211124T153000Z DTSTAMP:20260404T110829Z UID:UnibaMathPhys/9 DESCRIPTION:Title: A product formula and its application to Zeno quantum dynamic s\nby Pavel Exner (Prague) as part of UniBA Mathematical Physics Semin ar\n\n\nAbstract\nWe present a new product formula which involves a unitar y group generated by a positive self-adjoint operator and a continuous pro jection-valued function. The question has a direct physical motivation com ing from treatment of decaying quantum systems and\, in particular\, the Z eno effect associated with frequently repeated measurements. Used in this context\, the formula expresses the dynamics of such a system. We describe the background of the problem\, sketch the proof of the formula\, and pre sent an example of a permanent position ascertaining which leads to an eff ective constraint given by the Dirichlet condition.\n LOCATION:https://stable.researchseminars.org/talk/UnibaMathPhys/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesco Pepe (Bari) DTSTART:20211214T143000Z DTEND:20211214T153000Z DTSTAMP:20260404T110829Z UID:UnibaMathPhys/10 DESCRIPTION:Title: The many facets of quantum decay in a simple hopping model\nby Francesco Pepe (Bari) as part of UniBA Mathematical Physics Seminar \n\n\nAbstract\nThe decay of an unstable system is usually described by an exponential function\, following a classical statistical assumption. In a quantum mechanical context\, the exponential law emerges in the context o f perturbation theory\, and is characterized by a decay rate fixed by the Fermi golden rule. However\, quantum mechanics generally predicts deviatio ns from the exponential: the survival probability is characterized by an i nitial regime of quadratic decrease\, while at large times it must follow\ , in a very wide range of physical systems\, a power law\, with possible s uperimposed oscillations. In this seminar\, I will describe how all these features can be identified in the behavior of a semi-analytically solvable nearest-neigbor hopping model. Specifically\, I will analyze the quantum decay of an initial state in which the first site of a semi-infinite linea r array is populated\, showing that the model parameters can be tuned in o rder to enhance the relevance of the quadratic and the power-law decay reg ime.\n LOCATION:https://stable.researchseminars.org/talk/UnibaMathPhys/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Brian Hall (Notre Dame) DTSTART:20220330T133000Z DTEND:20220330T143000Z DTSTAMP:20260404T110829Z UID:UnibaMathPhys/11 DESCRIPTION:Title: PDE methods in random matrix theory\nby Brian Hall (Notr e Dame) as part of UniBA Mathematical Physics Seminar\n\n\nAbstract\nGirko ’s method for analyzing random matrix models is to study the log potenti al of the eigenvalue distribution. It is then sometimes useful to put in a regularization parameter $\\epsilon$ that avoids the singularity in the l og function. In recent work of mine with Driver and Kemp\, we studied a “multiplicative” random matrix model—Brownian motion in the general linear group—by showing that the regularized log potential satisfies a P DE. This PDE can then be analyzed by the method of characteristics to comp ute the limiting eigenvalue distribution\, which has a beautiful structure .\n\nI will discuss the PDE method and several random matrix models that c an be analyzed using it. The talk will be self-contained and have lots of pictures.\n LOCATION:https://stable.researchseminars.org/talk/UnibaMathPhys/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Zamparo (Bari) DTSTART:20220302T143000Z DTEND:20220302T153000Z DTSTAMP:20260404T110829Z UID:UnibaMathPhys/12 DESCRIPTION:Title: Large deviation principles in renewal-reward processes\n by Marco Zamparo (Bari) as part of UniBA Mathematical Physics Seminar\n\nL ecture held in Aula XI - Dipartimento di Matematica.\n\nAbstract\nRenewal- reward processes describe some event that is continuously renewed over tim e\, \ninvolving a reward at each occurrence. In this seminar\, I will esta blish a sharp large deviation \nprinciple for renewal-reward processes sup posing that rewards take values in a separable \nBanach space. My large de viation principle extends Cramér’s theorem to renewal theory. \nSome ap plications will be reviewed with special focus on renewal models of statis tical physics\, \nsuch as the Poland-Scheraga model of DNA denaturation\, which are Gibbs changes of measure \nof a renewal process.\n\nReferences:\ n- M. Zamparo\, Large deviations in discrete-time renewal theory\,\nStoch. Process. Their Appl. 139 (2021) 80-109 \n- M. Zamparo\, Large deviations in renewal models of statistical mechanics\,\nJ. Phys. A: Math. Theor. 52 (2019) 495004\n- M. Zamparo\, Critical fluctuations in renewal models of s tatistical mechanics\,\nJ. Math. Phys. 62 (2021) 113301\n- M. Zamparo\, La rge deviation principles for renewal-reward processes\,\nsubmitted to Ann. Appl. Probab. (arXiv:2111.01679)\n LOCATION:https://stable.researchseminars.org/talk/UnibaMathPhys/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Elia Bisi (Vienna) DTSTART:20220406T133000Z DTEND:20220406T143000Z DTSTAMP:20260404T110829Z UID:UnibaMathPhys/13 DESCRIPTION:Title: Matsumoto-Yor and Dufresne type theorems for a random walk o n positive definite matrices\nby Elia Bisi (Vienna) as part of UniBA M athematical Physics Seminar\n\n\nAbstract\nWe establish analogues of the g eometric Pitman 2M-X theorem of Matsumoto and Yor and of the classical Duf resne identity\, for a multiplicative random walk on positive definite mat rices with Beta type II distributed increments. The Dufresne type identity provides also an example of a stochastic matrix recursion that admits an explicit solution.\nJoint work with J. Arista and N. O'Connell.\n LOCATION:https://stable.researchseminars.org/talk/UnibaMathPhys/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Gregory Berkolaiko (Texas) DTSTART:20220427T133000Z DTEND:20220427T143000Z DTSTAMP:20260404T110829Z UID:UnibaMathPhys/14 DESCRIPTION:Title: Nodal deficiency\, spectral minimal partitions and the Diric hlet-to-Neumann map\nby Gregory Berkolaiko (Texas) as part of UniBA Ma thematical Physics Seminar\n\n\nAbstract\nIn this overview talk we will ex plore connections between the subjects\nmentioned in the title as well as some other notions such as the\nspectral shift and the Schur complement. For an eigenfunction of the\nDirichlet Laplacian\, the nodal deficiency is the difference between\nthe label of an eigenfunction (starting with 1 fo r the ground state)\nand the number of its nodal domains. It is known to be equal to the\nMorse index of a critical point of a certain spectral fun ctional\ndefined on the space of partitions of the manifold. The connecti on\nbetween the two is easier understood via the introduction of a two-sid ed\nDirichlet-to-Neumann map. On one hand\, the number of its negative\ne igenvalues is related to the spectral shift (which is a natural\ninterpret ation of the nodal deficiency). On the other hand\, the DtN\nmap is unita rily equivalent to the Hessian of the spectral functional\nat the critical point.\n\nThe talk is based on several papers of Yaiza Canzani\, Graham C ox\,\nBernard Helffer\, Peter Kuchment\, Jeremy Marzuola\, Uzy Smilansky a nd\nMikael Sundqvist\, with and without the speaker.\n LOCATION:https://stable.researchseminars.org/talk/UnibaMathPhys/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Nilanjana Datta (Cambridge) DTSTART:20220608T133000Z DTEND:20220608T143000Z DTSTAMP:20260404T110829Z UID:UnibaMathPhys/16 DESCRIPTION:Title: Majorization and entropic continuity bounds\nby Nilanjan a Datta (Cambridge) as part of UniBA Mathematical Physics Seminar\n\n\nAbs tract\nWe employ majorization theory to obtain a powerful tool for derivin g simple and universal proofs\nof continuity bounds for various entropies which are relevant in information theory. In obtaining this\, we first der ive a more general result which may be of independent interest: a necessar y and sufficient condition under which a state maximizes a concave\, conti nuous\, Gateaux-differentiable function in an epsilon-ball in trace distan ce. Examples of such a function include the von Neumann entropy\, and the conditional entropy of bipartite states. This is joint work with Eric Hans on.\n LOCATION:https://stable.researchseminars.org/talk/UnibaMathPhys/16/ END:VEVENT END:VCALENDAR