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Random Matrix Theory, Integrable Systems, and Topology in Physics: November 2-6, 2015

Random Matrix Theory, Integrable Systems, and Topology in Physics, November 2-6, 2015

Organized by Yan Fyodorov, Mario Kieburg, and Jacobus Verbaarschot

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This is the second workshop in the Simons Center Program on Foundations and Application of Random Matrix Theory in Mathematics and Physics. This workshop will highlight future and recent applications of Random Matrix Theory to physics with main focus on applications to quantum systems, integrable systems, and disordered systems. Since the first applications of Random Matrix Theory to the levels of nuclei and to the localization of wave functions in disordered solids over half a century ago, the field continues to generate a great deal of excitement in both in established topics and new areas such as quantum information and field theory. To mention a few of these developments, in QCD chiral RMT was extended to study non-zero matter density including lattice artifacts. These applications involve non-Hermitian random matrix ensembles interpolating between different ensembles in the ten-fold classification according to symmetric spaces. Such interpolating random matrix ensembles were also found in quantum chaos and recently in condensed matter theory. In the latter topic the strength of the magnetic field is the interpolating parameter. The crucial role of topology is a common factor in both QCD and condensed matter theory and can be understood in terms of RMT as well. In QCD, topology of the gauge field configurations is essential for the spectrum of the Dirac operator. In condensed matter theory topology led to the classification and discovery of topological insulators and superconductors. It enters in the transport properties of mesoscopic systems, and could be essential for the discovery of Majorana fermions as well as details of the localization properties of wave functions. Other developments of RMT can be found in quantum information where RMT has been used to describe decoherence and coupling of quantum states to the environment. In particular, randomly generated quantum states have been used to study entangled quantum systems. Also in this topic topology can be identified and reflects the rank of the density operator. These examples are particular cases of integrable systems associated to RMT. However the theory of integrable systems in RMT is not restricted to those examples alone. It became a research topic of its own and exhibits a plethora of application.

This workshop will bring together experts from particle physics, quantum information, and disordered systems together with specialists in mathematical physics and integrable systems. Topics to be discussed include experiments with microwave billiards, properties of the Wilson Dirac operator and the sign problem in QCD, localization and scaling relations of critical exponents, Brownian motion and deformations of random matrix theory, localization properties of band matrices, Anderson localization in QCD, transport in disordered media, Toda lattice structures and supersymmetry, disordered systems and entanglement entropy in quantum information.

Talk Schedule


Time Title Presenter Location
9:00 am Random Matrix Theory and Low-Energy QCD Poul Damgaard SCGP 102
10:00 am Coffee Break N/A  SCGP Lobby
10:30 am A new look at chiral random matrix theory Takuya Kanazawa  SCGP 102
11:30 am Massless QED in three dimensions with even number of flavors Rajamani Narayanan  SCGP 102
12:30 pm Lunch N/A  SCGP Cafe
2:00 pm The Anderson transition in lattice QCD Tamas Kovacs  SCGP 102
3:00 pm Tea Time N/A  SCGP Lobby
 3:30 pm Random Matrix Theory for Wilson Fermions Savvas Zafeiropoulos  SCGP 102


Time Title Presenter Location
9:00 am Topological Phases of Matter and the “Ten-Fold Way”: Overview of Approaches to the Classification of Topological Insulators and Superconductors of Non-Interacting Fermions, and Beyond Andreas Ludwig SCGP 102
10:00 am Coffee Break N/A SCGP Lobby
10:30 am Low-frequency conductivity of disordered wires: integrability and instantons Ilya Gruzberg SCGP 102
11:30 am Lunch  N/A SCGP Cafe
1:00 pm SCGP Weekly Talk: Random Matrices: Tour d’Horizonel  Thomas Guhr SCGP 102
2:15 pm
from replica Bethe ansatz solutions of Kardar Parisi Zhang growth to non-crossing directed paths in a random potential
Pierre Le Doussal SCGP 102
3:15 pm Tea Time N/A SCGP Lobby
3:45 pm Singular Values of Products of Ginibre Random Matrices and a generalisation of Painlev\’e III. Nicholas Witte SCGP 102


Time Title Presenter Location
9:00 am Products of random matrices: from independent to coupled matrices Gernot Akemann  SCGP 102
10:00 am Coffee Break N/A  SCGP Lobby
10:30 am Products of random matrices: from correlated to uncorrelated eigenvalues Jesper Ispen  SCGP 102
11:30 am Dynamics of Hermitian versus  non-Hermitian  random matrices – unexpected links Maciej Nowak  SCGP 102
12:30 pm Lunch N/A  SCGP Cafe
2:00 pm Hydrodynamics of the Polyakov loop and Dirac spectra Ismail Zahed  SCGP 102
3:00 pm Tea Time N/A  SCGP Lobby
3:30 pm Investigations into the a priori probability that pairs of quantum bits (qubits) are separable/disentangled Paul B. Slater  SCGP 102


Time Title Presenter Location
9:00 am Wilson loop eigenvalue distributions Herbert Neuberge SCGP 102
10:00 am Coffee Break N/A SCGP Lobby
10:30 am Spectral crossover and Anderson localization in QCD Dirac spectra Shinsuke M. Nishigaki SCGP 102
11:30 am The Dirac eigenvalues in high temperature QCD: connection with topology and RMT Sayantan Sharma SCGP 102
12:30 pm Lunch N/A SCGP Cafe
2:00 pm Zirnbaeur’s SUSY sigma model and Reinforced walks Thomas Spencer SCGP 102
3:00 pm Tea Time N/A SCGP Lobby
3:30 pm Anderson transitions and electron-electron interaction Alexander Mirlin SCGP 102
4:30 pm New and Exact Results for the Real, Correlated Wishart Model Thomas Guhr SCGP 102


Time Title Presenter Location
9:00 am Probing eigenfunction nonorthogonality by parametric shifts of resonance widths Dmitry Savin SCGP 102
10:00 am Coffe Break N/A SCGP Lobby
10:30 am Random-matrix approach to the statistical compound nuclear reaction at low energies using the Monte-Carlo technique Toshihiko Kawano SCGP 102
11:30 am Fine Asymptotic Behavior for Eigenvalues of Random Normal Matrices Roman Riser SCGP 102
12:30 pm Lunch N/A SCGP Cafe
2:00 pm On asymptotic behavior of pure complex spectrum probability for the real Ginibre matrix. Dr. Mihail Poplavskyi SCGP 102
3:00 pm Tea Time N/A SCGP Lobby
3:30 pm Semiclassics and random matrices for many-particle systems Sebastian Muller SCGP 102

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