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.
Mathematical and theoretical physics
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.
This book is the second of three collections of expository and research articles. This volume focuses on topology and physics.
Integrable Hamiltonian Systems: Geometry, Topology, Classification - CRC Press Book
The role of zero curvature equations outside of the traditional context of differential geometry has been recognized relatively recently, but it has been an extraordinarily productive one, and most of the articles in this volume make some reference to it. Symplectic geometry, Floer homology, twistor theory, quantum cohomology, and the structure of special equations of mathematical physics, such as the Toda field equations—all of these areas have gained from the integrable systems point of view and contributed to it.
Many of the articles in this volume are written by prominent researchers and will serve as introductions to the topics.
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It is intended for graduate students and researchers interested in integrable systems and their relations to differential geometry, topology, algebraic geometry, and physics. Graduate students and researchers interested in integrable systems and their relations to differential geometry, topology, algebraic geometry, and physics.
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