Related papers: Random Matrix Theories in Quantum Physics: Common …
Quantum General Relativity (QGR), sometimes called Loop Quantum Gravity, has matured over the past fifteen years to a mathematically rigorous candidate quantum field theory of the gravitational field. The features that distinguish it from…
Classical random matrix ensembles were originally introduced in physics to approximate quantum many-particle nuclear interactions. However, there exists a plethora of quantum systems whose dynamics is explained in terms of few-particle…
We consider a possible generalization of the random matrix theory, which involves the maximization of Tsallis' $q$-parametrized entropy. We discuss the dependence of the spacing distribution on $q$ using a non-extensive generalization of…
We introduce a notion of local level spacings and study their statistics within a random-matrix-theory approach. In the limit of infinite-dimensional random matrices, we determine universal sequences of mean local spacings and of their…
`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…
In the last 175 years, the physical understanding of nature has seen a revolutionary change. Until about 1850, Newton's theory and the mechanical world view derived from it provided the dominant view of the physical world, later…
We formulate gaussian and circular random-matrix models representing a coupled system consisting of an absorbing and an amplifying resonator, which are mutually related by a generalized time-reversal symmetry. Motivated by optical…
We provide a brief overview of tensor models and group field theories, focusing on their main common features. Both frameworks arose in the context of quantum gravity research, and can be understood as higher-dimensional generalizations of…
A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of…
Randomized algorithms for very large matrix problems have received a great deal of attention in recent years. Much of this work was motivated by problems in large-scale data analysis, and this work was performed by individuals from many…
Quantum chaotic systems are often defined via the assertion that their spectral statistics coincides with, or is well approximated by, random matrix theory. In this paper we explain how the universal content of random matrix theory emerges…
The traditional class of elliptical distributions is extended to allow for asymmetries. A completely robust dispersion matrix estimator (the `spectral estimator') for the new class of `generalized elliptical distributions' is presented. It…
We review our recent proposal for a background independent formulation of a holographic theory of quantum gravity. The present review incorporates the necessary background material on geometry of canonical quantum theory, holography and…
In this article, we discuss the remarkable connection between two very different fields, number theory and nuclear physics. We describe the essential aspects of these fields, the quantities studied, and how insights in one have been…
We present a general framework connecting global symmetries to the relativistic $S$-matrix through the lens of quantum information theory. Analyzing the 2-to-2 scattering of particles of any helicity, we systematically characterize…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…
General relativity and quantum mechanism are two separate rules of modern physics explaining how nature works. Both theories are accurate, but the direct connection between two theories was not yet clarified. Recently, researchers blur the…
We speak of chaos in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is a typical feature of atomic nuclei and other self-bound Fermi systems. How can the…
We propose a random matrix modeling for the parametric evolution of eigenstates. The model is inspired by a large class of quantized chaotic systems. Its unique feature is having parametric invariance while still possessing the…
The random matrix ensembles are applied to the quantum statistical systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…