Related papers: Random Matrix Theories in Quantum Physics: Common …
Relativistic quantum transport theory has begun to play an important role in the space-time description of matter under extreme conditions of high energy density in out-of-equilibrium situations. The following introductory lectures on some…
More than 15 years ago, a new approach to quantum mechanics was suggested, in which Hermiticity of the Hamiltonian was to be replaced by invariance under a discrete symmetry, the product of parity and time-reversal symmetry, $\mathcal{PT}$.…
We develop a novel approach to gravity that we call `matrix general relativity' (MGR) or `gravitational chromodynamics' (GCD or GQCD for quantum version). Gravity is described in this approach not by one Riemannian metric (i.e. a symmetric…
A causal, non-Hermitian, renormalizable, local, unitary and Lorentz convariant formulation of Quantum Theory (QT) (= Quantum Mechanics (QM) and Quantum Field Theory (QFT)) is developed which is free of formalistic problems we face in the…
The relational interpretation of quantum mechanics (RQM), introduced in its present form by Carlo Rovelli in 1996, involves a number of significant departures from other QM interpretations widely discussed in the literature. We begin here…
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…
At the beginning of the previous century, Newtonian mechanics fell victim to two new revolutionary theories, Quantum Mechanics (QM) and General Relativity (GR). Both theories have transformed our view of physical phenomena, with QM…
We present an exactly solvable quantum field theory which allows rearrangement collisions. We solve the model in the relevant sectors and demonstrate the orthonormality and completeness of the solutions, and construct the S-matrix. In the…
We review aspects of entanglement entropy in the quantum mechanics of $N\times N$ matrices, i.e. matrix quantum mechanics (MQM), at large $N$. In doing so we review standard models of MQM and their relation to string theory, D-brane…
The spectral properties of interacting strongly chaotic systems are investigated for growing interaction strength. A very sensitive transition from Poisson statistics to that of random matrix theory is found. We introduce a new random…
The adaptation of the Kramers-Kronig dispersion relations to the causal localization structure of QFT led to an important project in particle physics, the only one with a successful closure. The same cannot be said about the subsequent…
A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace…
We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
We discuss the semiclassical approximation to transport problems in quantum chaotic systems. The figures of merit are moments of the transmission matrix and of the time delay matrix. After reviewing a few results obtained by treating these…
We apply Tsallis's q-indexed entropy to formulate a non-extensive random matrix theory (RMT), which may be suitable for systems with mixed regular-chaotic dynamics. The joint distribution of the matrix elements is given by folding the…
This topical review gives a comprehensive overview and assessment of recent results in Causal Dynamical Triangulations (CDT), a modern formulation of lattice gravity, whose aim is to obtain a theory of quantum gravity nonperturbatively from…
There is a newly emerging understanding that in the chaotic domain of isolated finite interacting many particle systems smoothed densities define the statistical description of these systems and these densities follow from embedded…
A new formulation of relativistic quantum mechanics is presented and applied to a free, massive, and spin zero elementary particle in the Minkowski spacetime. The reformulation requires that time and space, as well as the timelike and…
The fine grained energy spectrum of quantum chaotic systems is widely believed to be described by random matrix statistics. A basic scale in such a system is the energy range over which this behavior persists. We define the corresponding…