Related papers: Quantum fluctuations and random matrix theory
We analyze the control by electromagnetic fields of quantum systems with infinite dimensional Hilbert space and a discrete spectrum. Based on recent mathematical results, we rigorously show under which conditions such a system can be…
Realistic quantum mechanics based on complex probability theory is shown to have a frequency interpretation, to coexist with Bell's theorem, to be linear, to include wavefunctions which are expansions in eigenfunctions of Hermitian…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
This study discusses the quantum behavior of a particle, which is controlled by fluctuations in the physical space-time (ST) variables, rather than provides a novel interpretation of quantum theory. The fluctuations, i.e., inhomogeneities…
Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose…
We introduce structured random matrix ensembles, constructed to model many-body quantum systems with local interactions. These ensembles are employed to study equilibration of isolated many-body quantum systems, showing that rather complex…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
A quantum mechanical generalization of superstatistics is presented here based on the positive operator valued measure transformation property of the system density matrix. This procedure reveals that the origin of the fluctuating factors…
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and quantum circuits are naturally interpretable in such structures. We…
The very notion of a current fluctuation is problematic in the quantum context. We study that problem in the context of nonequilibrium statistical mechanics, both in a microscopic setup and in a Markovian model. Our answer is based on a…
We review how the identification of gauge theory operators representing string states in the pp-wave/BMN correspondence and their associated anomalous dimension reduces to the determination of the eigenvectors and the eigenvalues of a…
We develop a means of simulating the evolution and measurement of a multipartite quantum state under discrete or continuous evolution using another quantum system with states and operators lying in a real Hilbert space. This extends…
We introduce and review briefly the phenomenon of quantum annealing and analog computation. The role of quantum fluctuation (tunneling) in random systems with rugged (free) energy landscapes having macroscopic barriers are discussed to…
We demonstrate the connection between an operator's matrix element distribution and entangling power via numerical simulations of random, pseudo-random, and quantum chaotic operators. Creating operators with a random distribution of matrix…
Relaxation in the time correlation between operators is studied. Quantized chaotic systems are shown to have distinct relaxation fluctuations that are universal and can be usefully modelled by Random Matrix Theory. Various quantized maps…
In this article we derive a useful expectation identity using the language of quantum statistical mechanics, where density matrices represent the state of knowledge about the system. This identity allows to establish relations between…
We study a motion of quantum particles, whose properties depend on one coordinate so that they can move freely in the perpendicular direction. A rotationally-symmetric Hamiltonian is derived and applied to study a general interface formed…