Related papers: On the quantum dynamics of non-commutative systems
We consider quantum Hamiltonian systems composed of mutually interacting "dynamical subsystem" with one or several degrees of freedom and "thermostat" with arbitrary many degrees of freedom, under assumptions that the interaction ensures…
We discuss systematically several possible inequivalent ways to describe the dynamics and the transition probabilities of a quantum system when its hamiltonian is not self-adjoint. In order to simplify the treatment, we mainly restrict our…
The driven quantum harmonic oscillator is fundamental to a number of important physical systems. Here, we consider the quantum harmonic oscillator under non-Hermitian, PT-symmetric driving, showing that the resulting set of Wigner-space…
We propose a scheme for data-driven parameterization of unresolved dimensions of dynamical systems based on the mathematical framework of quantum mechanics and Koopman operator theory. Given a system in which some components of the state…
We model the dynamics of a closed quantum system brought out of mechanical equilibrium, undergoing a non-driven, spontaneous, thermodynamic transformation. In particular, we consider a quantum particle in a box with a moving and insulating…
Quantum systems with a non-conserved probability can be described by means of non-Hermitian Hamiltonians and non-unitary dynamics. In this paper, the case in which the degrees of freedom can be partitioned in two subsets with light and…
We consider a problem of the consistent deformation of physical system introducing a new features, but preserving its fundamental properties. In particular, we study how to implement the noncommutativity of space-time without violation of…
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…
The article explores a new formalism for describing motion in quantum mechanics. The construction is based on generalized coherent states with evolving fiducial vector. Weyl-Heisenberg coherent states are utilised to split quantum systems…
A strong analog classical simulation of general quantum evolution is proposed, which serves as a novel scheme in quantum computation and simulation. The scheme employs the approach of geometric quantum mechanics and quantum informational…
The assumption that quantum systems relax to a stationary state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate…
Developments in the foundations of quantum mechanics have identified several attributes and tests associated with the "quantumness" of systems, including entanglement, nonlocality, quantum erasure, Bell test, etc. Here we introduce and…
A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as…
Closed quantum systems far from thermal equilibrium can show universal dynamics near attractor solutions, known as non-thermal fixed points, generically in the form of scaling behavior in space and time. A systematic classification and…
Following on from our recent work, we investigate a stochastic approach to non-equilibrium quantum spin systems. We show how the method can be applied to a variety of physical observables and for different initial conditions. We provide…
A quantum mechanical model for the systems consisting of interacting bodies is considered. The model takes into account the noncommutativity of the space and impulse operators and the correlation equations for the indeterminacy of these…
We derive stochastic master equation for a quantum system interacting with an environment prepared in a continuous-mode $N$-photon state. To determine the conditional evolution of the quantum system depending on continuous in time…
A formalism for studying the dynamics of quantum systems embedded in classical spin baths is introduced. The theory is based on generalized antisymmetric brackets and predicts the presence of open-path off-diagonal geometric phases in the…
This is the first of a series of papers in which a new formulation of quantum theory is developed for totally constrained systems, that is, canonical systems in which the hamiltonian is written as a linear combination of constraints…
We investigate a stochastic approach to non-equilibrium quantum spin systems based on recent insights linking quantum and classical dynamics. Exploiting a sequence of exact transformations, quantum expectation values can be recast as…