Related papers: Quantization of nonlinear non-Hamiltonian systems
We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is…
While quantum simulation is one of the most promising applications of modern quantum devices, accessible simulation times are fundamentally limited by finite coherence times due to omnipresent noise. Based on the ideas of relational…
Identifying the physiological processes in the central nervous system that underlie our conscious experiences has been at the forefront of cognitive neuroscience. While the principles of classical physics were long found to be…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
A recent promising arena for quantum advantage is simulating exponentially large classical systems. Here, we show how this advantage can be used to calculate the dynamics of open classical systems experiencing dissipation, including the…
Over the past two decades, open systems that are described by a non-Hermitian Hamiltonian have become a subject of intense research. These systems encompass classical wave systems with balanced gain and loss, semiclassical models with mode…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
We consider an arbitrary quantum system coupled non perturbatively to a large arbitrary and fully quantum environment. In [G. Ithier and F. Benaych-Georges, Phys. Rev. A 96, 012108 (2017)] the typicality of the dynamics of such an embedded…
Many numerical techniques for the description of quantum systems that are coupled to a continuous bath require the discretization of the latter. To this end, a wealth of methods has been developed in the literature, which we classify as (i)…
Non hermitian Hamiltonians play an important role in the study of dissipative quantum systems. We show that using states with time dependent normalization can simplify the description of such systems especially in the context of the…
Open quantum systems exhibit a rich phenomenology, in comparison to closed quantum systems that evolve unitarily according to the Schr\"odinger equation. The dynamics of an open quantum system are typically classified into Markovian and…
We resurrect a standard construction of analytical mechanics dating from the last century. The technique allows one to pass from any dynamical system whose first order evolution equations are known, and whose bracket algebra is not…
We consider quantum mechanics on constrained surfaces which have non-Euclidean metrics and variable Gaussian curvature. The old controversy about the ambiguities involving terms in the Hamiltonian of order hbar^2 multiplying the Gaussian…
Quantization of energy balance equations, which describe a separatrix -- like motion is presented. The method is based on an exact canonical transformation of the energy--time pair to the action-angle canonical pair, $ (E,t)\to (I,\theta)…
Stochastic quantization provides a connection between quantum field theory and statistical mechanics, with applications especially in gauge field theories. Euclidean quantum field theory is viewed as the equilibrium limit of a statistical…
Due to the exponential growth of the state space of coupled quantum systems it is not possible, in general, to numerically store the state of a very large number of quantum systems within a classical computer. We demonstrate a method for…
It is demonstrated that nonlinear dynamical systems with analytic nonlinearities can be brought down to the abstract Schr\"odinger equation in Hilbert space with boson Hamiltonian. The Fourier coefficients of the expansion of solutions to…
In this paper a generalization of Weyl quantization which maps a dynamical operator in a function space to a dynamical superoperator in an operator space is suggested. Quantization of dynamical operator, which cannot be represented as…
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…
We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev…