Related papers: A new method of quantization of classical solution…
This survey gives a comprehensive account of quantum correlations understood as a phenomenon stemming from the rules of quantization. Centered on quantum probability it describes the physical concepts related to correlations (both classical…
In this work we study how quantum fluctuations modify the quantum evolution of an initially classical field theory. We consider a scalar $\phi^4$ theory coupled to an external source as a toy model for the Color Glass Condensate description…
We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic processes with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary…
We study the stochastic quantization of the system with first class constraints in phase space. Though the Langevin equations of the canonical variables are defined without ordinary gauge fixing procedure, gauge fixing conditions are…
We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the…
Recently there has been increasing interest in alternate methods to compute quantum tunneling in field theory. Of particular interest is a stochastic approach which involves (i) sampling from the free theory Gaussian approximation to the…
A key component of variational quantum algorithms (VQAs) is the choice of classical optimizer employed to update the parameterization of an ansatz. It is well recognized that quantum algorithms will, for the foreseeable future, necessarily…
This paper extends the tools of C*-algebraic strict quantization toward analyzing the classical limits of unbounded quantities in quantum theories. We introduce the approach first in the simple case of finite systems. Then we apply this…
Canonical quantization has taught us great things. A common example is that of the harmonic oscillator, which is like swinging a ball on a string back and forth. However, the half-harmonic oscillator blocks the ball at the bottom and then…
The continuous quantum measurement within the probability representation of quantum mechanics is discussed. The partial classical propagator of the symplectic tomogram associated to a particular measurement outcome is introduced, for which…
Generic open quantum systems are notoriously difficult to simulate unless one looks at specific regimes. In contrast, classical dissipative systems can often be effectively described by stochastic processes, which are generally less…
We consider steady state heat conduction across a quantum harmonic chain connected to reservoirs modelled by infinite collection of oscillators. The heat, $Q$, flowing across the oscillator in a time interval $\tau$ is a stochastic variable…
Using a method of eigenfunction expansion, a stochastic equation is developed for the generalized Schr{\"o}dinger equation with random fluctuations. The wave field $ {\psi} $ is expanded in terms of eigenfunctions: $ {\psi} = \sum_{n} a_{n}…
We consider a simple quantum system subjected to a classical random force. Under certain conditions it is shown that the noise-averaged Wigner function of the system follows an integro-differential stochastic Liouville equation. In the…
Hybrid classical quantum optimization methods have become an important tool for efficiently solving problems in the current generation of NISQ computers. These methods use an optimization algorithm executed in a classical computer, fed with…
We consider the quantum evolution of classically chaotic systems in contact with surroundings. Based on $\hbar$-scaling of an equation for time evolution of the Wigner's quasi-probability distribution function in presence of dissipation and…
We illustrate how classical chaotic dynamics influences the quantum properties at mesoscopic scales. As a model case we study semiclassically coherent transport through ballistic mesoscopic systems within the Landauer formalism beyond the…
In this work we address the problem of the quantization of a simple harmonic oscillator that is perturbed by a time dependent force. The approach consists of removing the perturbation by a canonical change of coordinates. Since the…
We investigate oscillating solutions of the equation of motion for the Higgs potential. The solutions are described by Jacobian elliptic functions. Classifying the classical solutions, we evaluate a possible parameter-space for the initial…
The homotopy analysis method known from its successful applications to obtain quasi-analytical approximations of solutions of ordinary and partial differential equations is applied to stochastic differential equations with Gaussian…