Related papers: A stochastic model for quantum measurement
Exact generalized stochastic representation of deterministic interaction between two dynamical (quantum or classical) systems is derived which helps when considering one of them to replace another by equivalent commutative ($c$-number…
In this paper we consider the problem of tracking the state of a quantum system via a continuous measurement. If the system Hamiltonian is known precisely, this merely requires integrating the appropriate stochastic master equation.…
Stochastic models for quantum state reduction give rise to statistical laws that are in many respects in agreement with those of standard quantum measurement theory. Here we construct a counterexample involving a Hamiltonian with degenerate…
It is first shown that when the Schr\"{o}dinger equation for a wave function is written in the polar form, complete information about the system's {\em quantum-ness} is separated out in a single term $Q$, the so called `quantum potential'.…
This paper aims to first explain, somewhat more clearly, the Stochastic-Quantum correspondence put forward in by Barandes in 2023. Specifically, the quantum-mechanical bra-ket notation is used, illuminating some results of previous results.…
Statistical functions such as the moment-generating function, characteristic function, cumulant-generating function, and second characteristic function are cornerstone tools in classical statistics and probability theory. They provide a…
One of the remarkable notions in the recent development of quantum physics is the weak value related to weak measurements. We emulate it as a two-time conditional expectation in a classical stochastic model. We use the well known…
We use the stochastic quantization method to construct a supersymmetric version of the quantum spherical model. This is based on the equivalence between the Brownian motion described by a Langevin equation and the supersymmetric quantum…
The dynamical equation of quantum mechanics are rewritten in form of dynamical equations for the measurable, positive marginal distribution of the shifted, rotated and squeezed quadrature introduced in the so called "symplectic tomography".…
The quest for improved sampling methods to solve statistical mechanics problems of physical and chemical interest proceeds with renewed efforts since the invention of the Metropolis algorithm, in 1953. In particular, the understanding of…
We demonstrate how to simulate both discrete and continuous stochastic evolution of a quantum many body system subject to measurements using matrix product states. A particular, but generally applicable, measurement model is analyzed and a…
The dynamics of many open quantum systems are described by stochastic master equations. In the discrete-time case, we recall the structure of the derived quantum filter governing the evolution of the density operator conditioned to the…
In this article, we derive the stochastic master equations corresponding to the statistical model of a heat bath. These stochastic differential equations are obtained as continuous time limits of discrete models of quantum repeated…
Descriptions of molecular systems usually refer to two distinct theoretical frameworks. On the one hand the quantum pure state, i.e. the wavefunction, of an isolated system which is determined to calculate molecular properties and to…
The report presents an exhaustive review of the recent attempt to overcome the difficulties that standard quantum mechanics meets in accounting for the measurement (or macro-objectification) problem, an attempt based on the consideration of…
The information on a quantum process acquired through measurements plays a crucial role in the determination of its non-equilibrium thermodynamic properties. We report on the experimental inference of the stochastic entropy production rate…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
One of the broadest concepts of measurement in quantum theory is the generalized measurement. Another paradigm of measurement--arising naturally in quantum optics, among other fields--is that of continuous-time measurements, which can be…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start…