Related papers: Martingale Models for Quantum State Reduction
We investigate the entropic consequences of the relaxation of an open two-level quantum system towards a thermalised statistical state, using a framework of quantum state diffusion with a minimal set of raising and lowering Lindblad…
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…
Measurement based quantum computation (MBQC), which requires only single particle measurements on a universal resource state to achieve the full power of quantum computing, has been recognized as one of the most promising models for the…
Classical computation of electronic properties in large-scale materials remains challenging. Quantum computation has the potential to offer advantages in memory footprint and computational scaling. However, general and practical quantum…
The decoherence phenomenon arising from an environmental monitoring of the state of a quantum system, as opposed to monitoring of a preferred observable, is worked out in detail using two equivalent formulations, namely, repeated…
We prove a stochastic averaging theorem for stochastic differential equations in which the slow and the fast variables interact. The approximate Markov fast motion is a family of Markov process with generator ${\mathcal L}_x$ for which we…
By decoupling forward and backward stochastic trajectories, we construct a family of martingales and work theorems for both overdamped and underdamped Langevin dynamics. Our results are made possible by an alternative derivation of work…
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…
We generalize Holley-Stroock's perturbation argument from commutative to quantum Markov semigroups. As a consequence, results on (complete) modified logarithmic Sobolev inequalities and logarithmic Sobolev inequalities for self-adjoint…
A simple quantum model explains the Levy-unstable distributions for individual stock returns observed by ref.[1]. The probability density function of the returns is written as the squared modulus of an amplitude. For short time intervals…
The quantum statistical treatment of the Rutherford model, considering matter as a system of point charges (electrons and nuclei) is analyzed. First, in the historical context, the solutions of different fundamental problems, such as the…
This is a concise, pedagogical introduction to the dynamic field of open quantum systems governed by Markovian master equations. We focus on the mathematical and physical origins of the widely used Lindblad equation, its unraveling in terms…
Investigating the dynamics of learning in machine learning algorithms is of paramount importance for understanding how and why an approach may be successful. The tools of physics and statistics provide a robust setting for such…
An expression of the Lindbladian form is proposed that ensures an unambiguous time-continuous reduction of the initial system-pointer wave-packet to one in which the readings and the observable's values are aligned, formalized as the…
Dynamics of spontaneous symmetry breaking and fluctuations in the Lipkin-Meshkov-Glick model are investigated in a stochastic mean-field approach. Different from the standard mean-field, in the stochastic approach, initial state…
In open quantum systems, a basic question at the interface of quantum information, statistical physics, and many-body dynamics is how well can one infer the structure of noise and dissipation generators from finite-time measurement…
Here we demonstrate that tensor network techniques - originally devised for the analysis of quantum many-body problems - are well suited for the detailed study of rare event statistics in kinetically constrained models (KCMs). As concrete…
A quantum master equation of the Lindblad form is obtained in this paper by considering the spontaneous wave-packet reduction. Different classical equations can be derived after exactly mapping such a quantum master equation to a continuous…
We propose a microscopic stochastic approach to improve description of nuclear dynamics beyond the mean-field approximation at low energies. It is shown that, for small amplitude fluctuations, the proposed model gives a result for the…
A new energy-based stochastic extension of the Schrodinger equation for which the wave function collapses after the passage of a finite amount of time is proposed. An exact closed-form solution to the dynamical equation, valid for all…