Related papers: Martingale Models for Quantum State Reduction
Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain…
Stochastic unravelings represent a useful tool to describe the dynamics of open quantum systems and standard methods, such as quantum state diffusion (QSD), call for the complete positivity of the open-system dynamics. Here, we present a…
A procedure for model reduction of stochastic ordinary differential equations with additive noise was recently introduced in [Colangeli-Duong-Muntean, Journal of Physics A: Mathematical and Theoretical, 2022], based on the Invariant…
Stochastic mechanics is based on the hypothesis that all matter is subject to universal modified Brownian motion. In this report, we calculated probability density distributions using concepts of stochastic mechanics independent of…
The energy-based stochastic extension of the Schrodinger equation is a rather special nonlinear stochastic differential equation on Hilbert space, involving a single free parameter, that has been shown to be very useful for modelling the…
Previous years researchers began to simulate open quantum system, taking into account the interaction between system and the environment. One approach to deal with this problem is to use the density matrix within the Liouville-von-Neumann…
A theoretical description of quantum mechanical steady states is developed. Applications for simple quantum mechanical systems described in terms of coupled level structures yield a formulation equivalent to time independent scattering…
We explore whether quantum field theory can be understood as the statistical mechanics of a time-reversal-invariant stochastic generalization of Hamiltonian dynamics. The motivation for this project, started with this paper, is to assign…
A quantum system S undergoing continuous time measurement is usually described by a jump-diffusion stochastic differential equation. Such an equation is called a stochastic master equation and its solution is called a quantum trajectory.…
Concerning Numerical Stochastic Perturbation Theory, we discuss the convergence of the stochastic process (idea of the proof, features of the limit distribution, rate of convergence to equilibrium). Then we also discuss the expected…
In mathematical psychology, decision makers are modeled using the Lindbladian equations from quantum mechanics to capture important human-centric features such as order effects and violation of the sure thing principle. We consider…
Stochastic finite-state generators are compressed descriptions of infinite time series. Alternatively, compressed descriptions are given by quantum finite- state generators [K. Wiesner and J. P. Crutchfield, Physica D 237, 1173 (2008)].…
The development of methods of quantum statistical mechanics is considered in light of their applications to quantum solid-state theory. We discuss fundamental problems of the physics of magnetic materials and the methods of the quantum…
This paper gives a review of our recent work on the quantum Frenkel-Kontorova model. Using the squeezed state theory and the quantum Monte Carlo method, we have studied the effects of quantum fluctuations on the Aubry transition and the…
Capturing the correlation emerging between constituents of many-body systems accurately is one of the key challenges for the appropriate description of various systems whose properties are underpinned by quantum mechanical fundamentals.…
Models for deterministic quantum mechanics of Cartan-Randers type are introduced, together with the fundamental notions of the concentration of measure theory. We explain how the application of the concentration of measure to Cartan-Randers…
Statistical fluctuation problems are faced by all quantum key distribution (QKD) protocols under finite-key condition. Most of the current statistical fluctuation analysis methods work based on independent random samples, however, the…
A fundamental prediction of quantum theory that is derived from the "projection postulate" is that under continuous measurement, the state of a system traces out a "quantum trajectory" in time that depends upon its measurement record, and…
We present a general condition to obtain subspaces that decay uniformly in a system governed by the Lindblad master equation and use them to perform error mitigated quantum computation. The expectation values of dynamics encoded in such…
With the decline of the Copenhagen interpretation of quantum mechanics and the recent experiments indicating that quantum mechanics does actually embody 'objective reality', one might ask if a 'mechanical', conceptual model for quantum…