相关论文: Martingale Models for Quantum State Reduction
A non-ergodic quantum state of a many body system is in general random as well as multi-parametric, former due to a lack of exact information due to complexity and latter reflecting its varied behavior in different parts of the Hilbert…
We consider the time evolution of quantum states by many-body Schr\"odinger dynamics and study the rate of convergence of their reduced density matrices in the mean field limit. If the prepared state at initial time is of coherent or…
We derive the fluctuation theorem for quantum-state statistics that can be obtained when we initially measure the total energy of a quantum system at thermal equilibrium, let the system evolve unitarily, and record the quantum-state data…
Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a new…
The quasi-steady-state approximation (or stochastic averaging principle) is a useful tool in the study of multiscale stochastic systems, giving a practical method by which to reduce the number of degrees of freedom in a model. The method is…
In this paper we demonstrate that Lindblad equations characterized by a random rate variable arise after tracing out a complex structured reservoir. Our results follows from a generalization of the Born-Markov approximation, which relies in…
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…
We develop a dynamical framework for quantum measurement based on stochastic but unitary evolution in projective state space. Random Hamiltonians drawn from the Gaussian Unitary Ensemble generate stochastic unitary dynamics of the quantum…
We study the time evolution of quantum entanglement for a specific class of quantum dynamics, namely the locally scrambled quantum dynamics, where each step of the unitary evolution is drawn from a random ensemble that is invariant under…
Exotic stochastic processes are shown to emerge in the quantum evolution of complex systems. Using influence function techniques, we consider the dynamics of a system coupled to a chaotic subsystem described through random matrix theory. We…
It is known that state-dependent, multi-step Lyapunov bounds lead to greatly simplified verification theorems for stability for large classes of Markov chain models. This is one component of the "fluid model" approach to stability of…
In this paper, we establish a general theoretical framework for the description of continuous quantum measurements and the statistics of the results of such measurements. The framework concerns the measurement of an arbitrary quantum system…
We present a general theory of stochastic model reduction which is based on a normal form coordinate transform method of A.J. Roberts. This nonlinear, stochastic projection allows for the deterministic and stochastic dynamics to interact…
A phenomenological model for the calculation of reduction probabilities of a superposition of several states is presented. The approach bases only the idea that quantum state reduction has its origin in a mutual physical interaction between…
It is assumed that the quantum state that may describe a macroscopic system at a given instant of time is one of the eigenstates of the reduced density matrix calculated from the wave function of the system plus its environment. This…
We derive the classical Hamilton-Jacobi equation from first principles as the natural description for smooth stochastic processes when one neglects stochastic velocity fluctuations. The Schr\"{o}dinger equation is shown to be the natural…
The representation of a quantum wave function as a neural network quantum state (NQS) provides a powerful variational ansatz for finding the ground states of many-body quantum systems. Nevertheless, due to the complex variational landscape,…
The manifestation of measurements, randomly distributed in time, on the evolution of quantum systems are analyzed in detail. The set of randomly distributed measurements (RDM) is modeled within the renewal theory, in which the distribution…
We develop a systematic framework for the model reduction of multivariate geometric Brownian motions (GBMs), a fundamental class of stochastic processes with broad applications in mathematical finance, population biology, and statistical…
Quantum systems subjected to a continuous weak measurement process evolve according to stochastic differential equations (SDE). Depending on the outcomes of these stochastic measurements, the quantum state may diffuse in various directions…