Related papers: Periodicity in Ergodic Quantum Processes
This paper is concerned with an extended Galton-Watson process so as to allow individuals to live and reproduce for more than one unit time. We assume that each individual can live $k$ seasons (time-units) with probability $h_k$, and…
The origin of the nonlocal nature of quantum mechanics is investigated in the context of Everett's formulation of quantum mechanics. EPR phenomenon can fully be explained without introducing any kind of decoherence.
We consider a time inhomogeneous strong Markov process $(\xi_t)_{t\ge 0}$ taking values in a Polish state space whose semigroup has a $T$-periodic structure. We give simple conditions which imply ergodicity of the grid chain…
I develop a theory of classicality from quantum systems. This theory stems from the study of classical and quantum stationary stochastic processes. The stochastic processes are characterized by polyhedral (classical) and semidefinite…
Several stochastic processes with virtual particles in two dimensional space-time are presented whose mean field equations coincide with Schr\"odinger, Dirac, Klein-Gordon and the quantum mechanic equation for a photon. These processes…
We present exact, explicit, convergent periodic-orbit expansions for individual energy levels of regular quantum graphs. One simple application is the energy levels of a particle in a piecewise constant potential. Since the classical ray…
We investigate the asymptotic stability and ergodic properties of quantum trajectories under imperfect measurement, extending previous results established for the ideal case of perfect measurement. We establish a necessary and sufficient…
We define a natural ensemble of trace preserving, completely positive quantum maps and present algorithms to generate them at random. Spectral properties of the superoperator Phi associated with a given quantum map are investigated and a…
We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs the novel concept of harmonic time average [2], and is…
A process-theoretic approach to electrodynamics based on persistent Kac-type stochastic processes is developed. Finite-velocity stochastic propagation is taken as primary, while relativistic wave equations arise as emergent descriptions…
[This is the unpublished supplemental information from 1989 to the paper: J.M. Deutsch, "Quantum statistical mechanics in a closed system." Phys. Rev. A, 43(4), 2046 (1991).] A closed quantum mechanical system does not necessarily give time…
A piecewise-deterministic Markov process, specified by random jumps and switching semi-flows, as well as the associated Markov chain given by its post-jump locations, are investigated in this paper. The existence of an exponentially…
Canonical characterization techniques that rely upon mean squared displacement ($\mathrm{MSD}$) break down for non-ergodic processes, making it challenging to characterize anomalous diffusion from an individual time-series measurement.…
This work develops asymptotic properties of a class of switching jump diffusion processes. The processes under consideration may be viewed as a number of jump diffusion processes modulated by a random switching mechanism. The underlying…
The present paper is devoted to the study of resonances for one-dimensional quantum systems with a potential that is the restriction to some large box of an ergodic potential. For discrete models both on a half-line and on the whole line,…
It is shown that all of the basic properties of the hydrogen atom can be consistently described in terms of classical electrodynamics instead of taking the electron to be a particle; we consider an electrically charged classical wave field,…
In this work we explore how the heat kernel, which gives the solution to the diffusion equation and the Brownian motion, would change when we introduce quasiperiodicity in the scenario. We also study the random walk in the Fibonacci…
Phase transitions with spontaneous symmetry breaking are expected for group field theories as a basic feature of the geometogenesis scenario. The following paper aims to investigate the equilibrium phase for group field theory by using the…
We consider the almost sure asymptotic behavior of the periodogram of stationary and ergodic sequences. Under mild conditions we establish that the limsup of the periodogram properly normalized identifies almost surely the spectral density…
Single particle tracking has become a standard tool to investigate diffusive properties, especially in small systems such as biological cells. Usually the resulting time series are analyzed in terms of time averages over individual…