We establish quantitative bounds on the rate of approach to equilibrium for a system with infinitely many degrees of freedom evolving according to a one-dimensional focusing nonlinear Schrodinger equation with diffusive forcing. Equilibrium is described by a generalized grand canonical ensemble. Our analysis also applies to the easier case of defocusing nonlinearities
Quantum trajectories are Markov processes that describe the time-evolution of a quantum system undergoing continuous indirect measurement. Mathematically, they are defined as solutions of the so-called Stochastic Schrodinger Equations, which are nonl
inear stochastic differential equations driven by Poisson and Wiener processes. This paper is devoted to the study of the invariant measures of quantum trajectories. Particularly, we prove that the invariant measure is unique under an ergodicity condition on the mean time evolution, and a purification condition on the generator of the evolution. We further show that quantum trajectories converge in law exponentially fast towards this invariant measure. We illustrate our results with examples where we can derive explicit expressions for the invariant measure.
Standard derivations of the functional integral in non-equilibrium quantum field theory are based on the discrete time representation. In this work we derive the non-equilibrium functional integral for non-interacting bosons and fermions using a cont
inuum time approach by accounting for the statistical distribution through the boundary conditions and using them to evaluate the Greens function.
In this paper, we obtain upper and lower bounds for the moments of the solution to a class of fractional stochastic heat equations on the ball driven by a Gaussian noise which is white in time, and with a spatial correlation in space of Riesz kernel
type. We also consider the space-time white noise case on an interval.
This paper is devoted to prove the existence and nonexistence of positive solutions for a class of fractional Schrodinger equation in RN of the We apply a new methods to obtain the existence of positive solutions when f(u) is asymptotically linear with respect to u at infinity.
We construct quantum circuits for solving one-dimensional Schrodinger equations. Simulations of three typical examples, i.e., harmonic oscillator, square-well and Coulomb potential, show that reasonable results can be obtained with eight qubits. Our
simulations show that simple quantum circuits can solve the standard quantum mechanical problems.
Eric A. Carlen
,Jurg Frohlich
,Joel Lebowitz
.
(2017)
.
"Quantitative Bounds on the Rate of Approach to Equilibrium for some One-Dimensional Stochastic Non-Linear Schrodinger Equations"
.
Eric Carlen
هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا