Adiabatic Brownian motor with a stepwise potential perturbed by a dichotomous harmonic sygnal

Spectral asymptotics of harmonic oscillator perturbed by bounded potential

Consider the operator T = − d dx2 + x2 + q(x) in L2(R), where real functions q, q′ and ∫ x 0 q(s) ds are bounded. In particular, q is periodic or almost periodic. The spectrum of T is purely discrete and consists of the simple eigenvalues {μn}n=0, μn < μn+1. We determine their asymptotics μn = (2n+1)+(2π) −1 ∫ π −π q( √ 2n + 1 sin θ) dθ+O(n−1/3).

Adiabatic processes realized with a trapped Brownian particle.

The ability to implement adiabatic processes in the mesoscale is of key importance in the study of artificial or biological micro- and nanoengines. Microadiabatic processes have been elusive to experimental implementation due to the difficulty in isolating Brownian particles from their fluctuating environment. Here we report on the experimental realization of a microscopic quasistatic adiabatic...

Perturbed and Non-perturbed Brownian Taboo Processes

– In this paper we study the Brownian taboo process, which is a version of Brownian motion conditioned to stay within a finite interval, and the α-perturbed Brownian taboo process, which is an analogous version of an α-perturbed Brownian motion.We are particularly interested in the asymptotic behaviour of the supremum of the taboo process, and our main results give integral tests for upper and ...

Perturbed Brownian Motions

An Adiabatic Theorem for Singularly Perturbed Hamiltonians

The adiabatic approximation in quantum mechanics is considered in the case where the self-adjoint hamiltonian H0(t), satisfying the usual spectral gap assumption in this context, is perturbed by a term of the form εH1(t). Here ε → 0 is the adiabaticity parameter and H1(t) is a self-adjoint operator defined on a smaller domain than the domain of H0(t). Thus the total hamiltonian H0(t) + εH1(t) d...