Search results for "Markovian process"
showing 4 items of 4 documents
Geometric phase induced by a cyclically evolving squeezed vacuum reservoir
2006
We propose a new way to generate an observable geometric phase by means of a completely incoherent phenomenon. We show how to imprint a geometric phase to a system by "adiabatically" manipulating the environment with which it interacts. As a specific scheme we analyse a multilevel atom interacting with a broad-band squeezed vacuum bosonic bath. As the squeezing parameters are smoothly changed in time along a closed loop, the ground state of the system acquires a geometric phase. We propose also a scheme to measure such geometric phase by means of a suitable polarization detection.
First hitting time for a diffusion
2021
In this thesis, we focus our attention on the generation of the first exit time or the first passage time for diffusions in a one-dimensional context.In the first chapter, we present already well-known methods in order to generate such random variables. We particularly introduce the WOMS algorithm. This algorithm permits the generation of an approximation of the time needed by the Brownian motion in order to exit from a given interval.In the second and third chapters, we explain how to extend the previous algorithm in order to deal with diffusions strongly linked to the one-dimensional Brownian motion. We first consider the Ornstein-Uhlenbeck process, and then we consider a wide class of di…
Role of conditional probability in multiscale stationary markovian processes.
2010
The aim of the paper is to understand how the inclusion of more and more time-scales into a stochastic stationary Markovian process affects its conditional probability. To this end, we consider two Gaussian processes: (i) a short-range correlated process with an infinite set of time-scales bounded from below, and (ii) a power-law correlated process with an infinite and unbounded set of time-scales. For these processes we investigate the equal position conditional probability P(x,t|x,0) and the mean First Passage Time T(L). The function P(x,t|x,0) can be considered as a proxy of the persistence, i.e. the fact that when a process reaches a position x then it spends some time around that posit…
Observable geometric phase induced by a cyclically evolving dissipative process
2006
In a prevous paper (Phys. Rev. Lett. 96, 150403 (2006)) we have proposed a new way to generate an observable geometric phase on a quantum system by means of a completely incoherent phenomenon. The basic idea was to force the ground state of the system to evolve ciclically by "adiabatically" manipulating the environment with which it interacts. The specific scheme we have previously analyzed, consisting of a multilevel atom interacting with a broad-band squeezed vacuum bosonic bath whose squeezing parameters are smoothly changed in time along a closed loop, is here solved in a more direct way. This new solution emphasizes how the geometric phase on the ground state of the system is indeed du…