NonMarkovian dynamics for a free quantum particle subject to spontaneous collapse in space: General solution and main properties
Abstract
We analyze the nonMarkovian dynamics of a quantum system subject to spontaneous collapse in space. After having proved, under suitable conditions, the separation of the centerofmass and relative motions, we focus our analysis on the time evolution of the center of mass of an isolated system (freeparticle case). We compute the explicit expression of the Green’s function, for a generic Gaussian noise, and analyze in detail the case of an exponential correlation function. We study the time evolution of average quantities, such as the mean position, momentum, and energy. We eventually specialize to the case of Gaussian wave functions and prove that all basic facts about collapse models, which are known to be true in the whitenoise case, hold also in the more general case of nonMarkovian dynamics.
 Publication:

Physical Review A
 Pub Date:
 July 2009
 DOI:
 10.1103/PhysRevA.80.012116
 Bibcode:
 2009PhRvA..80a2116B
 Keywords:

 03.65.Ta;
 02.50.Ey;
 05.40.a;
 Foundations of quantum mechanics;
 measurement theory;
 Stochastic processes;
 Fluctuation phenomena random processes noise and Brownian motion