The strong Markov property for fermion Brownian motion

Alice Rogers

Andrea Rocco, Paolo Grigolini

Marek Bożejko, Roland Speicher

Eduardo Souza Fraga, Gastão I. Krein, L. F. Palhares

Aniello Lampo, Soon Hoe Lim, Jan Wehr +2 more

The theory of quantum Brownian motion describes the properties of a large class of open quantum systems. Nonetheless, its description in terms of a Born-Markov master equation, widely used in the literature, is known to violate the positivity of the density operator at very low temperatures. We study an extension of existing models, leading to an equation in the Lindblad form, which is free of this problem. We study the dynamics of the model, including the detailed properties of its stationary solution, for both constant and position-dependent coupling of the Brownian particle to the bath, focusing in particular on the correlations and the squeezing of the probability distribution induced by the environment.

Rocco, A, Grigolini, P

We revisit the Markov approximation necessary to derive ordinary Brownian motion from a model widely adopted in literature for this specific purpose. We show that this leads to internal inconsistencies, thereby implying that further search for a more satisfactory model is required.