Sub-exponential spin-boson decoherence in a finite bath

Finite kicked environments and the fluctuation-dissipation relation

In this work we derive a generalized map for a system coupled to a kicked environment composed of a finite number N of uncoupled harmonic oscillators. Dissipation is introduced via the interaction between system and environment which is switched on and off simultaneously (kicks) at regular time intervals. It is shown that kicked environments naturally generate a non-Markovian rotated dynamics, describe more complicated system-environment couplings which involve position and momentum, and satisfy an unusual fluctuation-dissipation relation. As an example, the motion of a kicked Brownian particle is discussed.

Dissipation and transport dynamics in a ratchet coupled to a discrete bath

We investigate a particle in a ratchet potential (the system) coupled to an harmonic bath of N=1-500 degrees of freedom (the discrete bath). The dynamics of the energy exchange between the system and the discrete bath is studied in the transition regime from low to high values of N . First manifestation of dissipation (energy lost by the system) appears for the bath composed of 10 less, similar N less, similar 20 oscillators, as expected. For low values of N , beside small dissipation effects, the system experiences the bath-induced particle transfer between different potential wells from the ratchet. We show that this effect decreases the mobility of particles along the ratchet. The hopping probability along the ratchet and the energy decay rates for the system are shown to obey the power law for late times, a behavior typical of discrete baths which for low and intermediate values of N always induce a non-Markovian process. The exponential decay is recovered for high bath frequencies distribution and for high values of N , where the Markovian limit is expected. Moreover, by including the external oscillating field with intensity F , we show that current reversal occurs in two situations: By increasing N and by switching from low to high frequencies distribution of the bath. The mobility of particles is shown to have a maximum at F=0.1 , which is N independent (for higher values of N ).

Non-Markovian Lévy diffusion in nonhomogeneous media

We study the diffusion equation with a position-dependent, power-law diffusion coefficient. The equation possesses the Riesz-Weyl fractional operator and includes a memory kernel. It is solved in the diffusion limit of small wave numbers. Two kernels are considered in detail: the exponential kernel, for which the problem resolves itself to the telegrapher's equation, and the power-law one. The resulting distributions have the form of the Lévy process for any kernel. The renormalized fractional moment is introduced to compare different cases with respect to the diffusion properties of the system.

Random Lindblad equations from complex environments

In this paper we demonstrate that Lindblad equations characterized by a random rate variable arise after tracing out a complex structured reservoir. Our results follows from a generalization of the Born-Markov approximation, which relies on the possibility of splitting the complex environment into a direct sum of subreservoirs, each one being able to induce by itself a Markovian system evolution. Strong non-Markovian effects, which microscopically originate from the entanglement with the different subreservoirs, characterize the average system decay dynamics. As an example, we study the anomalous irreversible behavior of a quantum tunneling system described in an effective two-level approximation. Stretched exponential and power law decay behaviors arise from the interplay between the dissipative and unitary hopping dynamics.