Manuel O. Cáceres

Functional characterization of generalized Langevin equations

We present an exact functional formalism to deal with linear Langevin equations with arbitrary memory kernels and driven by an arbitrary noise structure characterized through its characteristic functional. No other hypothesis is assumed over the noise, neither do we use the fluctuation–dissipation theorem. We find that the characteristic functional of the linear process can be expressed in terms of noise functional and the Green function of the deterministic (memory-like) dissipative dynamics. This yields a procedure for calculating the full Kolmogorov hierarchy of the non-Markov process. As examples, we have characterized through the 1-time probability a noise-induced interplay between the dissipative dynamics and the structure of different noises. Conditions that lead to non-Gaussian statistics and distributions with long tails are analysed. The introduction of arbitrary fluctuations in fractional Langevin equations has also been pointed out.

Non-equilibrium transition from dissipative quantum walk to classical random walk

We have investigated the time evolution of a free particle in interaction with a phonon thermal bath, using the tight-binding approach. A dissipative quantum walk can be defined and many important non-equilibrium decoherence properties can be investigated analytically. The non-equilibrium statistics of a pure initial state have been studied. Our theoretical results indicate that the evolving wave-packet shows the suppression of Anderson’s boundaries (ballistic peaks) by the presence of dissipation. Many important relaxation properties can be studied quantitatively, such as von Neumann’s entropy and quantum purity. In addition, we have studied Wigner’s function. The time-dependent behavior of the quantum entanglement between a free particle—in the lattice—and the phonon bath has been characterized analytically. This result strongly suggests the non-trivial time dependence of the off-diagonal elements of the reduced density matrix of the system. We have established a connection between the quantum decoherence and the dissipative parameter arising from interaction with the phonon bath. The time-dependent behavior of quantum correlations has also been pointed out, showing continuous transition from quantum random walk to classical random walk, when dissipation increases.

Bath-induced correlations in an infinite-dimensional Hilbert space

AbstractnQuantum correlations between two free spinless dissipative distinguishable particles (interacting with a thermal bath) are studied analytically using the quantum master equation and tools of quantum information. Bath-induced coherence and correlations in an infinite-dimensional Hilbert space are shown. We show that for temperature T> 0 the time-evolution of the reduced density matrix cannot be written as the direct product of two independent particles. We have found a time-scale that characterizes the time when the bath-induced coherence is maximum before being wiped out by dissipation (purity, relative entropy, spatial dispersion, and mirror correlations are studied). The Wigner function associated to thexa0Wannier lattice (where the dissipative quantum walks move) is studied as an indirect measure of the induced correlations among particles. We have supported the quantum character of the correlations by analyzing the geometric quantum discord.n

First passage time on pattern formation in a non-local Fisher population dynamics

We use stochastic dynamics to develop the patterned attractor of a non-local extended system. This is done analytically using the stochastic path perturbation approach scheme, where a theory of perturbation in the small noise parameter is introduced to analyze the random escape of the stochastic field from the unstable state. Emphasis is placed on the specific mode selection that these types of systems exhibit. Concerning the stochastic propagation of the front we have carried out Monte Carlo simulations which coincide with our theoretical predictions.