Fluctuating observation time ensembles in the thermodynamics of trajectories

The dynamics of stochastic systems, both classical and quantum, can be studied by analysing the statistical properties of dynamical trajectories. The properties of ensembles of such trajectories for long, but fixed, times are described by large-deviation (LD) rate functions. These LD functions play the role of dynamical free-energies: they are cumulant generating functions for time-integrated observables, and their analytic structure encodes dynamical phase behaviour. This "thermodynamics of trajectories" approach is to trajectories and dynamics what the equilibrium ensemble method of statistical mechanics is to configurations and statics. Here we show that, just like in the static case, there is a variety of alternative ensembles of trajectories, each defined by their global constraints, with that of trajectories of fixed total time being just one of these. We show that an ensemble of trajectories where some time-extensive quantity is constant (and large) but where total observation time fluctuates, is equivalent to the fixed-time ensemble, and the LD functions that describe one ensemble can be obtained from those that describe the other. We discuss how the equivalence between generalised ensembles can be exploited in path sampling schemes for generating rare dynamical trajectories.Comment: 12 pages, 5 figure

Non-Markovian non-stationary completely positive open quantum system dynamics

By modeling the interaction of a system with an environment through a renewal approach, we demonstrate that completely positive non-Markovian dynamics may develop some unexplored non-standard statistical properties. The renewal approach is defined by a set of disruptive events, consisting in the action of a completely positive superoperator over the system density matrix. The random time intervals between events are described by an arbitrary waiting-time distribution. We show that, in contrast to the Markovian case, if one performs a system-preparation (measurement) at an arbitrary time, the subsequent evolution of the density matrix evolution is modified. The non-stationary character refers to the absence of an asymptotic master equation even when the preparation is performed at arbitrary long times. In spite of this property, we demonstrate that operator expectation values and operators correlations have the same dynamical structure, establishing the validity of a non-stationary quantum regression hypothesis. The non-stationary property of the dynamic is also analyzed through the response of the system to an external weak perturbation.Comment: 13 pages, 3 figure

Lindblad rate equations

In this paper we derive an extra class of non-Markovian master equations where the system state is written as a sum of auxiliary matrixes whose evolution involve Lindblad contributions with local coupling between all of them, resembling the structure of a classical rate equation. The system dynamics may develops strong non-local effects such as the dependence of the stationary properties with the system initialization. These equations are derived from alternative microscopic interactions, such as complex environments described in a generalized Born-Markov approximation and tripartite system-environment interactions, where extra unobserved degrees of freedom mediates the entanglement between the system and a Markovian reservoir. Conditions that guarantees the completely positive condition of the solution map are found. Quantum stochastic processes that recover the system dynamics in average are formulated. We exemplify our results by analyzing the dynamical action of non-trivial structured dephasing and depolarizing reservoirs over a single qubit.Comment: 12 pages, 2 figure

Quantum regression theorem for non-Markovian Lindblad equations

We find the conditions under which a quantum regression theorem can be assumed valid for non-Markovian master equations consisting in Lindblad superoperators with memory kernels. Our considerations are based on a generalized Born-Markov approximation, which allows us to obtain our results from an underlying Hamiltonian description. We demonstrate that a non-Markovian quantum regression theorem can only be granted in a stationary regime if the dynamics satisfies a quantum detailed balance condition. As an example we study the correlations of a two level system embedded in a complex structured reservoir and driven by an external coherent field.Comment: 14 pages, 5 figures. Extended version. The GBMA is deduced from projector technique. A new appendix is adde

Aggregate formation prevents dTDP-43 neurotoxicity in the Drosophila melanogaster eye

TDP-43 inclusions are an important histopathological feature in various neurodegenerative disorders, including Amyotrophic Lateral Sclerosis and Fronto-Temporal Lobar Degeneration. However, the relation of these inclusions with the pathogenesis of the disease is still unclear. In fact, the inclusions could be toxic themselves, induce loss of function by sequestering TDP-43 or a combination of both. Previously, we have developed a cellular model of aggregation using the TDP-43 Q/N rich amino acid sequence 331-369 repeated 12 times (12xQ/N) and have shown that these cellular inclusions are capable of sequestering the endogenous TDP-43 both in non-neuronal and neuronal cells. We have tested this model in vivo in the Drosophila melanogaster eye. The eye structure develops normally in the absence of dTDP-43, a fact previously seen in knock out fly strains. We show here that expression of EGFP 12xQ/N does not alter the structure of the eye. In contrast, TBPH overexpression is neurotoxic and causes necrosis and loss of function of the eye. More important, the neurotoxicity of TBPH can be abolished by its incorporation to the insoluble aggregates induced by EGFP 12xQ/N. This data indicates that aggregation is not toxic per se and instead has a protective role, modulating the functional TBPH available in the tissue. This is an important indication for the possible pathological mechanism in action on ALS patients. © 2014

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 any noise structure characterized through its characteristic functional. No others hypothesis are assumed over the noise, neither the fluctuation dissipation theorem. We found that the characteristic functional of the linear process can be expressed in terms of noise's functional and the Green function of the deterministic (memory-like) dissipative dynamics. This object allow us to get a procedure to calculate all the 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 analyzed. The introduction of arbitrary fluctuations in fractional Langevin equations have also been pointed out

Analysis of strawberry ripening by dynamic speckle measurements

This work seeks to determine the age of a fruit from observation of its dynamic speckle pattern. A mobile speckle pattern originates on the fruit's surface due to the interference of the wavefronts reflected from moving scatterers. For this work we analyzed two series of photographs of a strawberry speckle pattern, at different stages of ripening, acquired with a CMOS camera. The first day, we took ten photographs at an interval of one second. The same procedure was repeated the next day. From each series of images we extracted several statistical descriptors of pixel-to-pixel gray level variation during the observation time. By comparing these values from the first to the second day we noticed a diminution of the speckle activity. This decay demonstrated that after only one day the ripening process of the strawberry can be detected by dynamic speckle pattern analysis. For this study we employed a simple new algorithm to process the data obtained from the photographs. This algorithm allows defining a global mobility index that indicates the evolution of the fruit's ripening.Fil: Mulone, C.. Universidad Tecnológica Nacional. Facultad Regional Paraná; ArgentinaFil: Budini, Nicolas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico - CONICET- Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química (i); Argentina. Universidad Tecnológica Nacional. Facultad Regional Paraná; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico - CONICET - Santa Fe. Instituto de Física del Litoral; ArgentinaFil: Vincitorio, F. M.. Universidad Tecnológica Nacional. Facultad Regional Paraná; ArgentinaFil: Freyre, C.. Universidad Tecnológica Nacional. Facultad Regional Paraná; ArgentinaFil: López Díaz, A. J.. Universidad da Coruña; España;Fil: Ramil Rego, A.. Universidad da Coruña; España

Entropy, non-ergodicity and non-Gaussian behaviour in ballistic transport

Ballistic transportation introduces new challenges in the thermodynamic properties of a gas of particles. For example, violation of mixing, ergodicity and of the fluctuation-dissipation theorem may occur, since all these processes are connected. In this work, we obtain results for all ranges of diffusion, i.e., both for subdiffusion and superdiffusion, where the bath is such that it gives origin to a colored noise. In this way we obtain the skewness and the non-Gaussian factor for the probability distribution function of the dynamical variable. We put particular emphasis on ballistic diffusion, and we demonstrate that in this case, although the second law of thermodynamics is preserved, the entropy does not reach a maximum and a non-Gaussian behavior occurs. This implies the non-applicability of the central limit theorem.Comment: 9 pages, 2 figure

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.Comment: Submitted for publication. 17 pages, 6 figure

The Effect of Stochastic Noise on Quantum State Transfer

We consider the effect of classical stochastic noise on control laser pulses used in a scheme for transferring quantum information between atoms, or quantum dots, in separate optical cavities via an optical connection between cavities. We develop a master equation for the dynamics of the system subject to stochastic errors in the laser pulses, and use this to evaluate the sensitivity of the transfer process to stochastic pulse shape errors for a number of different pulse shapes. We show that under certain conditions, the sensitivity of the transfer to the noise depends on the pulse shape, and develop a method for determining a pulse shape that is minimally sensitive to specific errors.Comment: 10 pages, 9 figures, to appear in Physical Review