arXiv subjects
Publications and source records attributed to Jerzy Luczka.
The role of initial qubit-environment correlations on trace distance between two qubit states is studied in the framework of non--Markovian pure dephasing. The growth of mixedness of reduced state quantified by linear entropy is shown to be related to the degree of initial qubit--environment correlations.
Properties of transport of molecular motors are investigated. A simplified model based on the concept of Brownian ratchets is applied. We analyze a stochastic equation of motion by means of numerical methods. The transport is systematically studied with respect to its energetic efficiency and quality expressed by an effective diffusion coefficient. We demonstrate the role of friction and non-equilibrium driving on the transport quantifiers and identify regions of a parameter space where motors are optimally transported.
We study transport properties of an inertial Brownian particle moving in viscous symmetric periodic structures and driven by an oscillating signal of two harmonic components. We analyze the influence of symmetric, antisymmetric and asymmetric signals on directed transport and reveal the shift symmetry of the stationary averaged velocity of the Brownian particle with respect to the relative phase of two components of the signal. The shift symmetry holds true in all regimes.
We propose four different mechanisms responsible for paramagnetic or diamagnetic persistent currents in normal metal rings and determine the circumstances for change of the current from paramagnetic to diamagnetic ones and {\it vice versa}. It might qualitatively reproduce the experimental results of Bluhm et al. (Phys. Rev. Lett. 102, 136802 (2009)).
We study an inertial Brownian particle moving in a symmetric periodic substrate, driven by a zero-mean biharmonic force and correlated thermal noise. The Brownian motion is described in terms of a Generalized Langevin Equation with an exponentially correlated Gaussian noise term, obeying the fluctuation-dissipation theorem. We analyse impact of non-zero correlation time of thermal noise on transport properties of the Brownian particle. We identify regimes where the increase of the correlation time intensifies long-time transport of the Brownian particle. The opposite effect is also found: longer correlation time reduces the stationary velocity of the particle. The correlation time induced multiple current reversal is detected. We reveal that thermal noise of non-zero correlation time can radically enhance long-time velocity of the Brownian particle in regimes where in the white noise limit the velocity is extremely small. All transport properties can be tested in the setup consisting of a resistively and capacitively shunted Josephson junction device.
In normal mesoscopic metals of a ring topology persistent currents can be induced by threading the center of the ring with a magnetic flux. This phenomenon is an example of the famous Aharonov-Bohm effect. In the paper we study the current {\it vs} the external constant magnetic flux characteristics of the system driven by both the classical and the quantum thermal fluctuations. The problem is formulated in terms of Langevin equations in classical and quantum Smoluchowski regimes. We analyze the impact of the quantum thermal fluctuations on the current-flux characteristics. We demonstrate that the current response can be changed from paramagnetic to diamagnetic when the quantum nature of the thermal fluctuations increases.
We investigate an optimal regime of negative-valued conductance, emerging in a resistively and capacitively shunted Josephson junction, which is driven simultaneously by both, a time-periodic (ac) and a constant (dc) current. We analyze the current-voltage characteristics in the regime of absolute negative conductance. We additionally explore the stability of the negative response with respect to the ac-current frequency.
We extend the projective covariant bookmaker's bets model to the forecasting gamblers case. The probability of correctness of forecasts shifts probabilities of branching. The formula for the shift of probabilities leads to the velocity addition rule of the special theory of relativity. In the absence of information about bookmaker's wagers the stochastic logarithmic rates completely determines the optimal stakes of forecast gambler.
Kinetics of magnetic flux in a thin mesoscopic ring biased by a strong external magnetic field is described equivalently by dynamics of a Brownian particle in a tilted washboard potential. The 'flux velocity', i.e. the averaged time derivative of the total magnetic flux in the ring, is a candidate for a novel characteristics of mesoscopic rings. Its global properties reflect the possibility of accommodating persistent currents in the ring.
The directed transport of an overdamped Brownian motor moving in a spatially periodic potential that lacks reflection symmetry (i.e. a ratchet potential) is studied when driven by thermal and dichotomic nonequilibrium noise in the presence of an external, constant load force. We consider both, the classical and the quantum tunneling assisted regimes. The current-load characteristics are investigated as a function of the system parameters like the load force, the temperature and the amplitude strength of the applied two-state noise.
In order to optimize the directed motion of an inertial Brownian motor, we identify the operating conditions that both maximize the motor current and minimize its dispersion. Extensive numerical simulation of an inertial rocked ratchet displays that two quantifiers, namely the energetic efficiency and the Péclet number (or equivalently the Fano factor), suffice to determine the regimes of optimal transport. The effective diffusion of this rocked inertial Brownian motor can be expressed as a generalized fluctuation theorem of the Green -- Kubo type. Addendum and Erratum The expression for the effective diffusion of an inertial, periodically driven Brownian particle in an asymmetric, periodic potential is compared with the step number diffusion which is extracted from the corresponding coarse grained hopping process specifying the number of covered spatial periods within each temporal period. The two expressions are typically different and involve the correlations between the number of hops.
The statistics of transitions between the metastable states of a periodically driven bistable Brownian oscillator are investigated on the basis of a two-state description by means of a master equation with time-dependent rates. The results are compared with extensive numerical simulations of the Langevin equation for a sinusoidal driving force. Very good agreement is achieved both for the counting statistics of the number of transitions and the residence time distribution of the process in either state. The counting statistics corroborate in a consistent way the interpretation of stochastic resonance as a synchronisation phenomenon for a properly defined generalized Rice phase.
The reduction of a continuous Markov process with multiple metastable states to a discrete rate process is investigated in the presence of slow time dependent parameters such as periodic external forces or slowly fluctuating barrier heights. A quantitative criterion is provided under which condition a kinetic description with time dependent frozen rates applies. Finally it is shown how the long time behavior of the underlying continuous process can be retrieved from the knowledge of the discrete process by means of an appropriate random decoration of the discrete states. As a particular example of the presented theory an over-damped bistable Brownian oscillator with periodic driving is discussed.