Jerzy Luczka

Consistent description of quantum Brownian motors operating at strong friction.

A quantum Smoluchowski equation is put forward that consistently describes thermal quantum states. In particular, it notably does not induce a violation of the second law of thermodynamics. This so modified kinetic equation is applied to study {\it analytically} directed quantum transport at strong friction in arbitrarily shaped ratchet potentials that are driven by nonthermal two-state noise. Depending on the mutual interplay of quantum tunneling and quantum reflection these quantum corrections can induce both, either a sizable enhancement or a suppression of transport. Moreover, the threshold for current reversals becomes markedly shifted due to such quantum fluctuations.

Distance growth of quantum states due to initial system-environment correlations

Intriguing features of the distance between two arbitrary states of an open quantum system are identified that are induced by initial system-environment correlations. As an example, we analyze a qubit dephasingly coupled to a bosonic environment. Within tailored parameter regimes, initial correlations are shown to substantially increase the distance between two qubit states evolving to long-time-limit states according to exact non-Markovian dynamics. It exemplifies the breakdown of the distance contractivity of the reduced dynamics.

Negative mobility induced by colored thermal fluctuations.

Anomalous transport of non-Markovian thermal Brownian particle dynamics in spatially periodic symmetric systems that is driven by time-periodic symmetric driving and constant bias is investigated numerically. The Brownian dynamics is modeled by a generalized Langevin equation with exponentially correlated Gaussian thermal noise, obeying the fluctuation-dissipation theorem. We study the role of nonzero correlation time of thermal fluctuations for the occurrence of absolute negative (linear) mobility (ANM) near zero bias, negative-valued, nonlinear mobility (NNM), and negative differential mobility (NDM) at finite bias away from equilibrium. We detect that a nonzero thermal correlation time can either enhance or also diminish the value of ANM. Moreover, finite thermal noise correlation can induce NDM and NNM in regions of parameter space for which such ANM and NNM behaviors are distinctly absent for limiting white thermal noise. In parts of the parameter space, we find a complex structure of regions of linear and nonlinear negative mobility: islands and tongues which emerge and vanish under parameters manipulation. While certain such anomalous transport regimes fade away with increasing temperature some specific regions interestingly remain rather robust. Outside those regimes with anomalous mobility, the ac/dc driven transport is either normal or the driven Brownian particles are not transported at all.

Optimal strategy for controlling transport in inertial Brownian motors

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.

Magnetic flux in mesoscopic rings : Quantum Smoluchowski regime

Magnetic flux in mesoscopic rings under the quantum Smoluchowski regime is investigated. Quantum corrections to the dissipative current are shown to form multistable steady states and can result in statistical enhancement of the magnetic flux. The relevance of quantum correction effects is supported v ia the entropic criterion. A possible application for a qutrit architecture of quantum information is proposed.

Absolute negative mobility of inertial Brownian particles induced by noise

We study transport of a harmonically driven inertial particle moving in a symmetric periodic potential and subjected to both unbiased Gaussian thermal equilibrium noise and biased non-equilibrium Poissonian shot noise. The dependence of the average velocity on noise parameters exhibits a rich variety of anomalous transport characteristics: We identify an absolute negative mobility around zero biasing noise, the emergence of a negative differential mobility and the occurrence of a negative nonlinear mobility. As a feasible physical system we propound a setup consisting of a single resistively and capacitively shunted Josephson junction device.

Geometric phase of neutrino propagating through dissipative matter

We study the geometric phase (GP) in neutrino oscillation for both Dirac and Majorana neutrinos. We apply the kinematic generalization of the GP to quantum open systems that take into account the coupling to a dissipative environment. In the dissipationless case, the GP does not depend on the Majorana angle. It is not the case in the presence of dissipation and hence the GP can serve as a tool determining the type of the Dirac vs the Majorana neutrino.

On the averaging method in the weak-coupling theory of quantum open systems

The Krylov-Bogoliubov-Mitropolsky averaging method is applied directly to the Liouville equation for the study of weak-coupling dynamics of a quantum open system. For an example of a spin-boson system, where the boson subsystem is treated as a heat bath, an evolution equation for a statistical operator of the spin subsystem is derived. Equations of motion for three components of the spin S = 1/2 are obtained and their properties are discussed. Some anomalies of interest of the model are demonstrated.

Brownian motor efficiency enhanced by nonequilibrium noise

We study transport properties of an inertial Brownian motor which moves in a symmetric spatially periodic potential and is subjected to both a symmetric, unbiased time-periodic driving α cos (ωt) and a static constant force F or, likewise, nonequlibrium noise of equal mean value 〈(η(t)〉 = F. We focus on the efficiency of the motor and discuss various definitions. We show that within selected parameter regimes, nonequilibrium noise η (t) can be significantly more effective than the deterministic force F. This implies that the motor moves much faster and its efficiency distinctly increases. These features are independent of the assumed Brownian motor efficiency measure. We demonstrate this feature with detailed simulations by resource to generalized white Poissonian noise. Our theoretical results can be tested and corroborated experimentally by use of a setup that consists of a resistively and capacitively shunted Josephson junction.