Jerzy Łuczka

University of Silesia in Katowice

We present a perspective of simple models of nonequilibrium directed transport described in terms of a Langevin equation formalism. We consider a Brownian particle under various circumstances and driven by thermal (equilibrium) and non-thermal (active) fluctuations. Three examples of startling behavior are unveiled: giant transport, multiple curren...

We present a perspective of simple models of nonequilibrium directed transport described in terms of a Langevin equation formalism. We consider a Brownian particle under various circumstances and driven by thermal (equilibrium) and non-thermal (active) fluctuations. Three examples of startling behavior are unveiled: giant transport, multiple curren...

Analysis of non-Markovian systems and memory induced phenomena poses an everlasting challenge for physics. As a paradigmatic example we consider a classical Brownian particle of mass $M$ subjected to an external force and exposed to correlated thermal fluctuations. We show that the recently developed approach to this system, in which its non-Markov...

Analysis of non-Markovian systems and memory-induced phenomena poses an everlasting challenge in the realm of physics. As a paradigmatic example, we consider a classical Brownian particle of mass M subjected to an external force and exposed to correlated thermal fluctuations. We show that the recently developed approach to this system, in which its...

Recent pioneering experiments on non-Markovian dynamics done, e.g., for active matter have demonstrated that our theoretical understanding of this challenging yet hot topic is rather incomplete and there is a wealth of phenomena still awaiting discovery. It is related to the fact that typically for simplification the Markovian approximation is empl...

We extend our previous studies on a counter-intuitive effect in which a directed transport of a free Brownian particle induced by active fluctuations can be significantly enhanced when the particle is placed in a periodic potential. It is in clear contrast to a common situation when the velocity of the Brownian particle is notably reduced if the pe...

We analyze the impact of temperature on the diffusion coefficient of an inertial Brownian particle moving in a symmetric periodic potential and driven by a symmetric time-periodic force. Recent studies have revealed the low-friction regime in which the diffusion coefficient shows giant damped quasiperiodic oscillations as a function of the amplitud...

We analyse the impact of temperature on the diffusion coefficient of an inertial Brownian particle moving in a symmetric periodic potential and driven by a symmetric time-periodic force. Recent studies have revealed the low friction regime in which the diffusion coefficient shows giant damped quasi-periodic oscillations as a function of the amplitu...

Active fluctuations are detected in a growing number of systems due to self-propulsion mechanisms or collisions with an active environment. They drive the system far from equilibrium and can induce phenomena that are forbidden at equilibrium states by, e.g., fluctuation-dissipation relations and detailed balance symmetry. Understanding their role i...

The diffusion of small particles is omnipresent in many processes occurring in nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject of exploration that we opt here to narrow our survey to the case of the diffusion coefficient for a Brownian particle that c...

Diffusion of small particles is omnipresent in a plentiful number of processes occurring in Nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject of exploration that we opt here to narrow down our survey for the case of the diffusion coefficient for a Brown...

We revisit the problem of diffusion in a driven system consisting of an inertial Brownian particle moving in a symmetric periodic potential and subjected to a symmetric time-periodic force. We reveal parameter domains in which diffusion is normal in the long time limit and exhibits intriguing giant damped quasiperiodic oscillations as a function of...

Active fluctuations are detected in a growing number of systems due to self-propulsion mechanisms or collisions with active environment. They drive the system far from equilibrium and can induce phenomena which at equilibrium states are forbidden by e.g. fluctuation-dissipation relations and detailed balance symmetry. Understanding of their role in...

We revisit the problem of diffusion in a driven system consisting of an inertial Brownian particle moving in a symmetric periodic potential and subjected to a symmetric time-periodic force. We reveal parameter domains in which diffusion is normal in the long time limit and exhibits intriguing giant damped quasiperiodic oscillations as a function of...

Multistability, i.e., the coexistence of several attractors for a given set of system parameters, is one of the most important phenomena occurring in dynamical systems. We consider it in the velocity dynamics of a Brownian particle, driven by thermal fluctuations and moving in a biased periodic potential. In doing so, we focus on the impact of ergo...

Multistability, i.e. the coexistence of several attractors for a given set of system parameters is one of the most important phenomena occurring in dynamical systems. We consider it in velocity dynamics of a Brownian particle driven by thermal fluctuations and moving in a biased periodic potential. In doing so we focus on the impact of ergodicity -...

The weak-noise limit of dissipative dynamical systems is often the most fascinating one. In such a case fluctuations can interact with a rich complexity, frequently hidden in deterministic systems, to give rise to phenomena that are absent for both noiseless and strong fluctuations regimes. Unfortunately, this limit is also notoriously hard to appr...

Multistability is one of the most important phenomena in dynamical systems, e.g., bistability enables the implementation of logic gates and therefore computation. Recently multistability has attracted a greatly renewed interest related to memristors and graphene structures, to name only a few. We investigate tristability in velocity dynamics of a B...

The weak noise limit of dissipative dynamical systems is often the most fascinating one. In such a case fluctuations can interact with a rich complexity frequently hidden in deterministic systems to give rise of completely new phenomena that are absent for both noiseless and strong fluctuations regimes. Unfortunately, this limit is also notoriously...

Multistability is one of the most important phenomena in dynamical systems, e.g. bistability enables the implementation of logic gates and therefore computation. Recently multistability has attracted a greatly renewed interest related to memristors and graphene structures. We investigate tristability in velocity dynamics of a Brownian particle subj...

In a recent paper by B. G. da Costa et al. [Phys. Rev. E 102, 062105 (2020)], the phenomenological Langevin equation and the corresponding Fokker-Planck equation for an inhomogeneous medium with a position-dependent particle mass and position-dependent damping coefficient have been studied. The aim of this comment is to present a microscopic deriva...

Experimentalists have come to temperatures very close to absolute zero at which physics that was once ordinary becomes extraordinary. In such a regime quantum effects and fluctuations start to play a dominant role. In this context we study the simplest open quantum system, namely, a free quantum Brownian particle coupled to thermal vacuum, i.e. the...

In a recent paper by B. G. da Costa {\it et al.} [Phys. Rev. E 102, 062105(2020)], the phenomenological Langevin equation and the corresponding Fokker-Planck equation for an inhomogeneous medium with a position-dependent particle mass and position-dependent damping coefficient have been studied. The aim of this comment is to present a microscopic d...

We report on Brownian, yet non-Gaussian diffusion, in which the mean square displacement of the particle grows linearly with time, and the probability density for the particle spreading is Gaussian like, but the probability density for its position increments possesses an exponentially decaying tail. In contrast to recent works in this area, this b...

We report on novel Brownian, yet non-Gaussian diffusion, in which the mean square displacement of the particle grows linearly with time, the probability density for the particle spreading is Gaussian-like, however, the probability density for its position increments possesses an exponentially decaying tail. In contrast to recent works in this area,...

It is shown that the recently proposed quantum analogue of classical energy equipartition theorem for two paradigmatic, exactly solved models (i.e., a free Brownian particle and a dissipative harmonic oscillator) also holds true for all quantum systems which are composed of an arbitrary number of non-interacting or interacting particles, subjected...

We analyze an averaged energy $E$ of a free quantum Brownian particle coupled to an environment of absolute zero temperature (quantum vacuum) and study its dependence on the coupling strength $c$ between the particle and its surroundings. Impact of selected dissipation mechanisms is considered. In the weak coupling limit the energy tends to zero as...

The celebrated Sutherland-Einstein relation for systems at thermal equilibrium states that spread of trajectories of Brownian particles is an increasing function of temperature. Here, we scrutinize the diffusion of underdamped Brownian motion in a biased periodic potential and analyze regimes in which a diffusion coefficient decreases with increasi...

The celebrated Sutherland-Einstein relation for systems at thermal equilibrium states that spread of trajectories of Brownian particles is an increasing function of temperature. Here, we scrutinize diffusion of underdamped Brownian motion in a biased periodic potential and analyse regimes in which a diffusion coefficient decreases with increasing t...

We consider a generic system operating under non-equilibrium conditions. Explicitly, we consider an inertial classical Brownian particle dwelling a periodic structure with a spatially broken reflection symmetry. The particle is coupled to a bath of temperature $T$ and is driven by an unbiased time-periodic force. In the asymptotic long time regime...

We investigate advantages and disadvantages of using Gazeau–Klauder coherent states for optical communication. In this short paper we show that using an alphabet consisting of coherent Gazeau–Klauder states related to a Kerr-type nonlinear oscillator instead of standard Perelomov coherent states results in lowering of the Helstrom bound for error p...

It is shown that the recently proposed quantum analogue of energy equipartition theorem for a free Brownian particle and a dissipative harmonic oscillator also holds true for quantum systems composed of an arbitrary number of interacting particles, subjected to a potential and coupled to thermostat of arbitrary strength.

An effective approach to isolation of submicrometer-sized particles is desired to separate cancer cells and healthy cells or in therapy for Parkinson’s disease and Alzheimer’s disease. However, since bioparticles span a large size range covering several orders of magnitude, the development of an adequate separation method is a challenging task. We...

An effective approach to isolation of sub-micro sized particles is desired to separate cancer and healthy cells or in therapy of Parkinson's and Alzheimer's disease. However, since bioparticles span a large size range comprising several orders of magnitude, development of an adequate separation method is a challenging task. We consider a collection...

Using extensive numerical studies we demonstrate that absolute negative mobility of a Brownian particle (i.e. the net motion into the direction opposite to a constant biasing force acting around zero bias) does coexist with anomalous diffusion (AD). The latter is characterised in terms of a nonlinear scaling with time of the mean-square deviation o...

Using extensive numerical studies we demonstrate that absolute negative mobility of a Brownian particle (i.e. the net motion into the direction opposite to a constant biasing force acting around zero bias) does coexist with anomalous diffusion. The latter is characterized in terms of a nonlinear scaling with time of the mean-square deviation of the...

We reveal a new face of the old clich\'ed system: a dissipative quantum harmonic oscillator. We formulate and study a quantum counterpart of the energy equipartition theorem satisfied for classical systems.Both mean kinetic energy $E_k$ and mean potential energy $E_p$ of the oscillator are expressed as $E_k = \langle \mathcal E_k \rangle$ and $E_p...

We study the quantum counterpart of the theorem on energy equipartition for classical systems. We consider a free quantum Brownian particle modelled in terms of the Caldeira-Leggett framework: a system plus thermostat consisting of an infinite number of harmonic oscillators. By virtue of the theorem on the averaged kinetic energy $E_k$ of the quant...

We consider energetics of a free quantum Brownian particle coupled to thermostat of temperature $T$ and study this problem in terms of the lately formulated quantum analogue of the energy equipartition theorem. We show how this quantum counterpart can be derived from the Callen-Welton fluctuation-dissipation relation and rephrased in terms of super...

One of the fundamental laws of classical statistical physics is the energy equipartition theorem which states that for each degree of freedom the mean kinetic energy E k equals E k = k B T/2, where is the Boltzmann constant and T is the temperature of the system. Despite the fact that quantum mechanics has already been developed for more than 100 y...

A prerequisite for isolating diseased cells requires a mechanism for effective mass-based separation. This objective, however, is generally rather challenging because typically no valid correlation exists between the size of the particles and their mass value. We consider an inertial Brownian particle moving in a symmetric periodic potential and su...

A prerequisite for isolating diseased cells requires a mechanism for effective mass-based separation. This objective, however, is generally rather challenging because typically no valid correlation exists between the size of the particles and their mass value. We consider an inertial Brownian particle moving in a symmetric periodic potential and su...

We study occupation of certain regions of phase space of an asymmetric superconducting quantum interference device (SQUID) driven by thermal noise, subjected to an external ac current and threaded by a constant magnetic flux. Thermally activated transitions between the states which reflect three deterministic attractors are analyzed in the regime o...

We study the quantum counterpart of the theorem on energy equipartition for classical systems. We consider a free quantum Brownian particle modeled in terms of the Caldeira-Leggett framework: a system plus thermostat consisting of an infinite number of harmonic oscillators. By virtue of the theorem on the averaged kinetic energy Ek of the quantum p...

We reveal a new face of the old clichéd system: a dissipative quantum harmonic oscillator. We formulate and study a quantum counterpart of the energy equipartition theorem satisfied for classical systems. Both mean kinetic energy Ek and mean potential energy Ep of the oscillator are expressed as Ek = 〈εk〉 and Ep = 〈εp〉, where 〈εk〉 and 〈εp〉 are mean...

The stochastic dynamics of a quantum system driven by N statistically independent random sudden quenches in a fixed time interval is studied. We reveal that with increasing N the system approaches a deterministic limit, indicating self-averaging with respect to its temporal unitary evolution. This phenomenon is quantified by the variance of the uni...

We study occupation of certain regions of phase space of an asymmetric superconducting quantum interference device (SQUID) driven by thermal noise, subjected to an external ac current and threaded by a constant magnetic flux. Thermally activated transitions between the states which reflect three deterministic attractors are analyzed in the regime o...

One of the fundamental laws of classical statistical physics is the energy equipartition theorem which states that for each degree of freedom the average kinetic energy equals $E_k=k_B T/2$, where $k_B$ is the Boltzmann constant and $T$ is temperature of the system. Despite the fact that quantum mechanics has already been developed for more than 10...

Stochastic dynamics of a quantum system driven by $N$ statistically independent random sudden quenches in a fixed time interval is studied. We reveal that with growing $N$ the system approaches a deterministic limit indicating self-averaging with respect to its temporal unitary evolution. This phenomenon is quantified by the variance of the unitary...

We consider a paradigmatic model of a quantum Brownian particle coupled to a thermostat consisting of harmonic oscillators. In the framework of a generalized Langevin equation, the memory (damping) kernel is assumed to be in the form of exponentially-decaying oscillations. We discuss a quantum counterpart of the equipartition energy theorem for a f...

We reveal the mechanism of subdiffusion which emerges in a straightforward, one dimensional classical nonequilibrium dynamics of a Brownian ratchet driven by both a time-periodic force and Gaussian white noise. In a tailored parameter set for which the deterministic counterpart is in a non-chaotic regime, subdiffusion is a long-living transient who...

We provide insights into energetics of a Brownian oscillator in contact with a heat bath and driven by an external unbiased time-periodic force that takes the system out of thermodynamic equilibrium. Solving the corresponding Langevin equation, we compute average kinetic and potential energies in the long-time stationary state. We also derive the e...

We study impact of inertia on directed transport of a Brownian particle under non-equilibrium conditions: the particle moves in a one-dimensional periodic and symmetric potential, is driven by both an unbiased time-periodic force and a constant force, and is coupled to a thermostat of temperature T. Within selected parameter regimes this system exh...

The statistics of work performed on a system by a sudden random quench is investigated. Considering systems with finite dimensional Hilbert spaces we model a sudden random quench by randomly choosing elements from a Gaussian unitary ensemble (GUE) consisting of hermitean matrices with identically, Gaussian distributed matrix elements. A probability...

We study diffusion properties of an inertial Brownian motor moving on a ratchet substrate, i.e. a periodic structure with broken reflection symmetry. The motor is driven by an unbiased time-periodic symmetric force which takes the system out of thermal equilibrium. For selected parameter sets, the system is in a non-chaotic regime in which we can i...

The spreading of a cloud of independent Brownian particles typically proceeds more effectively at higher temperatures, as it derives from the commonly known Sutherland–Einstein relation for systems in thermal equilibrium. Here, we report on a non-equilibrium situation in which the diffusion of a periodically driven Brownian particle moving in a per...

The violation of the Leggett–Garg inequality is studied for a quantum top (with angular momentum \(J_z\) of integer or half-integer size), being driven by classical Gaussian white noise. The form of a longitudinal \((J_z)\) or a transverse \((J_x)\) coupling of noise to the angular momentum affects both (i) to what extent the Leggett–Garg inequalit...

Diffusion is a key phenomenon in almost all branches of natural science that describes irregularity of motion. The latter can arise from two main sources. First, the dynamics of the system can be deterministically chaotic. Second, irregularity in the motion occurs due to the unavoidable presence of noise in any real setup. It is expected that the m...

A network of quantum gates designed to implement universal quantum cloning machine is studied. We analyze how thermal environment coupled to auxiliary qubits, ‘blank paper’ and ‘toner’ required at the preparation stage of copying, modifies an output fidelity of the cloner. Thermal environment is described in terms of the Markovian Davies theory. We...

We study far from equilibrium transport of a periodically driven inertial Brownian particle moving in a periodic potential. As detected recently for a SQUID ratchet dynamics (Spiechowicz J. & Luczka J. Phys. Rev. E 91, 062104 (2015)), the mean square deviation of the particle position from its average may involve three distinct intermediate, althou...

Recently Ru-Yin Chen et al. (Phys. Lett. A 379 (2015) 2169–2173) presented results on the absolute negative mobility (ANM) in a one-dimensional overdamped system and claimed that a new minimal model of ANM was proposed. We suggest that the authors introduced a mistake in their calculations. Then we perform a precise numerical simulation of the corr...

We study energetics of a Josephson tunnel junction connecting a superconducting loop pierced by an external magnetic flux (an rf SQUID) and coupled to two independent thermal reservoirs of different temperature. In the framework of the theory of quantum dissipative systems, we analyze energy currents in stationary states. The stationary energy flow...

We study transport of an inertial Brownian particle moving in a \emph{symmetric} and periodic one-dimensional potential, and subjected to both a \emph{symmetric}, unbiased external harmonic force as well as biased dichotomic noise $\eta(t)$ also known as a random telegraph signal or a two state continuous-time Markov process. In doing so, we concen...

We revisit the problem of transport of a harmonically driven inertial particle moving in a {\it symmetric} periodic potential, subjected to {\it unbiased} non-equilibrium generalized white Poissonian noise and coupled to thermal bath. Statistical asymmetry of Poissonian noise is sufficient to induce transport and under presence of external harmonic...

Currents in metallic rings with a quantum dot are studied in the framework of a Langevin equation for a magnetic flux passing through the ring. Two scenarios are considered: one in which thermal fluctuations of the dissipative part of the current are modeled by classical Johnson–Nyquist noise and one in which quantum character of thermal fluctuatio...

We study transport properties of an inertial Brown-ian 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 vari...

We study diffusion in ratchet systems. As a particular experimental realization we consider an asymmetric SQUID subjected to an external ac current and a constant magnetic flux. We analyze mean-square displacement of the Josephson phase and find that within selected parameter regimes it evolves in three distinct stages: initially as superdiffusion,...

We reply to the comment by Aleksiejunas on our article Dajka J and Łuczka J 2012 J. Phys. A: Math. Theor. 45 244006. We point that the mistake mentioned in the comment is trivial and rather technical and does not influence main physical content of our work.

We study diffusion of the Josephson phase in the asymmetric SQUID subjected to a time-periodic current and pierced by an external magnetic flux. We analyze a relation between phase diffusion and quality of transport characterized by the dc voltage across the SQUID and efficiency of the device. In doing so, we concentrate on the previously reported...

We study diffusion of the Josephson phase in the asymmetric superconducting quantum interference device (SQUID) subjected to a time-periodic current and pierced by an external magnetic flux. We analyze a relation between phase diffusion and quality of transport characterized by the dc voltage across the SQUID and efficiency of the device. In doing...

Currents in a metallic ring with a quantum dot are studied in the framework of a Langevin equation for a magnetic flux passing through the ring. Two scenarios are considered: one in which thermal fluctuations of the dissipative part of the current are modelled by classical Johnson-Nyquist noise and one in which quantum character of thermal fluctuat...

We study violation of the Leggett-Garg inequality for the correlator ${K}_{3}$ in two cases: (i) for a qubit weakly coupled to a thermal decohering (dissipative and/or dephasing) environment and (ii) for a pair of qubits with only one of them coupled to the environment. In the case of a single qubit, we identify conditions depending both on initial...

We study theoretically the efficiency of an asymmetric superconducting quantum interference device (SQUID) which is constructed as a loop with three capacitively and resistively shunted Josephson junctions. Two junctions are placed in series in one arm and the remaining one is located in the other arm. The SQUID is threaded by an external magnetic...

We study a noisy drive mechanism for efficiency enhancement of Brownian motors operating on the micro-scale domain. It was proven [J. Spiechowicz et al., J. Stat. Mech. P02044, (2013)] that biased noise $\eta(t)$ can induce normal and anomalous transport processes similar to those generated by a static force $F$ acting on inertial Brownian particle...

We study transport in an asymmetric SQUID which is composed of a loop with three capacitively and resistively shunted Josephson junctions: two in series in one arm and the remaining one in the other arm. The loop is threaded by an external magnetic flux and the system is subjected to both a time-periodic and a constant current. We formulate the det...

We analyze the geometric phase in the neutrino oscillation phenomenon, which follows the pion decay \pi+ --> \mu+ + \nu_{\mu}. Its value \pi is consistent with the present-day global analysis of the Standard Model neutrino oscillation parameters, accounting for the nonzero value of \theta_13. The impact of the charge-parity (CP) violating phase \de...

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 ident...

Purity as a quantifier of an impact of environment on an open quantum system is studied for a qubit dephasingly interacting with its environment. We analyze how time evolution of the purity depends on initial states of the composite system both in the case of infinite and finite environments. It is shown that for a certain class of initial preparat...

Quantum channel teleporting one party of a bipartite entangled state is considered. It is assumed that resource is coupled to thermal decohering (dissipative and/or pure dephasing) environment. We investigate both the fidelity of the channel and its ability to swap the initial correlation to the final state of the system in which subsystems did not...

We research the transport properties of inertial Brownian particles which move in a symmetric periodic potential and are subjected to both a symmetric, unbiased time-periodic external force and biased Poissonian white shot noise (of non-zero average F) being composed of a random sequence of delta-shaped pulses with random amplitudes. Upon varying t...

We study superconducting and non-superconducting nanorings and look for non-classical features of magnetic flux passing through nanorings. We show that the magnetic flux can exhibit purely quantum properties in some peculiar states with quadrature squeezing. We identify a subset of Gazeau-Klauder states in which the magnetic flux can be squeezed an...

Transport properties of two coupled Josephson junctions driven by ac currents and thermal fluctuations are studied with the purpose of determining dc voltage characteristics. It is a physical realization of directed transport induced by a non-biased zero averaged external signal. The ac current is applied either to (A) only one junction as a biharm...

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.

We investigate the time evolution of negativity and quantum discord for a pair of non-interacting qubits with one being weakly coupled to a decohering Davies--type Markovian environment. At initial time of preparation, the qubits are prepared in one of the maximally entangled pure Bell states. In the limiting case of pure decoherence (i.e. pure dep...

Generalization of single-mode Schrödinger cat states is proposed, and their construction in terms of superposition of Gazeau–Klauder coherent states is presented. A comparative analysis of selected properties of this novel states for a nonlinear Kerr oscillator and the 'traditional' Schrödinger cats is given with emphasis on the photon statistics a...

Geometric phase of open quantum systems is reviewed. An emphasis is given on specific features of the geometric phase which can serve as an indicator of type and strength of interaction between two-level system (qubit) and its bosonic environment. We study three examples: (i) a single qubit dephasingly coupled to the environment, (ii) a qubit being...

We study transport properties of two Josephson junctions coupled by an external shunt resistance. One of the junction (say, the first) is driven by an unbiased ac current consisting of two harmonics. The device can rectify the ac current yielding a dc voltage across the first junction. For some values of coupling strength, controlled by an external...

We report on a theoretical study of transport properties of two coupled Josephson junctions and compare two scenarios for controlling the current-voltage characteristics when the system is driven by an external biased DC current and unbiased AC current consisting of one harmonic. In the first scenario, only one junction is subjected to both DC and...

We consider a deterministic process described by a discrete one-dimensional chaotic map and study its diffusive-like properties. Starting with the corresponding Frobenius-Perron equation we derive an approximate evolution equation for the probability distribution which is a partial differential equation of a hyperbolic type. Consequently, the proce...

The time evolution of the trace distance between two states of an open quantum system may increase due to initial system-environment correlations, thus exhibiting a breakdown of distance contractivity of the reduced dynamics. We analyze how the time evolution of the distance depends on the chosen distance measure. Here we elucidate the behavior of...

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 di...

One-dimensional transport of an overdamped Brownian particle biased by an external constant force does not exhibit negative mobility. However, when the particle is coupled to another particle, negative mobility can arise. We present a minimal model and propose a scenario in which only one (say, the first) particle is dc biased by a constant force a...

We investigate the qubit geometric phase and its properties in dependence on the mechanism for decoherence of a qubit weakly coupled to its environment. We consider two sources of decoherence: dephasing coupling (without exchange of energy with environment) and dissipative coupling (with exchange of energy). Reduced dynamics of the qubit is studied...

An overdamped dynamical system, biased by an external constant force, does not exhibit negative mobility. However, when the system is coupled to its copy, negative mobility can arise. We show it by the example of an experimentally realizable system of two coupled resistively shunted Josephson junctions. The first junction is dc-biased by a constant...

Transport properties of a Brownian particle in thermal-inertial ratchets subject to an external time-oscillatory drive and a constant bias force are investigated. Since the phenomena of negative mobility, resonant activation and noise-enhance stability were reported before, in the present paper, we report some additional aspects of negative mobilit...

We propose four different mechanisms responsible for the paramagnetic or diamagnetic persistent currents in normal metal rings and determine the circumstances for changes of the current from paramagnetic to diamagnetic and vice versa. This might qualitatively reproduce the experimental results of Bluhm et al (2009 Phys. Rev. Lett.?102 136802).

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 vs the external constant magnetic flux characteristics of the system driven by both the classical and the quan...

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 analyze impact of non...