New paradoxical games based on brownian ratchets

Based on Brownian ratchets, a counterintuitive phenomenon has recently emerged-namely, that two losing games can yield, when combined, a paradoxical tendency to win. A restriction of this phenomenon is that the rules depend on the current capital of the player. Here we present new games where all the rules depend only on the history of the game and not on the capital. This new history-dependent structure significantly increases the parameter space for which the effect operates.     

Quantum Information Approach to the Ultimatum Game

The paper is devoted to quantization of extensive games with the use of both the Marinatto-Weber and the Eisert-Wilkens-Lewenstein concept of quantum game. We revise the current conception of quantum ultimatum game and we show why the proposal is unacceptable. To support our approach, we present a new idea of the quantum ultimatum game. Our scheme also makes a point of departure for a general protocol for quantizing extensive games.     

Brownian ratchets and Parrondo's games

Parrondo's games present an apparently paradoxical situation where individually losing games can be combined to win. In this article we analyze the case of two coin tossing games. Game B is played with two biased coins and has state-dependent rules based on the player's current capital. Game B can exhibit detailed balance or even negative drift (i.e., loss), depending on the chosen parameters. Game A is played with a single biased coin that produces a loss or negative drift in capital. However, a winning expectation is achieved by randomly mixing A and B. One possible interpretation pictures game A as a source of "noise" that is rectified by game B to produce overall positive drift-as in a Brownian ratchet. Game B has a state-dependent rule that favors a losing coin, but when this state dependence is broken up by the noise introduced by game A, a winning coin is favored. In this article we find the parameter space in which the paradoxical effect occurs and carry out a winning rate analysis. The significance of Parrondo's games is that they are physically motivated and were originally derived by considering a Brownian ratchet-the combination of the games can be therefore considered as a discrete-time Brownian ratchet. We postulate the use of games of this type as a toy model for a number of physical and biological processes and raise a number of open questions for future research. (c) 2001 American Institute of Physics.     

A feedback-controlled Brownian ratchet operated by a temperature switch

In this paper, we present a model of the Brownian motor in a feedback controlled ratchet, in which the application of the flashing potential depends on the state of the particle to be controlled. We derive an analytical expression for the velocity induced by the feedback ratchet, which is a function of several parameters, including the ratio of the two switching temperatures and the asymmetry parameter of the potential field. The motor shows a current inversion when either parameter is varied.     

A feedback controlled Brownian ratchet operated by temperature switch

In this paper, we present a model of the Brownian motor in a feedback controlled ratchet, in which the application of the flashing potential depends on the state of the particle to be controlled. We derive an analytical expression for the velocity induced by the feedback ratchet, which is a function of several parameters, including the ratio of the two switching temperatures and the asymmetry parameter of the potential field. The motor shows a current inversion when either parameter is varied.     

Josephson effect for superconductors lacking time-reversal and inversion symmetries

Because of the absence of a center of inversion in some superconducting compounds, a p-wave admixture to the dominant d-wave (or s) order parameter must exist. If time reversal is also violated, an allowed invariant is the product of the d wave (or s wave), p wave, and an appropriately directed current. We show that this leads to a new and remarkable property of the Josephson current for tunneling into a s-wave superconductor along the direction parallel to the axis of the p-wave component. These ideas are applied to the heavy-fermion compounds which lack center of inversion due to crystalline symmetry, as well as time-reversal symmetry, such as CePt(3)Si. They also apply to the superconducting state of the cuprates in the pseudogap region of the phase diagram where in the normal phase some experiments have detected a time-reversal and inversion symmetry broken phase.     

Segregation in arch formation

We report new segregation phenomena in the clogging arches formed during the discharge of granular piles. Results from molecular dynamics simulations show segregation effects with respect to both size and density ratios used in piles built with bidisperse mixtures of grains. The clogging arch is preferentially constituted of large grains when size bidisperse piles were discharged, whereas for density bidisperse mixtures there is a predominance of light grains in the arch for large orifice widths but, for small widths, an inversion in the preference is observed, with a slightly higher incidence of heavy grains forming the arches. We present arguments based on the reverse buoyancy effect and the statistics collected for the avalanche size distributions to explain how these effects can be understood as a crossover between two different segregation mechanisms acting independently at small and large orifice width limits.     

Quantum games via search algorithms

We build new quantum games, similar to the spin flip game, where as a novelty the players perform measurements on a quantum system associated to a continuous time search algorithm. The measurements collapse the wave function into one of the two possible states. These games are characterized by a continuous space of strategies and the selection of a particular strategy is determined by the moments when the players measure.     

Novel 0–π transitions in Josephson junctions between noncentrosymmetric superconductors

We study the Josephson effect between two noncentrosymmetric superconductors(NCSs) with opposite polarization vectors of Rashba spin–orbit coupling(RSOC).We find a 0–π transition driven by the triplet–singlet ratio of NCSs.Different from conventional 0–π transitions,the Andreev bound states change their energy range instead of phase shift in the 0–π transition found here.This novel property results in a feature that the critical current becomes almost zero at the transition point,not only a minimum.Furthermore,when the directions of RSOC polarization vectors are the same in two NCSs,the similar effect can also be found in the presence of a perpendicular exchange field or a Dresselhause spin–orbit coupling in the interlayer.We find novel oscillations of critical current without 0–π transition.These novel 0–π transitions or oscillations of critical current present new understanding of the Josephson effect and can also serve as a tool to determine the unknown triplet–singlet ratio of NCSs.     

Noise induced transport

We study the overdamped motion of a particle in a one-dimensional periodic potential driven by a stochastic force. If the stochastic force is correlated in time (non-white), and if the potential has no inversion symmetry, a current is generated. In the case of a piecewise linear potential we obtain a closed expression for the current as a ratio of two determinants. This allows us to calculate the current as a function of the noise strength, the correlation time and the temperature of the system for several stochastic processes. We examine several limiting situations. Depending on the statistics of the noise process, the direction of the current may change. Two different mechanisms for this effect are discussed.     

Influence of Doppler broadening and spontaneously generated coherence on propagation effect in a quasi lambda-type four-level system

In this paper we study influences of Doppler broadening, spontaneously generated coherence, and other system parameters on propagation effect in a quasi lambda-type four-level atomic system. It is shown that when the Doppler broadening is present, generally speaking, the values of gain and intensity of lasing without inversion (i.e. the probe field) in the co-propagating probe and driving fields case are much larger than those in the counter-propagating case; considerably larger gain and intensity of lasing without inversion than those without the Doppler broadening can be obtained by choosing appropriate values of the Doppler broadening width and spontaneously generated coherence strength. The gain and intensity of lasing without inversion increase with the increase of spontaneously generated coherence strength; when spontaneously generated coherence is present, much larger gain and intensity of lasing without inversion than those in the case without spontaneously generated coherence can be obtained. Choosing suitable values of the probe detuning, Rabi frequencies of the driving and pump fields at the entrance of the medium also can remarkably enhance the gain and intensity of lasing without inversion.     

Transport in a fluctuating potential

We study the overdamped motion of a particle in a fluctuating one-dimensional periodic potential. The potential has no inversion symmetry, and the fluctuations are correlated in time. At finite temperatures, a stationary current is induced. The amplitude and the direction of the current depend on the details of the noise process that is responsible for the potential fluctuations. We discuss several limiting situations for a general case. Furthermore we calculate the current in the case of a piecewise linear potential for different noise processes and parameters. A detailed discussion of the results is given, including a discussion of the mechanism that is responsible for the current reversal. We compare the present results with results for transport in a ratchet-like potential due to a fluctuating force. We also discuss the biological relevance of the present models for molecular motors. We present a model for the motion of molecular motors that explains why similar molecular motors can move in different directions.     

Imaging of the dissipation in quantum-Hall-effect experiments

The spatial distribution of heat dissipation in quantum-Hall-effect devices was imaged utilizing the fountain pressure effect of superfluid helium. This was done by observing visually the local thickness of a helium film covering the sample. We found that dissipation takes place only in two opposite corners at the current contacts. Unexpected asymmetries between the two corners were observed if the Hall currents exceeded a threshold value. A new and striking dissipative effect was found when current is passed from narrow to wide 2 DEG areas which also was asymmetric upon current reversal.     

Chiral magnetic effect without chirality source in asymmetric Weyl semimetals

We describe a new type of the chiral magnetic effect (CME) that should occur in Weyl semimetals (WSMs) with an asymmetry in the dispersion relations of the left- and right-handed (LH and RH) chiral Weyl fermions. In such materials, time-dependent pumping of electrons from a non-chiral external source can generate a non-vanishing chiral chemical potential. This is due to the different capacities of the LH and RH chiral Weyl cones arising from the difference in the density of states in the LH and RH cones. The chiral chemical potential then generates, via the chiral anomaly, a current along the direction of an applied magnetic field even in the absence of an external electric field. The source of chirality imbalance in this new setup is thus due to the band structure of the system and the presence of (non-chiral) electron source, and not due to the parallel electric and magnetic fields. We illustrate the effect by an argument based on the effective field theory, and by the chiral kinetic theory calculation for a rotationally invariant WSM with different Fermi velocities in the left and right chiral Weyl cones; we also consider the case of a WSM with Weyl nodes at different energies. We argue that this effect is generically present in WSMs with different dispersion relations for LH and RH chiral Weyl cones, such as SrSi₂ recently predicted as a WSM with broken inversion and mirror symmetries, as long as the chiral relaxation time is much longer than the transport scattering time.     

Magnetoresistance of an asymmetric quantum-size structure in a parallel magnetic field: Field asymmetry independent of the current direction

A new phenomenon, viz., field-asymmetric transverse magnetoresistance of a doped asymmetric quantum-size structure discovered in a magnetic field parallel to the heteroboundary planes, is studied experimentally and theoretically. The magnetoresistance asymmetry relative to the field direction, which is independent of the direction of transport current, is observed when a lateral electric field is embedded in the structure with the help of alloyed metallic contacts. In the theoretical part of the paper, it is shown that the contribution to current, which is asymmetric in the magnetic field, can be consistently described in the framework of the theory of spontaneous current states and photovoltaic effect in systems without an inversion center; the reason behind the emergence of this current is associated with the asymmetry of the energy spectrum of charge carriers relative to the quasimomentum. It is shown that the change in the size and shape of Fermi contours in a magnetic field determines the magnitude of the strong negative magnetoresistance associated with the intersubband scattering under investigation and is found to be responsible for the emergence of a qualitatively new effect mentioned in the title of this paper.     

Group chase and escape with conversion from targets to chasers

We study the effect of converting caught targets into new chasers in the context of the recently proposed ‘group chase and escape’ problem. Numerical simulations have shown that this conversion can substantially reduce the lifetimes of the targets when a large number of them are initially present. At the same time, it also leads to a non-monotonic dependence on the initial number of targets, resulting in the existence of a maximum lifetime. As a counter-effect for this conversion, we further introduce self-multiplying abilities to the targets. We found that the longest lifetime exists when a suitable combination of these two effects is created.     

On the relation between Bell's inequalities and nonlocal games

We investigate the relation between Bell's inequalities and nonlocal games by presenting a systematic method for their bilateral conversion. In particular, we show that while to any nonlocal game there naturally corresponds a unique Bell's inequality, the converse is not true. As an illustration of the method we present a number of nonlocal games that admits better odds when played using quantum resources.     

Duality, phase structures, and dilemmas in symmetric quantum games

Symmetric quantum games for 2-player, 2-qubit strategies are analyzed in detail by using a scheme in which all pure states in the 2-qubit Hilbert space are utilized for strategies. We consider two different types of symmetric games exemplified by the familiar games, the Battle of the Sexes (BoS) and the Prisoners’ Dilemma (PD). These two types of symmetric games are shown to be related by a duality map, which ensures that they share common phase structures with respect to the equilibria of the strategies. We find eight distinct phase structures possible for the symmetric games, which are determined by the classical payoff matrices from which the quantum games are defined. We also discuss the possibility of resolving the dilemmas in the classical BoS, PD, and the Stag Hunt (SH) game based on the phase structures obtained in the quantum games. It is observed that quantization cannot resolve the dilemma fully for the BoS, while it generically can for the PD and SH if appropriate correlations for the strategies of the players are provided.     

Helical vortex phase in the noncentrosymmetric CePt3Si

We consider the role of magnetic fields on the broken inversion superconductor CePt3Si. We show that the upper critical field for a field along the c axis exhibits a much weaker paramagnetic effect than for a field applied perpendicular to the c axis. The in-plane paramagnetic effect is strongly reduced by the appearance of helical structure in the order parameter. We find that, to get good agreement between theory and recent experimental measurements of H(c2), this helical structure is required. We propose a Josephson junction experiment that can be used to detect this helical order. In particular, we predict that the Josephson current will exhibit a magnetic interference pattern for a magnetic field applied perpendicular to the junction normal. We also discuss unusual magnetic effects associated with the helical order.