Directed motion in a periodic potential of a quantum system coupled to a heat bath driven by a colored noise

The motion of Brownian particles in a spatial symmetric periodic potential is considered. In the absence of any external driving forces, when the potential profile fluctuates cyclically between three states, directed motion can be induced. For a cosine potential, the finite probability current is evaluated.

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Thermodynamics of Quantum Information Systems — Hamiltonian Description

Open Systems & Information Dynamics ◽

10.1023/b:opsy.0000047566.72717.71 ◽

2004 ◽

Vol 11 (03) ◽

pp. 205-217 ◽

Cited By ~ 71

Author(s):

Robert Alicki ◽

Michał Horodecki ◽

Paweł Horodecki ◽

Ryszard Horodecki

Keyword(s):

Quantum System ◽

Weak Coupling ◽

Heat Bath ◽

Quantum Correlations ◽

Weak Coupling Limit ◽

Second Law ◽

Hamiltonian Description ◽

Landauer’S Principle ◽

Thermodynamical Laws ◽

The Cost

It is often claimed, that from a quantum system of d levels, and entropy S and heat bath of temperature T one can draw kT lnd–TS amount of work. However, the usual arguments basing on Szilard engine, are not fully rigorous. Here we prove the formula within Hamiltonian description of drawing work from a quantum system and a heat bath, at the cost of entropy of the system. We base on the derivation of thermodynamical laws and quantities in [10] within weak coupling limit. Our result provides fully physical scenario for extracting thermodynamical work form quantum correlations [4]. We also derive Landauer's principle as a consequence of the second law within the considered model.

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Collective Directional Transport of Coupled Oscillators in Symmetric Periodic Potentials

International Journal of Modern Physics B ◽

10.1142/s0217979203022544 ◽

2003 ◽

Vol 17 (22n24) ◽

pp. 4415-4422

Author(s):

Zhigang Zheng ◽

Jian Gao ◽

Gang Hu

Keyword(s):

Coupled Oscillators ◽

Periodic Potential ◽

Mode Locking ◽

Circle Map ◽

Directed Motion ◽

Directed Transport ◽

Collective Transport ◽

Periodic Potentials ◽

Transport Velocity ◽

Directional Transport

Collective directional transport of particles in symmetric periodic potentials is studied. An example is given to reveal the directed motion of a single particle in a symmetric periodic potential and subject to an asymmetric ac force with zero mean. It is then shown that the asymmetric coupling can give rise to a directed transport. The transport failure (pinning of the lattice) is related to the phase delocalization (crisis) in the circle map. For symmetric couplings, it is found that a train of plane wave can also lead to a directed transport. The mode-locking steps of the transport velocity is found and analyzed. The collective transport can be well optimized by adjusting parameters in the system.

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DIRECTED MOTION INDUCED BY SHIFTING RATCHET

International Journal of Modern Physics B ◽

10.1142/s0217979200002235 ◽

2000 ◽

Vol 14 (24) ◽

pp. 2609-2616 ◽

Cited By ~ 1

Author(s):

YUXIAO LI ◽

XIZHEN WU ◽

YIZHONG ZHUO

Keyword(s):

Driving Force ◽

Transition Rate ◽

Average Velocity ◽

Thermal Noise ◽

Periodic Potential ◽

Directed Motion ◽

Brownian Particles

The motion of Brownian particles in a spatial asymmetric periodic potential is considered. In the absence of any external macroscopic driving force, when the potential transits stochastically between two configurations which are shifted by a distance relative to each other, directed motion can be induced. The dependence of the average velocity on the transition rate, the strength of thermal noise and the shift distance between the two configurations of potential are analyzed. The efficiency of the system is evaluated.

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Decoherence and dissipation of an open quantum system with a squeezed and frequency-modulated heat bath

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2004.01.001 ◽

2004 ◽

Vol 337 (1-2) ◽

pp. 67-80 ◽

Cited By ~ 6

Author(s):

Subhashish Banerjee

Keyword(s):

Quantum System ◽

Open Quantum System ◽

Heat Bath ◽

Open Quantum

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A Framework for Sequential Measurements and General Jarzynski Equations

Zeitschrift für Naturforschung A ◽

10.1515/zna-2019-0272 ◽

2020 ◽

Vol 75 (3) ◽

pp. 265-284 ◽

Cited By ~ 1

Author(s):

Heinz-Jürgen Schmidt ◽

Jochen Gemmer

Keyword(s):

Quantum System ◽

Thermal Contact ◽

Local Equilibrium ◽

Standard Form ◽

Heat Bath ◽

Boltzmann Distribution ◽

Standard Quantum ◽

Periodically Driven ◽

Canonical Ensembles ◽

Sequential Measurements

AbstractWe formulate a statistical model of two sequential measurements and prove a so-called J-equation that leads to various diversifications of the well-known Jarzynski equation including the Crooks dissipation theorem. Moreover, the J-equation entails formulations of the Second Law going back to Wolfgang Pauli. We illustrate this by an analytically solvable example of sequential discrete position–momentum measurements accompanied with the increase of Shannon entropy. The standard form of the J-equation extends the domain of applications of the standard quantum Jarzynski equation in two respects: It includes systems that are initially only in local equilibrium, and it extends this equation to the cases where the local equilibrium is described by microcanononical, canonical, or grand canonical ensembles. Moreover, the case of a periodically driven quantum system in thermal contact with a heat bath is shown to be covered by the theory presented here if the quantum system assumes a quasi-Boltzmann distribution. Finally, we shortly consider the generalised Jarzynski equation in classical statistical mechanics.

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