The stochastic pump effect and geometric phases in dissipative and stochastic systems

2009/03/31 by N A Sinitsyn, N. A. Sinitsyn · 6 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Diffusion and Search Dynamics #Dissipative system #Dynamics (music) #Geometric phase #Motion (physics) #Nonlinear system #Quantum #Stochastic process #cond-mat.mes-hall #cond-mat.stat-mech #math-ph #math.MP #physics.chem-ph #stochastic dynamics and bifurcation

paper · pdf · doi:10.1088/1751-8113/42/19/193001

published as J. Phys. A: Math, Theor, 42 (2009) 193001 · Review. 35 pages. J. Phys. A: Math, Theor. (in press)

arxiv created 2009/04/15 · openalex publication_date 2009/04/22 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).

Citations

• Experimental Determination of the Berry Phase in a Superconducting Charge Pump
• Fluctuation statistics in networks: A stochastic path integral approach
• Stochastic Dynamics of a Josephson Junction Threshold Detector
• Berry’s phase in the degenerate parametric amplifier
• Angle variable holonomy in adiabatic excursion of an integrable Hamiltonian
• Semiclassical theories of the anomalous Hall effect
• Geometric Nature of the Environment-Induced Berry Phase and Geometric Dephasing
• Conditional statistics of electron transport in interacting nanoscale conductors
• Dynamics of Domain Walls in Magnetic Nanostrips
• Universal Intrinsic Spin Hall Effect
• Quantum pumping in closed systems, adiabatic transport, and the Kubo formula
• Topological Transition in a Non-Hermitian Quantum Walk
• Dissipationless Quantum Spin Current at Room Temperature
• Geometric phase for non-Hermitian Hamiltonians and its holonomy interpretation
• Directed Flow in Nonadiabatic Stochastic Pumps
• Transport Statistics of Bistable Systems
• Quantal phase factors accompanying adiabatic changes
• Classification of phase transitions in reaction-diffusion models

Cited by

• Colloquium: Phononics: Manipulating heat flow with electronic analogs and beyond
• Stochastic thermodynamics for a periodically driven single-particle pump
• No-Pumping Theorem for Many Particle Stochastic Pumps
• Noncyclic and nonadiabatic geometric phase for counting statistics
• Robust quantization of a molecular motor motion in a stochastic environment
• Large deviations of currents in diffusions with reflective boundaries