Stochastic pump effect and geometric phases in dissipative and stochastic systems

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).

Review. 35 pages. J. Phys. A: Math, Theor. (in press)

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Cited by in corpus (54)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Phononics: Manipulating heat flow with electronic analogs and beyond
• Berry-Phase induced Heat Pumping and its Impact on the Fluctuation Theorem
• Geometry of quantum phase transitions
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• Emergence and control of heat current from strict zero thermal bias
• Topological protection of multiparticle dissipative transport
• Nonequilibrium thermodynamics as a gauge theory
• Mimicking Nonequilibrium Steady States with Stochastic Pumps
• Dynamic control of quantum geometric heat flux in a nonequilibrium spin-boson model
• Geometric Heat Flux for Classical Thermal Transport in Interacting Open Systems
• Geometric Heat Pump: Controlling Thermal Transport with Time-dependent Modulations
• Braid Group and Topological Phase Transitions in Nonequilibrium Stochastic Dynamics
• Heat, molecular vibrations, and adiabatic driving in non-equilibrium transport through interacting quantum dots
• Geometric magnetism in open quantum systems
• Large deviations of currents in diffusions with reflective boundaries
• Mapping current fluctuations of stochastic pumps to nonequilibrium steady states
• A proof by graphical construction of the no-pumping theorem of stochastic pumps
• Fractional charges in conventional sequential electron tunneling
• Lattice symmetries and the topological protected transport of colloidal particles
• Gauge freedom in observables and Landsbergs nonadiabatic geometric phase: pumping spectroscopy of interacting open quantum systems
• Quantization and Fractional Quantization of Currents in Periodically Driven Stochastic Systems I: Average Currents
• Stochastic thermodynamics for a periodically driven single-particle pump
• No-pumping theorem for many particle stochastic pumps
• How quantum evolution with memory is generated in a time-local way
• Geometric Thermoelectric Pump: Energy Harvesting beyond Seebeck and Pyroelectric Effects
• Robust quantization of a molecular motor motion in a stochastic environment
• Attractive and driven interaction in quantum dots: mechanisms for geometric pumping
• Geometric energy transport and refrigeration with driven quantum dots
• The connection between time-local and time-nonlocal perturbation expansions
• Non-divergent representation of non-Hermitian operator near the exceptional point with application to a quantum Lorentz gas
• Duality and fluctuation relations for statistics of currents on cyclic graphs
• Quantization and Fractional Quantization of Currents in Periodically Driven Stochastic Systems II: Full Counting Statistics
• Algebraic probability, classical stochastic processes, and counting statistics
• Unification and new extensions of the no-pumping theorems of stochastic pumps
• Fitness in time-dependent environments includes a geometric contribution
• Geometric quantum pumping in the presence of dissipation
• Dissipative and stochastic geometric phase of a qubit within a canonical Langevin framework
• Discrete changes of current statistics in periodically driven stochastic systems
• Noncyclic and nonadiabatic geometric phase for counting statistics
• Work statistics in slow thermodynamic processes
• Hybrid models of molecular machines and the no-pumping theorem
• Current reversal in interacting colloids under time-periodic drive
• Hannay Angles in Magnetic Dynamics
• A [3]-catenane non-autonomous molecular motor model: geometric phase, no-pumping theorem, and energy transduction
• Spin polarization control by electric stirring: proposal for a spintronic device
• Speed limit, dissipation bound and dissipation-time trade-off in thermal relaxation processes
• Stochastic Dynamics of Extended Objects in Driven Systems: I. Higher-Dimensional Currents in the Continuous Setting
• The validity of the no-pumping theorem in systems with finite-range interactions between particles
• Thermodynamic large fluctuations from uniformized dynamics
• Stochastic Dynamics of Extended Objects in Driven Systems II: Current Quantization in the Low-Temperature Limit
• Noncyclic geometric phase in counting statistics and its role as an excess contribution
• Geometric phase-control of a spin-torque oscillator
• Geometric pumping induced by shear flow in dilute liquid crystalline polymer solutions