Quantum ratchet with Lindblad rate equations
arXiv:2311.15713 · doi:10.1103/PhysRevE.109.054128
Abstract
A quantum random walk model is established on a one-dimensional periodic lattice that fluctuates between two possible states. This model is defined by Lindblad rate equations that incorporate the transition rates between the two lattice states. Leveraging the system's symmetries, the particle velocity can be described using a finite set of equations, even though the state space is of infinite dimension. These equations yield an analytical expression for the velocity in the long-time limit, which is employed to analyze the characteristics of directed motion. Notably, the velocity can exhibit multiple inversions, and to achieve directed motion, distinct, nonzero transition rates between lattice states are required.
10 pages, 4 figures
References in corpus (25)
- Brownian motors: noisy transport far from equilibrium
- Artificial Brownian motors: Controlling transport on the nanoscale
- Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates
- Voltage rectification by a SQUID ratchet
- Directed Transport of Atoms in a Hamiltonian Quantum Ratchet
- Periodically driven Quantum Ratchets: Symmetries and Resonances
- Robust Digital Holography For Ultracold Atom Trapping
- Lindblad rate equations
- Soliton ratchets induced by ac forces with harmonic mixing
- Soliton ratchets
- Coherent spin ratchets: A spin-orbit based quantum ratchet mechanism for spin-polarized currents in ballistic conductors
- Ratchet behavior in nonlinear Klein-Gordon systems with point-like inhomogeneities
- Flux reversal in a two-state symmetric optical thermal ratchet
- Quantum Ratchets
- Circular and linear magnetic quantum ratchet effects in dual-grating-gate CdTe-based nanostructures
- Soliton ratchets out of point-like inhomogeneities
- A regular Hamiltonian halting ratchet for matter wave transport
- Many-body Quantum Chaos and Entanglement in a Quantum Ratchet
- Scaling Theory of Quantum Ratchet
- Quantum ratchet transport with minimal dispersion rate
- Interplay between quantum dissipation and an in-plane magnetic field in the spin ratchet effect
- Charge ratchet from spin flip: space-time symmetry paradox
- Phonon-induced quantum ratchet in the exciton spin dynamics in diluted magnetic semiconductors in a magnetic field
- Flux reversal in a simple random walk model on a fluctuating symmetric lattice
- Quantum stochastic transport along chains