Criticality-induced universality in ratchets. (English) Zbl 1194.81101
J. Phys. A, Math. Theor. 43, No. 32, Article ID 322001, 8 p. (2010); corrigendum ibid. 54, No. 20, Article ID 209501, 2 p. (2021).
Summary: Conclusive mathematical arguments are presented supporting the ratchet conjecture [R. Chacón, J. Phys. A, Math. Theor. 40, No. 22, F413–F419 (2007; Zbl 1114.81050)], i.e. the existence of a universal force waveform which optimally enhances directed transport by symmetry breaking. Specifically, such a particular waveform is shown to be unique for both temporal and spatial biharmonic forces, and general (non-perturbative) laws providing the dependence of the strength of directed transport on the force parameters are deduced for these forces. The theory explains previous results for a great diversity of systems subjected to such biharmonic forces and provides a universal quantitative criterion to optimize any application of the ratchet effect induced by symmetry breaking of temporal and spatial biharmonic forces.
MSC:
81Q37 | Quantum dots, waveguides, ratchets, etc. |
82C70 | Transport processes in time-dependent statistical mechanics |
82C28 | Dynamic renormalization group methods applied to problems in time-dependent statistical mechanics |
81R40 | Symmetry breaking in quantum theory |