Scaling theory of a quantum ratchet

Article

关键词: CHAOTIC TRANSPORT;    BROWNIAN-MOTION;    LOCALIZATION;    DYNAMICS;    POTENTIALS;    DIFFUSION;    PARTICLE;   

DOI  :  10.1103/PhysRevB.99.064307

来源: SCIE

【 摘 要 】

The asymmetric responses of the system between the external force of the right and left directions are called nonreciprocal. There are many examples of nonreciprocal responses, such as the rectification by the p-n junction. However, the quantum-mechanical wave does not distinguish between the right and the left directions as long as the time-reversal symmetry is intact, and it is a highly nontrivial issue how the nonreciprocal nature originates in quantum systems. Here we demonstrate by the quantum ratchet model, i.e., a quantum particle in an asymmetric periodic potential, that the dissipation characterized by a dimensionless coupling constant a plays an essential role for nonlinear nonreciprocal response. The temperature (T) dependence of the second-order nonlinear mobility mu(2) is found to be mu(2) similar to T(6/alpha)-4 for alpha < 1, and mu similar to T2(alpha-1) for alpha > 1, respectively, where alpha(c) = 1 is the critical point of the localization-delocalization transition, i.e., Schmid transition. On the other hand, mu(2)shows the behavior mu 2 similar to T-11/4 in the high-temperature limit. Therefore, mu(2) shows the nonmonotonous temperature dependence corresponding to the classical-quantum crossover. The generic scaling form of the velocity v as a function of the external field F and temperature T is also discussed. These findings are relevant to the heavy atoms in metals, resistive superconductors with vortices and Josephson junction system and will pave a way to control the nonreciprocal responses.

【 授权许可】

Free