2002/05/22 by D. A. Gorokhov, Denis A. Gorokhov, Daniel S. Fisher +2 · 1 citation
Physics and Astronomy · #Opinion Dynamics and Social Influence #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech #cond-mat.supr-con
paper · pdf · doi:10.1103/physrevb.66.214203
published as Phys. Rev. B 66, 214203 (2002) · RevTeX, 30 pages, 8 figures inserted
arxiv created 2002/05/22 · openalex publication_date 2002/12/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The dynamics of an elastic medium driven through a random medium by a small applied force is investigated in the low-temperature limit where quantum fluctuations dominate. The motion proceeds via tunneling of segments of the manifold through barriers whose size grows with decreasing driving force f. At zero temperature and in the limit of small drive, the average velocity has the form v\ensuremath∝exp[\ensuremath-const/\ensuremath\Elzxh^\ensuremathαf^\ensuremathμ]. For strongly dissipative dynamics, there is a wide range of forces where the dissipation dominates and the velocity--force characteristics takes the form v\ensuremath∝exp[\ensuremath-S(f)/\ensuremath\Elzxh], with S(f)\ensuremath∝1/f^(d+2\ensuremathζ)/(2\ensuremath-\ensuremathζ) the action for a typical tunneling event, the force dependence being determined by the roughness exponent \ensuremathζ of the d-dimensional manifold. This result agrees with the one obtained via simple scaling considerations. Surprisingly, for asymptotically low forces or for the case when the massive dynamics is dominant, the resulting quantum creep law is not of the usual form with a rate proportional to exp[\ensuremath-S(f)/\ensuremath\Elzxh]; rather we find v\ensuremath∝exp\ensuremath-[S(f)/\ensuremath\Elzxh]2 corresponding to \ensuremathα=2 and \ensuremathμ=2(d+2\ensuremathζ\ensuremath-1)/(2\ensuremath-\ensuremathζ), with \ensuremathμ/2 the naive scaling exponent for massive dynamics. Our analysis is based on the quasiclassical Langevin approximation with a noise obeying the quantum fluctuation-dissipation theorem. The many space and time scales involved in the dynamics are treated via a functional renormalization group analysis related to that used previously to treat the classical dynamics of such systems. Various potential difficulties with these approaches to the multi-scale dynamics---both classical and quantum---are raised and questions about the validity of the results are discussed.