1 2 M ar 2 00 3 Variable range hopping and quantum creep in one dim ension

Com puting theresponseofa disordered elasticsystem to an externaldriving force isa long standing problem . Thisisoftheoreticalim portance and also relevantfora host ofexperim entalsystem s,both classicaland quantum .Forclassicalsystem s,typicalexperim entalrealizations are dom ain walls [1,2]and vortex lattice in type IIsuperconductors[3,4]. Pinned quantum crystalsare charge or spin density waves [5],W igner crystalin two dim ensionalelectron gas[6,7]and disordered Luttinger liquids [8]. In the absence ofquantum or therm al uctuationsdisorderleadsto pinning orlocalization.Itwas initiallybelieved thattherm alactivation overbarriersbetween pinned stateswould result[9]in v(F ) F albeit with an exponentially sm allm obility . However,the glassy natureofsuch disordered elasticsystem sleadsinstead to divergentbarriersand to a non linearresponse [10,11]oftheform v = exp( F )known ascreep [3].