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• W3214944432 abstract "Abstract We investigate the biased quenched trap model on top of a two-dimensional lattice in the case of diverging expected dwell times. By utilizing the double-subordination approach and calculating the return probability in 2D, we explicitly obtain the disorder averaged probability density function of the particle’s position as a function of time (for any given bias) in the limit of large times ( t → ∞). The first and second moments are calculated, and a formula for a general μ th moment is found. The behavior of the first moment, i.e. ⟨ x ( t )⟩, presents non-linear response both in time and in the applied external force F 0 . While the non-linearity in time occurs for any measurement time t , the non-linearity in F 0 is expected only when <?CDATA $t;gtrsim ;{left({F}_{0}leftvert mathrm{ln}({F}_{0})rightvert right)}^{-2/alpha }$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline overflow=scroll> <mml:mi>t</mml:mi> <mml:mspace width=thinmathspace /> <mml:mo>≳</mml:mo> <mml:mspace width=thinmathspace /> <mml:msup> <mml:mrow> <mml:mfenced close=) open=(> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>F</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mfenced close=| open=|> <mml:mrow> <mml:mi>ln</mml:mi> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>F</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> <mml:mo>/</mml:mo> <mml:mi>α</mml:mi> </mml:mrow> </mml:msup> </mml:math> where α = T / T g , for temperatures T < T g . We support our analytic results by comparison to numerical simulations." @default.
• W3214944432 created "2021-12-06" @default.
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• W3214944432 date "2022-03-01" @default.
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• W3214944432 title "The case of the biased quenched trap model in two dimensions with diverging mean dwell times" @default.
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