Einstein relation and linear response in one-dimensional Mott variable-range hopping

Faggionato, Alessandra; Gantert, Nina; Salvi, Michele

doi:10.48550/arxiv.1708.09610

Cited by 3 publications

(9 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hence, due to Proposition 2, the family of Radon-Nykodim derivatives dQ λ dQ0 , λ ∈ [0, λ 0 ], is relatively compact for the L 2 (Q 0 )-weak topology. In [6] we then prove that any limit point of this family is given by 1. As a byproduct of the representation Q λ (f ) = Q 0 ( dQ λ dQ0 f ) and of the weak convergence dQ λ dQ0 1, we get the continuity of ( 8) at λ = 0.…”

Section: Linear Response and Einstein Relation For The Biased 1d Mott...mentioning

confidence: 90%

“…Theorem 3 [6] Suppose that E[e pZ0 ] < ∞ for some p ≥ 2 and let q be the conjugate exponent of p, i.e. q satisfies 1 p + 1 q = 1.…”

Section: Linear Response and Einstein Relation For The Biased 1d Mott...mentioning

confidence: 99%

“…Without entering into the details of the proof (which can be found in [6]) we give some comments on the derivation of Theorem 3 from Proposition 2. To this aim, we take for simplicity p = 2.…”

Section: Linear Response and Einstein Relation For The Biased 1d Mott...mentioning

confidence: 99%

“…As discussed with more details in [6] as ε goes to zero the family of potential forms ∇g f ε converges in L 2 (M ) to a potential form h f :…”

Section: Linear Response and Einstein Relation For The Biased 1d Mott...mentioning

confidence: 99%

“…Theorem 4 [6] Suppose E(e pZ0 ) < ∞ for some p > 2. Then, for any f ∈ H −1 ∩ L 2 (Q 0 ), ∂ λ=0 Q λ (f ) exists.…”

Section: Linear Response and Einstein Relation For The Biased 1d Mott...mentioning

confidence: 99%

See 4 more Smart Citations

1D Mott Variable-Range Hopping with External Field

Faggionato

2019

Springer Proceedings in Mathematics &Amp; Statistics

View full text Add to dashboard Cite

Mott variable-range hopping is a fundamental mechanism for electron transport in disordered solids in the regime of strong Anderson localization. We give a brief description of this mechanism, recall some results concerning the behavior of the conductivity at low temperature and describe in more detail recent results (obtained in collaboration with N. Gantert and M. Salvi) concerning the one-dimensional Mott variablerange hopping under an external field 1 .

show abstract

Section: Linear Response and Einstein Relation For The Biased 1d Mott...mentioning

confidence: 90%

“…Theorem 3 [6] Suppose that E[e pZ0 ] < ∞ for some p ≥ 2 and let q be the conjugate exponent of p, i.e. q satisfies 1 p + 1 q = 1.…”

Section: Linear Response and Einstein Relation For The Biased 1d Mott...mentioning

confidence: 99%

Section: Linear Response and Einstein Relation For The Biased 1d Mott...mentioning

confidence: 99%

“…As discussed with more details in [6] as ε goes to zero the family of potential forms ∇g f ε converges in L 2 (M ) to a potential form h f :…”

Section: Linear Response and Einstein Relation For The Biased 1d Mott...mentioning

confidence: 99%

“…Theorem 4 [6] Suppose E(e pZ0 ) < ∞ for some p > 2. Then, for any f ∈ H −1 ∩ L 2 (Q 0 ), ∂ λ=0 Q λ (f ) exists.…”

Section: Linear Response and Einstein Relation For The Biased 1d Mott...mentioning

confidence: 99%

See 3 more Smart Citations

1D Mott Variable-Range Hopping with External Field

Faggionato

2019

Springer Proceedings in Mathematics &Amp; Statistics

View full text Add to dashboard Cite

show abstract

Regularity of biased 1D random walks in random environment

Faggionato¹,

Salvi²

2019

ALEA

View full text Add to dashboard Cite

We study the asymptotic properties of nearest-neighbor random walks in 1d random environment under the influence of an external field of intensity λ ∈ R. For ergodic shift-invariant environments, we show that the limiting velocity v(λ) is always increasing and that it is everywhere analytic except at most in two points λ− and λ+. When λ− and λ+ are distinct, v(λ) might fail to be continuous. We refine the assumptions in [34] for having a recentered CLT with diffusivity σ 2 (λ) and give explicit conditions for σ 2 (λ) to be analytic. For the random conductance model we show that, in contrast with the deterministic case, σ 2 (λ) is not monotone on the positive (resp. negative) half-line and that it is not differentiable at λ = 0. For this model we also prove the Einstein Relation, both in discrete and continuous time, extending the result of [25].

show abstract

Scaling of sub-ballistic 1D Random Walks among biased Random Conductances

Berger¹,

Salvi²

2017

Preprint

View full text Add to dashboard Cite

We consider two models of one-dimensional random walks among biased i.i.d. random conductances: the first is the classical exponential tilt of the conductances, while the second comes from the effect of adding an external field to a random walk on a point process (the bias depending on the distance between points). We study the case when the walk is transient to the right but sub-ballistic, and identify the correct scaling of the random walk: we find α P r0, 1s such that log Xn{ log n Ñ α. Interestingly, α does not depend on the intensity of the bias in the first case, but it does in the second case.

show abstract

Einstein relation and linear response in one-dimensional Mott variable-range hopping

Cited by 3 publications

References 32 publications

1D Mott Variable-Range Hopping with External Field

1D Mott Variable-Range Hopping with External Field

Regularity of biased 1D random walks in random environment

Scaling of sub-ballistic 1D Random Walks among biased Random Conductances

Contact Info

Product

Resources

About