Localization of thermal packets and metastable states in Sinai model

We consider the Sinai model describing a particle diffusing in a 1D random force field. As shown by Golosov, this model exhibits a strong localization phenomenon for the thermal packet: the disorder average of the thermal distribution of the relative distance y=x-m(t), with respect to the (disorder-dependent) most probable position m(t), converges in the limit of infinite time towards a distribution P(y). In this paper, we revisit this question of the localization of the thermal packet. We first generalize the result of Golosov by computing explicitly the joint asymptotic distribution of relative position y=x(t)-m(t) and relative energy u=U(x(t))-U(m(t)) for the thermal packet. Next, we compute in the infinite-time limit the localization parameters Y_k, representing the disorder-averaged probabilities that k particles of the thermal packet are at the same place, and the correlation function C(l) representing the disorder-averaged probability that two particles of the thermal packet are at a distance l from each other. We moreover prove that our results for Y_k and C(l) exactly coincide with the thermodynamic limit of the analog quantities computed for independent particles at equilibrium in a finite sample of length L. Finally, we discuss the properties of the finite-time metastable states that are responsible for the localization phenomenon and compare with the general theory of metastable states in glassy systems, in particular as a test of the Edwards conjecture.Comment: 17 page

Strain localization driven by thermal decomposition during seismic shear

Field and laboratory observations show that shear deformation is often extremely localized at seismic slip rates, with a typical deforming zone width on the order of a few tens of microns. This extreme localization can be understood in terms of thermally driven weakening mechanisms. A zone of initially high strain rate will experience more shear heating and thus weaken faster, making it more likely to accommodate subsequent deformation. Fault zones often contain thermally unstable minerals such as clays or carbonates, which devolatilize at the high temperatures attained during seismic slip. In this paper, we investigate how these thermal decomposition reactions drive strain localization when coupled to a model for thermal pressurization of in situ groundwater. Building on Rice et al. (2014), we use a linear stability analysis to predict a localized zone thickness that depends on a combination of hydraulic, frictional, and thermochemical properties of the deforming fault rock. Numerical simulations show that the onset of thermal decomposition drives additional strain localization when compared with thermal pressurization alone and predict localized zone thicknesses of ∼7 and ∼13 μm for lizardite and calcite, respectively. Finally we show how thermal diffusion and the endothermic reaction combine to limit the peak temperature of the fault and that the pore fluid released by the reaction provides additional weakening of ∼20–40% of the initial strength

Thermal behavior induced by vacuum polarization on causal horizons in comparison with the standard heat bath formalism

Modular theory of operator algebras and the associated KMS property are used to obtain a unified description for the thermal aspects of the standard heat bath situation and those caused by quantum vacuum fluctuations from localization. An algebraic variant of lightfront holography reveals that the vacuum polarization on wedge horizons is compressed into the lightray direction. Their absence in the transverse direction is the prerequisite to an area (generalized Bekenstein-) behavior of entropy-like measures which reveal the loss of purity of the vacuum due to restrictions to wedges and their horizons. Besides the well-known fact that localization-induced (generalized Hawking-) temperature is fixed by the geometric aspects, this area behavior (versus the standard volume dependence) constitutes the main difference between localization-caused and standard thermal behavior.Comment: 15 page Latex, dedicated to A. A. Belavin on the occasion of his 60th birthda

Localization properties of the anomalous diffusion phase x tμx ~ t^{\mu} in the directed trap model and in the Sinai diffusion with bias

We study the anomalous diffusion phase $x ~ t^{\mu}$ with $0<\mu<1$ which exists both in the Sinai diffusion at small bias, and in the related directed trap model presenting a large distribution of trapping time $p(\tau) \sim 1/\tau^{1+\mu}$. Our starting point is the Real Space Renormalization method in which the whole thermal packet is considered to be in the same renormalized valley at large time : this assumption is exact only in the limit $\mu \to 0$ and corresponds to the Golosov localization. For finite $\mu$, we thus generalize the usual RSRG method to allow for the spreading of the thermal packet over many renormalized valleys. Our construction allows to compute exact series expansions in $\mu$ of all observables : at order $\mu^n$, it is sufficient to consider a spreading of the thermal packet onto at most $(1+n)$ traps in each sample, and to average with the appropriate measure over the samples. For the directed trap model, we show explicitly up to order $\mu^2$ how to recover the diffusion front, the thermal width, and the localization parameter $Y_2$. We moreover compute the localization parameters $Y_k$ for arbitrary $k$, the correlation function of two particles, and the generating function of thermal cumulants. We then explain how these results apply to the Sinai diffusion with bias, by deriving the quantitative mapping between the large-scale renormalized descriptions of the two models.Comment: 33 pages, 3 eps figure

Looking beyond the Thermal Horizon: Hidden Symmetries in Chiral Models

In thermal states of chiral theories, as recently investigated by H.-J. Borchers and J. Yngvason, there exists a rich group of hidden symmetries. Here we show that this leads to a radical converse of of the Hawking-Unruh observation in the following sense. The algebraic commutant of the algebra associated with a (heat bath) thermal chiral system can be used to reprocess the thermal system into a ground state system on a larger algebra with a larger localization space-time. This happens in such a way that the original system appears as a kind of generalized Unruh restriction of the ground state sytem and the thermal commutant as being transmutated into newly created ``virgin space-time region'' behind a horizon. The related concepts of a ``chiral conformal core'' and the possibility of a ``blow-up'' of the latter suggest interesting ideas on localization of degrees of freedom with possible repercussion on how to define quantum entropy of localized matter content in Local Quantum Physics.Comment: 17 pages, tcilatex, still more typos removed and one reference correcte