We study various models of independent particles hopping between energy `traps' with a density barriers , on d-dimensional lattice or fully connected lattice. If decays exponentially, true dynamical phase transition high-temperature `liquid' and low-temperature `aging' occurs. More generally, however, one expects that for large class `interrupted' aging effects appear at low enough temperatures, an ergodic time growing faster than exponentially. The relaxation functions exhibit...

We consider the one-dimensional lattice model of interacting fermions with disorder studied previously by Oganesyan and Huse [Phys. Rev. B 75, 155111 (2007)]. To characterize a possible many-body localization transition as function strength $W$, we use an exact renormalization procedure in configuration space that generalizes Aoki real-space for Anderson one-particle models [H. Aoki, J. Phys. C 13, 3369 (1980)]. focus on statistical properties renormalized hopping ${V}_{L}$ between two...

Abstract For the discrete-time or continuous-time Markov spin models for image generation when each pixel <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mo>.</mml:mo> <mml:mi>N</mml:mi> </mml:mrow> </mml:math> can take only two values <mml:msub> <mml:mi>S</mml:mi> </mml:msub> <mml:mo>±</mml:mo> , finite-time forward propagator depends on initial and final configurations of...

Sinai's model of diffusion in one dimension with random local bias is studied by a real space renormalization group, which yields exact results at long times. The effects an additional small uniform force are also studied. We obtain analytically the scaling form distribution position x(t) particle, probability it not returning to origin, and distributions first passage times, infinite sample as well presence boundary finite but large sample. compute meeting time two particles same...

The nonequilibrium Fokker-Planck dynamics in an arbitrary force field f[over ⃗](x[over ⃗]) dimension N is revisited via the correspondence with non-Hermitian quantum mechanics a real scalar potential V(x[over and purely imaginary vector [-iA[over ⃗])] of amplitude A[over ⃗]). relevant parameters irreversibility are then N(N-1)/2 magnetic matrix elements B_{nm}(x[over ⃗])=-B_{mn}(x[over ⃗])=∂_{n}A_{m}(x[over ⃗])-∂_{m}A_{n}(x[over ⃗]), while it enlightening to explore corresponding gauge...

Sinai's model of diffusion in one dimension with random local bias is studied by a real space renormalization group which yields asymptotically exact long time results. The distribution the position particle and probability it not returning to origin are obtained, as well two-time exhibits ``aging'' $\mathrm{ln}t/\mathrm{ln}{t}^{\ensuremath{'}}$ scaling singularity at $x(t)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}x({t}^{\ensuremath{'}})$. effects small uniform force also studied....

The paper deals with exponential functionals of the linear Brownian motion which arise in different contexts, such as continuous time finance models and one-dimensional disordered models. We study some properties these relation problem a particle coupled to heat bath Wiener potential. Explicit expressions for distribution free energy are presented.

Abstract The large deviation properties of trajectory observables for chaotic non-invertible deterministic maps as studied recently by Smith (2022 Phys. Rev. E 106 L042202) and Gutierrez et al (2023 arXiv:2304.13754 ) are revisited in order to analyze detail the similarities differences with case stochastic Markov chains. More concretely, we focus on simplest example displaying two essential local stretching global folding, namely doubling map <?CDATA $ x_{t+1} = 2 x_t [\text{mod} 1] $?>...

Abstract The Pelikan random trajectories <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>x</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:mo>∈</mml:mo> <mml:mo stretchy="false">[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> are generated by choosing the chaotic doubling map <mml:mo>+</mml:mo> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> <mml:mi>mod</mml:mi> stretchy="false">]</mml:mo> with...

Abstract In the field of Markov models for image generation, main idea is to learn how non-trivial images are gradually destroyed by a trivial forward dynamics over large time window <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>t</mml:mi> stretchy="false">]</mml:mo> </mml:mrow> </mml:math> converging towards pure noise accent="false" stretchy="false">→</mml:mo>...

Within the Wilson RG of 'incomplete integration' as a function RG-time $t$, non-linear differential flow for energy $E_t[\phi(.)]$ translates probability distribution $P_t[\phi(.)] \sim e^{- E_t[\phi(.)]} $ into linear Fokker-Planck associated to independent non-identical Ornstein-Uhlenbeck processes Fourier modes. The corresponding Langevin stochastic equation real-space field $\phi_t(\vec x)$ can be then interpreted within Carosso perspective genuine infinitesimal...

We give a physical description in terms of percolation theory the phase transition that occurs when disorder increases random antiferromagnetic spin-1 chain between gapless with hidden topological order and singlet phase. study statistical properties clusters by numerical simulations, we compute exact exponents characterizing real-space renormalization group calculation.

Markov processes with stochastic resetting towards the origin generically converge non-equilibrium steady-states. Long dynamical trajectories can be thus analyzed via large deviations at Level 2.5 for joint probability of empirical density and flows, or semi-Markov excursions between consecutive resets. The properties general time-additive observables involving position increments trajectory are then in terms appropriate tilted corresponding conditioned obtained generalization Doob's...

Abstract For the 2D matrix Langevin dynamics that correspond to continuous-time limit of products some 2 × random matrices, finite-time Lyapunov exponent can be written as an additive functional associated Riccati process submitted on infinite periodic ring. Its large deviations properties thus analyzed from two points view are equivalent in end by consistency but give different perspectives. In first approach, one starts at level 2.5 for joint probability empirical density and current...

The nonequilibrium dynamics of classical random Ising spin chains with nonconserved magnetization are studied using an asymptotically exact real space renormalization group (RSRG). We focus on field model (RFIM) and without a uniform applied field, as well glass in field. For the RFIM we consider universal regime where temperature both much smaller than exchange coupling. In this regime, Imry-Ma length that sets scale equilibrium correlations is large coarsening domains from initial...

We study some transport properties of a one dimensional disordered system finite length N. In this particles are subject to random forces resulting both from thermal noise and fom quenched force F(x) which models the inhomogeneous medium. The latter is distributed as white with non-zero average bias. Imposing fixed concentration at end points chain yields steady current J(N) depends on environments {F(x)}. problem computing probability distribution P(J) over addressed. Our approach based...

We study by exact diagonalization the localization properties of phonons in mass-disordered harmonic crystals dimension $d=1,2,3$. focus on behavior typical Inverse Participation Ratio $Y_2(\omega,L)$ as a function frequency $\omega$ and linear length $L$ disordered samples. In dimensions $d=1$ $d=2$, we find that low-frequency part $\omega \to 0$ spectrum satisfies following finite-size scaling $L Y_2(\omega,L)=F_{d=1}(L^{1/2} \omega)$ $L^2 Y_2(\omega,L)=F_{d=2}((\ln L)^{1/2} with...

Filyokov and Karpov [Inzhenerno-Fizicheskii Zhurnal 13, 624 (1967)] have proposed a theory of non-equilibrium steady states in direct analogy with the equilibrium : principle is to maximize Shannon entropy associated probability distribution dynamical trajectories presence constraints, including macroscopic current interest, via method Lagrange multipliers. This maximization leads directly generalized Gibbs for trajectories, some fluctuation relation integrated current. The simplest...

Abstract The large deviations at level 2.5 are applied to Markov processes with absorbing states in order obtain the explicit extinction rate of metastable quasi-stationary terms their empirical time-averaged density and flows over a time-window T . standard spectral problem for slowest relaxation mode can be recovered from full optimization all these observables equivalence understood via Doob generator process conditioned survive up time deviation properties any time-additive observable...

Abstract Behind the nice unification provided by notion of level 2.5 in field large deviations for time-averages over a long Markov trajectory, there are nevertheless very important qualitative differences between meaning diffusion processes on one hand, and chains either discrete-time or continuous-time other hand. In order to analyze these detail, it is thus useful consider two types random walks converging towards given process dimension d involving arbitrary space-dependent forces...

For Anderson localization on the Cayley tree, we study statistics of various observables as a function disorder strength W and number N generations. We first consider Landauer transmission TN. In localized phase, its logarithm follows traveling wave form where (i) disorder-averaged value moves linearly length diverges with νloc = 1 (ii) variable t* is fixed random power-law tail P*(t*) ∼ 1/(t*)1+β(W) for large 0 < β(W) ⩽ 1/2, so that all integer moments TN are governed by rare events....