The one-dimensional contact process with weak to intermediate quenched disorder in its transmission rates is investigated via quasi-stationary Monte Carlo simulation. We address the contested questions of both the nature of dynamical scaling, conventional or activated, as well as of universality of critical exponents by employing a scaling analysis of the distribution of lifetimes and the quasi-stationary density of infection. We find activated scaling to be the appropriate description for all disorder strengths considered. Critical exponents are disorder dependent and approach the values expected for the limit of strong disorder as predicted by strong-disorder renormalization group analysis of the process. However, even for the strongest disorder under consideration no strong-disorder exponents are found.
The critical behavior of the contact process in disordered and periodic binary 2d-lattices is investigated numerically by means of Monte Carlo simulations as well as via an analytical approximation and standard mean field theory. Phase-separation lines calculated numerically are found to agree well with analytical predictions around the homogeneous point. For the disordered case, values of static scaling exponents obtained via quasi-stationary simulations are found to change with disorder strength. In particular, the finite-size scaling exponent of the density of infected sites approaches a va…
Motivated by mapping from a stochastic system with spatially random rates, we consider disordered non-conserving free-fermion systems using a scaling procedure for the equations of motion. This approach demonstrates disorder-induced localization acting in competition with the asymmetric driving. We discuss the resulting implications for the original stochastic system.
The supercritical series expansion of the survival probability for the one-dimensional contact process in heterogeneous and disordered lattices is used for the evaluation of the loci of critical points and critical exponents $β$. The heterogeneity and disorder are modeled by considering binary regular and irregular lattices of nodes characterized by different recovery rates and identical transmission rates. Two analytical approaches based on Nested Padé approximants and Partial Differential approximants were used in the case of expansions with respect to two variables (two recovery rates) for …
We elucidate the effects of chiral quenched disorder on the scaling properties of pure systems by considering a reduced model that is a variant of the quenched disordered cubic anisotropic O(N) model near its second order phase transition. A generic short-ranged Gaussian disorder distribution is considered. For distributions not invariant under spatial inversion ({hence chiral}), the scaling exponents are found to depend continuously on a model parameter that describes the extent of inversion symmetry breaking. Experimental and phenomenological implications of our results are discussed.
The packing of hard-core particles in contact with their neighbors is considered as the simplest model of disordered particulate media. We formulate the statically determinate problem which allows analytical investigation of the statistical distribution of contact force magnitude. The toy-model of the Boltzmann type equation for the probability of contact force distribution is formulated and studied. An experimentally observed exponential distribution is derived.
The critical behavior of a quenched random hypercubic sample of linear size $L$ is considered, within the ``random-$T_{c}$'' field-theoretical mode, by using the renormalization group method. A finite-size scaling behavior is established and analyzed near the upper critical dimension $d=4-ε$ and some universal results are obtained. The problem of self-averaging is clarified for different critical regimes.
We study the local persistence probability during non-stationary time evolutions in disordered contact processes with long-range interactions by a combination of the strong-disorder renormalization group (SDRG) method, a phenomenological theory of rare regions, and numerical simulations. We find that, for interactions decaying as an inverse power of the distance, the persistence probability tends to a non-zero limit not only in the inactive phase but also in the critical point. Thus, unlike in the contact process with short-range interactions, the persistence in the limit $t\to\infty$ is a dis…
The critical behavior of the contact process (CP) in heterogeneous periodic and weakly-disordered environments is investigated using the supercritical series expansion and Monte Carlo (MC) simulations. Phase-separation lines and critical exponents $β$ (from series expansion) and $η$ (from MC simulations) are calculated. A general analytical expression for the locus of critical points is suggested for the weak-disorder limit and confirmed by the series expansion analysis and the MC simulations. Our results for the critical exponents show that the CP in heterogeneous environments remains in the …
We find that the statistics of levels undergoing metal-insulator transition in systems with multi-parametric Gaussian disorders and non-interacting electrons behaves in a way similar to that of the single parametric Brownian ensembles \cite{dy}. The latter appear during a Poisson $\to$ Wigner-Dyson transition, driven by a random perturbation. The analogy provides the analytical evidence for the single parameter scaling of the level-correlations in disordered systems as well as a tool to obtain them at the critical point for a wide range of disorders.
We consider the three-dimensional site-diluted Ising model with power-law correlated defects and study the critical behavior of the second-moment correlation length and the magnetic susceptibility in the high-temperature phase. By comparing, for various defect correlation strengths, the extracted critical exponents $ν$ and $γ$ with the results of our previous finite-size scaling study, we consolidate the exponent estimates.
We study coarsening dynamics in the ferromagnetic random bond Ising model in d = 1; 2. We focus on the validity of super-universality and the scaling properties of the response functions. In the d = 1 case, we obtain a complete understanding of the evolution, from pre- asymptotic to asymptotic behavior. The corresponding response function shows a clear violation of super-universality. Further, our results for d = 1; 2 settle the controversy regarding the decay exponent which characterizes the response function.
An asymmetric variant of the contact process where the activity spreads with different and independent random rates to the left and to the right is introduced. A real space renormalization scheme is formulated for model by means of which it is shown that the local asymmetry of spreading is irrelevant on large scales if the model is globally (statistically) symmetric. Otherwise, in the presence of a global bias in either direction, the renormalization method predicts two distinct phase transitions, which are related to the spreading of activity in and against the direction of the bias. The latt…
One of the major factors governing the mode of failure in disordered solids is the effective range $R$, over which the stress field is modified following a local rupture event. In random fiber bundle model, considered as a prototype of disordered solids, we show that the failure mode is nucleation dominated in the large system size limit, as long as $R$ scales slower than $L^ζ$, with $ζ=2/3$. For a faster increase in $R$, the failure properties are dominated by the mean-field critical point, where the damages are uncorrelated in space. In that limit, the precursory avalanches of all sizes are …
We study the scaling laws of diffusion in two-dimensional media with long-range correlated disorder through exact enumeration of random walks. The disordered medium is modelled by percolation clusters with correlations decaying with the distance as a power law, $r^{-a}$, generated with the improved Fourier filtering method. To characterize this type of disorder, we determine the percolation threshold $p_{\text c}$ by investigating cluster-wrapping probabilities. At $p_{\text c}$, we estimate the (sub-diffusive) walk dimension $d_{\text w}$ for different correlation exponents $a$. Above $p_{\te…
The absorbing-state transition in the three-dimensional contact process with and without quenched randomness is investigated by means of Monte-Carlo simulations. In the clean case, a reweighting technique is combined with a careful extrapolation of the data to infinite time to determine with high accuracy the critical behavior in the three-dimensional directed percolation universality class. In the presence of quenched spatial disorder, our data demonstrate that the absorbing-state transition is governed by an unconventional infinite-randomness critical point featuring activated dynamical scal…
We investigate the nonequilibrium phase transition of the disordered contact process in five space dimensions by means of optimal fluctuation theory and Monte Carlo simulations. We find that the critical behavior is of mean-field type, i.e., identical to that of the clean five-dimensional contact process. It is accompanied by off-critical power-law Griffiths singularities whose dynamical exponent $z'$ saturates at a finite value as the transition is approached. These findings resolve the apparent contradiction between the Harris criterion which implies that weak disorder is renormalization-gro…
Experiments measuring contact formation between a probe and quencher in disordered chains provide information on the fundamental dynamical timescales relevant to protein folding, but their interpretation usually relies on simplified one-dimensional (1D) diffusion models. Here, we use all-atom molecular simulations to capture both the time-scales of contact formation, as well as the scaling with the length of the peptide for tryptophan triplet quenching experiments. Capturing the experimental quenching times depends on the water viscosity, but more importantly on the configurational space explo…
We derive exact probability distributions for the strain ($ε$) at which the first stress drop event occurs in uniformly strained disordered crystals, with quenched disorder introduced through polydispersity in particle sizes. We characterize these first stress drop events numerically as well as theoretically, and identify them with the first contact breaking event in the system. Our theoretical results are corroborated with numerical simulations of quasistatic volumetric strain applied to disordered near-crystalline configurations of athermal soft particles. We develop a general technique to d…
We study the approach to jamming in hard-sphere packings, and, in particular, the pair correlation function $g_{2}(r)$ around contact, both theoretically and computationally. Our computational data unambiguously separates the narrowing delta-function contribution to $g_{2}$ due to emerging interparticle contacts from the background contribution due to near contacts. The data also shows with unprecedented accuracy that disordered hard-sphere packings are strictly isostatic, i.e., the number of exact contacts in the jamming limit is exactly equal to the number of degrees of freedom, once rattler…
We revisit the effects of short-ranged random quenched disorder on the universal scaling properties of the classical $N$-vector model with cubic anisotropy. We set up the nonconserved relaxational dynamics of the model, and study the universal dynamic scaling near the second order phase transition. We extract the critical exponents and the dynamic exponent in a one-loop dynamic renormalisation group calculation with short-ranged isotropic disorder. We show that the dynamics near a critical point is generically slower when the quenched disorder is relevant than when it is not, independent of wh…
We study the nonequilibrium phase transition in the one-dimensional contact process with quenched spatial disorder by means of large-scale Monte-Carlo simulations for times up to $10^9$ and system sizes up to $10^7$ sites. In agreement with recent predictions of an infinite-randomness fixed point, our simulations demonstrate activated (exponential) dynamical scaling at the critical point. The critical behavior turns out to be universal, even for weak disorder. However, the approach to this asymptotic behavior is extremely slow, with crossover times of the order of $10^4$ or larger. In the Grif…
Scaling properties of an interface representation of the critical contact process are studied in dimensions 1 - 3. Simulations confirm the scaling relation beta_W = 1 - theta between the interface-width growth exponent beta_W and the exponent theta governing the decay of the order parameter. A scaling property of the height distribution, which serves as the basis for this relation, is also verified. The height-height correlation function shows clear signs of anomalous scaling, in accord with Lopez' analysis [Phys. Rev. Lett. 83, 4594 (1999)], but no evidence of multiscaling.
We study the nonequilibrium phase transition in the two-dimensional contact process on a randomly diluted lattice by means of large-scale Monte-Carlo simulations for times up to $10^{10}$ and system sizes up to $8000 \times 8000$ sites. Our data provide strong evidence for the transition being controlled by an exotic infinite-randomness critical point with activated (exponential) dynamical scaling. We calculate the critical exponents of the transition and find them to be universal, i.e., independent of disorder strength. The Griffiths region between the clean and the dirty critical points exhi…
We study the continuous absorbing-state phase transition in the contact process on the Voronoi-Delaunay lattice. The Voronoi construction is a natural way to introduce quenched coordination disorder in lattice models. We simulate the disordered system using the quasistationary simulation method and determine its critical exponents and moment ratios. Our results suggest that the critical behavior of the disordered system is unchanged with respect to that on a regular lattice, i.e., that of directed percolation.
We study the time-dependence of the local persistence probability during a non-stationary time evolution in the disordered contact process in $d=1,2$, and $3$ dimensions. We present a method for calculating the persistence with the strong-disorder renormalization group (SDRG) technique, which we then apply in the critical point analytically for $d=1$ and numerically for $d=2,3$. According to the results, the average persistence decays at late times as an inverse power of the logarithm of time, with a universal, dimension-dependent generalized exponent. For $d=1$, the distribution of sample-dep…
For disordered elastic manifolds in the ground state (equilibrium) we obtain the critical exponents for the roughness and the correction-to-scaling up to 3-loop order, i.e. third order in $ε=4-d$, where $d$ is the internal dimension $d$. We also give the full 2-point function up to order $ε^{2}$, i.e. at 2-loop order.
We consider numerically the depinning transition in the random-field Ising model. Our analysis reveals that the three and four dimensional model displays a simple scaling behavior whereas the five dimensional scaling behavior is affected by logarithmic corrections. This suggests that d=5 is the upper critical dimension of the depinning transition in the random-field Ising model. Furthermore, we investigate the so-called creep regime (small driving fields and temperatures) where the interface velocity is given by an Arrhenius law.
We show, using detailed numerical analysis and theoretical arguments, that the normalized participation number of the stationary solutions of disordered nonlinear lattices obeys a one-parameter scaling law. Our approach opens a new way to investigate the interplay of Anderson localization and nonlinearity based on the powerful ideas of scaling theory.
We study the diffusion on an annealed disordered lattice with a local dynamical reorganization of bonds. We show that the typical rearrangement time depends on the renewal rate like $t_r \sim τ^α$ with $α\neq 1$. This implies that the crossover time to normal diffusion in a slow rearrangement regime shows a critical behavior at the percolation threshold. New scaling relations for the dependence of the diffusion coefficient on the renewal rate are obtained. The derivation of scaling exponents confirms the crucial role of singly connected bonds in transport properties. These results are checked …
We study the scaling properties of a one-dimensional interface at equilibrium, at finite temperature and in a disordered environment with a finite disorder correlation length. We focus our approach on the scalings of its geometrical fluctuations as a function of its length. At large lengthscales, the roughness of the interface, defined as the variance of its endpoint fluctuations, follows a power-law behaviour whose exponent characterises its superdiffusive behaviour. In 1+1 dimensions, the roughness exponent is known to be the characteristic 2/3 exponent of the Kardar-Parisi-Zhang (KPZ) unive…
Folklore has, that the universal scaling properties of linear polymers in disordered media are well described by the statistics of self-avoiding walks Folklore has, that the universal scaling properties of linear polymers in disordered media are well described by the statistics of self-avoiding walks (SAWs) on percolation clusters and their critical exponent $ν_{\text{SAW}}$, with SAW implicitly referring to \emph{average} SAW. Hitherto, static averaging has been commonly used, e.g. in numerical simulations, to determine what the \emph{average} SAW is. We assert that only kinetic, rather than …
The nearest neighbor contacts between the two halves of an N-site lattice self-avoiding walk offer an unusual example of scaling random geometry: for N going to infinity they are strictly finite in number but their radius of gyration Rc is power law distributed, ~ Rc^{-τ}, where τ>1 is a novel exponent characterizing universal behavior. A continuum of diverging lengths scales is associated to the Rc distribution. A possibly super-universal τ=2 is also expected for the contacts of a self-avoiding or random walk with a confining wall.
We study Barkhausen noise in a diluted two-dimensional Ising model with the extended domain wall and weak random fields occurring due to coarse graining. We report two types of scaling behavior corresponding to (a) low disorder regime where a single domain wall slips through a series of positions when the external field is increased, and (b) large disorder regime, which is characterized with nucleation of many domains. The effects of finite concentration of nonmagnetic ions and variable driving rate on the scaling exponents is discussed in both regimes. The universal scaling behavior at low di…
We study Lévy walks in quenched disordered one-dimensional media, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling relations for the random-walk probability and for the resistivity in the equivalent electric problem, we obtain the asymptotic behavior of the mean square displacement as a function of the exponent characterizing the scatterers distribution. We demonstrate that in quenched media different average procedures can display different asymptotic behavior. In particular, we estimate the moments of the displacement averaged over processes starting f…
The onset of rigidity in interacting liquids, as they undergo a transition to a disordered solid, is associated with a rearrangement of the low-frequency vibrational spectrum. In this letter, we derive scaling forms for the singular dynamical response of disordered viscoelastic networks near both jamming and rigidity percolation. Using effective-medium theory, we extract critical exponents, invariant scaling combinations and analytical formulas for universal scaling functions near these transitions. Our scaling forms describe the behavior in space and time near the various onsets of rigidity, …
Disordered viscoelastic materials are ubiquitous and exhibit fascinating invariant scaling properties. In a companion article, we have presented comprehensive new results for the critical behavior of the dynamic susceptibility of disordered elastic systems near the onset of rigidity. Here we provide additional details of the derivation of the singular scaling forms of the longitudinal response near both jamming and rigidity percolation. We then discuss global aspects associated with these forms, and make scaling collapse plots for both undamped and overdamped dynamics in both the rigid and flo…
The quantum critical behavior of disordered itinerant ferromagnets is determined exactly by solving a recently developed effective field theory. It is shown that there are logarithmic corrections to a previous calculation of the critical behavior, and that the exact critical behavior coincides with that found earlier for a phase transition of undetermined nature in disordered interacting electron systems. This confirms a previous suggestion that the unspecified transition should be identified with the ferromagnetic transition. The behavior of the conductivity, the tunneling density of states, …
We present large-scale Monte-Carlo simulations of a two-dimensional (2d) bilayer quantum Heisenberg antiferromagnet with random dimer dilution. In contrast to the exotic scaling scenarios found in many other random quantum systems, the quantum phase transition in this system is characterized by a finite-disorder fixed point with power-law scaling. After accounting for strong corrections to scaling, characterized by a leading irrelevant exponent of ω= 0.48, we find universal, i.e., disorder-independent, critical exponents z=1.310(6) and ν=1.16(3). We discuss the consequences of these findings a…
Using extensive Monte Carlo simulations we study aging properties of two disordered systems quenched below their critical point, namely the two-dimensional random-bond Ising model and the three-dimensional Edwards-Anderson Ising spin glass with a bimodal distribution of the coupling constants. We study the two-times autocorrelation and space-time correlation functions and show that in both systems a simple aging scenario prevails in terms of the scaling variable $L(t)/L(s)$, where $L$ is the time-dependent correlation length, whereas $s$ is the waiting time and $t$ is the observation time. The…
Localization is one of the most fundamental interference phenomena caused by randomness, and its universal aspects have been extensively explored from the perspective of one-parameter scaling mainly for static properties. We numerically study dynamics of fermions on disordered onedimensional potentials exhibiting localization and find dynamical one-parameter scaling for surface roughness, which represents particle-number fluctuations at a given lengthscale, and for entanglement entropy when the system is in delocalized phases. This dynamical scaling corresponds to the Family-Vicsek scaling ori…
For phase transitions in disordered systems, an exact theorem provides a bound on the finite size correlation length exponent: ν_{FS}<= 2/d. It is believed that the true critical exponent νof a disorder induced phase transition satisfies the same bound. We argue that in disordered systems the standard averaging introduces a noise, and a corresponding new diverging length scale, characterized by ν_{FS}=2/d. This length scale, however, is independent of the system's own correlation length ξ. Therefore νcan be less than 2/d. We illustrate these ideas on two exact examples, with ν< 2/d. We propose…
We investigate the equilibrium and off-equilibrium behaviors of systems at thermal first-order transitions (FOTs) when the boundary conditions favor one of the two phases. As a theoretical laboratory we consider the two-dimensional Potts model. We show that an anomalous finite-size scaling emerges in systems with open boundary conditions favoring the disordered phase, associated with a mixed regime where the two phases are spatially separated. Correspondingly, if the system is slowly heated across the transition, the characteristic times of the off-equilibrium dynamics scale with a power of th…
The critical behavior of the disordered ferromagnetic Ising model is studied numerically by the Monte Carlo method in a wide range of variation of concentration of nonmagnetic impurity atoms. The temperature dependences of correlation length and magnetic susceptibility are determined for samples with various spin concentrations and various linear sizes. The finite-size scaling technique is used for obtaining scaling functions for these quantities, which exhibit a universal behavior in the critical region; the critical temperatures and static critical exponents are also determined using scaling…
Simulations of charge transport in amorphous semiconductors are often performed in microscopically sized systems. As a result, charge carrier mobilities become system-size dependent. We propose a simple method for extrapolating a macroscopic, nondispersive mobility from the system-size dependence of a microscopic one. The method is validated against a temperature-based extrapolation [Phys. Rev. B 82, 193202 (2010)]. In addition, we provide an analytic estimate of system sizes required to perform nondispersive charge transport simulations in systems with finite charge carrier density, derived f…
We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy in the scaling theory and in place of the Boltzmann probability in a position-space renormalization scheme. We derive a scaling relation between critical exponents which we test in a variety of models in one and two dimensions. We then apply the renormalization to disordered systems. In one dimension the renormalized disorder strength tends to infinity indica…
Renyi Mutual information (RMI), computed from second Renyi entropies, can identify classical phase transitions from their finite-size scaling at the critical points. We apply this technique to examine the presence or absence of finite temperature phase transitions in various two-dimensional models on a square lattice, which are extensions of the conventional Ising model by adding a quenched disorder. When the quenched disorder causes the nearest neighbor bonds to be both ferromagnetic and antiferromagnetic, (a) a spin glass phase exists only at zero temperature, and (b) a ferromagnetic phase e…
We present a constructive approach to obtain information about the compactness and shape of large-scale lowest excitations in disordered systems by studying order-parameter fluctuations (OPF) at low temperatures. We show that the parameter $G$ which measures OPF is 1/3 at T=0 provided the ground state is unique and the probability distribution for the lowest excitations is gapless and with finite weight at zero-excitation energy. We then apply zero-temperature scaling to describe the energy and volume spectra of the lowest large-scale excitations which scale with the system size and have a wei…
We investigate Anderson localization on various 1D structures having flat bands. The main focus is on the scaling laws obeyed by the localization length at weak disorder in the vicinity of flat-band energies. A careful distinction is made between situations where the scaling functions are universal (i.e., depend on the disorder distribution only through its width) and where they keep depending on the full shape of the disorder distribution, even in the weak-disorder scaling regime. Three examples are analyzed in detail. On the stub chain, one central flat band is isolated from two lateral disp…
Disordered biopolymer gels have striking mechanical properties including strong nonlinearities. In the case of athermal gels (such as collagen-I) the nonlinearity has long been associated with a crossover from a bending dominated to a stretching dominated regime of elasticity. The physics of this crossover is related to the existence of a central-force isostatic point and to the fact that for most gels the bending modulus is small. This crossover induces scaling behavior for the elastic moduli. In particular, for linear elasticity such a scaling law has been demonstrated [Broedersz et al. Natu…
We study heat conduction mediated by longitudinal phonons in one dimensional disordered harmonic chains. Using scaling properties of the phonon density of states and localization in disordered systems, we find non-trivial scaling of the thermal conductance with the system size. Our findings are corroborated by extensive numerical analysis. We show that a system with strong disorder, characterized by a `heavy-tailed' probability distribution, and with large impedance mismatch between the bath and the system satisfies Fourier's law. We identify a dimensionless scaling parameter, related to the t…
Dynamical scaling and ageing in disordered systems far from equilibrium is reviewed. Particular attention is devoted to the question to what extent a recently introduced generalization of dynamical scaling to local scale-invariance can describe data for either non-glassy systems quenched to below $T_c$ or else for spin glasses at criticality. The dependence of the scaling behaviour on the distribution of the random couplings is discussed. It is shown that finite-time corrections to scaling can become quite sizable in these systems. Numerically determined ageing quantities are confronted with a…
Entropy production plays a fundamental role in the study of non-equilibrium systems by offering a quantitative handle on the degree of time-reversal symmetry breaking. It depends crucially on the degree of freedom considered as well as on the scale of description. It was hitherto unknown how the entropy production at one resolution of the degrees of freedom is related to the entropy production at another resolution. This relationship is of particular relevance to coarse grained and continuum descriptions of a given phenomenon. In this work, we derive the scaling of the entropy production under…
We investigate some aspects of the ageing behavior observed in the contact process after a quench from its active phase to the critical point. In particular we discuss the scaling properties of the two-time response function and we calculate it and its universal ratio to the two-time correlation function up to first order in the field-theoretical epsilon-expansion. The scaling form of the response function does not fit the prediction of the theory of local scale invariance. Our findings are in good qualitative agreement with recent numerical results.
In this paper, we explore quantum criticality in the disordered Aubry-André (AA) model. For the pure AA model, it is well-known that it hosts a critical point separating an extended phase and a localized insulator phase by tuning the strength of the quasiperiodic potential. Here we unearth that the disorder strength $Δ$ contributes an independent relevant direction near the critical point of the AA model. Our scaling analyses show that the localization length $ξ$ scales with $Δ$ as $ξ\proptoΔ^{-ν_Δ}$ with $ν_Δ$ a new critical exponent, which is estimated to be $ν_Δ\approx0.46$. This value is r…
We study scaling properties of energy spreading in disordered strongly nonlinear Hamiltonian lattices. Such lattices consist of nonlinearly coupled local linear or nonlinear oscillators, and demonstrate a rather slow, subdiffusive spreading of initially localized wave p ackets. We use a fractional nonlinear diffusion equation as a heuristic model of this process, and confirm that the scaling predictions resulting from a self-similar solution of this equation are indeed applicable to all studied cases. We s how that the spreading in nonlinearly coupled linear oscillators slows down compared to …
The phase-ordering kinetics of the ferromagnetic two-dimensional Ising model with uniform disorder is investigated by intensive Monte Carlo simulations. Taking into account finite-time corrections to scaling, simple ageing behaviour is observed in the two-time responses and correlators. The dynamical exponent z and the form of the scaling functions only depend on the ratio eps/T, where eps describes the width of the distribution of the disorder. The agreement of the predictions of local scale-invariance generalised to z<> 2 for the two-time scaling functions of response and correlations with t…
Dynamics of a system exhibits non-adiabaticity even for slow quenches near critical points. We analyze the response to disorder in quenches on a non-adiabaticity quantifier for the quantum Rabi model, which possesses a phase transition between normal and superradiant phases. We consider a disordered version of a quench in the Rabi model, in which the system residing in the ground state of an initial Hamiltonian of the normal phase is quenched to the final Hamiltonian corresponding to the critical point. The disorder is inserted either in the total time the quench or in the quench parameter its…
