Related papers: A New Look at Broken Ergodicity
We identify a fundamental phenomenon of heterogeneous one dimensional random walks: the escape (traversal) time is maximized when the heterogeneity in transition probabilities forms a pyramid-like potential barrier. This barrier corresponds…
The present note reviews recent results on resonances for one-dimensional quantum ergodic systems constrained to a large box. We restrict ourselves to one dimensional models in the discrete case. We consider two type of ergodic potentials…
We attempt to give a bird's eye view of the physical mechanisms leading to anomalous relaxation, and the relation of this phenomenon with anomalous diffusion and transport. Whereas in some cases these two notions are indeed deeply related,…
In systems with detailed balance, the stationary distribution and the equilibrium distribution are identical, creating a clear connection between energetic and entropic quantities. Many driven systems violate detailed balance and still pose…
Consider a stochastic nonlinear system controlled over a possibly noisy communication channel. An important problem is to characterize the largest class of channels for which there exist coding and control policies so that the closed-loop…
In a preceding paper, Mukhopadhyay and I studied the diffusive motion of a tagged molecule in a heterogeneous glass-forming liquid at temperatures just above a glass transition. Among other features of this system, we postulated a relation…
We study, on a $d$ dimensional hypercubic lattice, a random walk which is homogeneous except for one site. Instead of visiting this site, the walker hops over it with arbitrary rates. The probability distribution of this walk and the…
We consider a system of independent one-dimensional random walks in a common random environment under the condition that the random walks are transient with positive speed $v_P$. We give upper bounds on the quenched probability that at…
Disordered solids exhibit unusual properties of their vibrational states and thermal conductivities. Recent progresses have well established the concept of "elastic heterogeneity", i.e., disordered materials show spatially inhomogeneous…
Self-consistent N-body simulations are efficient tools to study galactic dynamics. However, using them to study individual trajectories (or ensembles) in detail can be challenging. Such orbital studies are important to shed light on global…
In globally coupled oscillators, it is believed that strong higher harmonics of coupling functions are essential for multibranch entrainment (MBE), in which there exist many stable states, whose number scales as $\sim$ $O(\exp N)$ (where N…
A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…
We perform simulations for one dimensional continuous-time random walks in two dynamic random environments with fast (independent spin-flips) and slow (simple symmetric exclusion) decay of space-time correlations, respectively. We focus on…
We survey our recent articles dealing with one dimensional attractive zero range processes moving under site disorder. We suppose that the underlying random walks are biased to the right and so hyperbolic scaling is expected. Under the…
The effects of floppy modes in the thermodynamical properties of a system are studied. From thermodynamical arguments, we deduce that floppy modes are not at zero frequency and thus a modified Debye model is used to take into account this…
A heterogeneous continuous time random walk is an analytical formalism for studying and modeling diffusion processes in heterogeneous structures on microscopic and macroscopic scales. In this paper we study both analytically and numerically…
The heterochaos baker maps are piecewise affine maps of the unit square or cube introduced in [Nonlinearity 34, 2021, 5744--5761], to provide a hands-on, elementary understanding of complicated phenomena in systems of large degrees of…
A one-dimensional system of masses with nearest-neighbor interactions and periodic boundary conditions is used to study mode decay and ergodicity in nonlinear, disordered systems. The system is given an initial periodic displacement, and…
Peridynamics provides a versatile tool for fracture modelling in materials where fracture pathways cannot be predicted beforehand, but must be envisaged as an emergent features of the deformation process. One class of materials where this…
Ergodicity has been one of the fundamental concepts underpinning our understanding of thermalization in isolated systems since the first developments in classical statistical mechanics. Recently, a similar notion has been introduced for…