Related papers: Build-up of macroscopic eigenstates in a memory-ba…
It is shown that due to memory effects the complex behaviour of components in a stochastic system can be transmitted to macroscopic evolution of the system as a whole. Within the Markov approximation widely using in ordinary statistical…
The counterintuitive emergence of order from noise is a central phenomenon in science, ranging from pattern formation and synchronization to order-by-disorder in frustrated systems. While large-scale spatial self-organization induced by…
Random walks on dynamic graphs have received increasingly more attention from different academic communities over the last decade. Despite the relatively large literature, little is known about random walks that construct the graph where…
The discrete-time quantum walk dynamics can be generated by a time-dependent Hamiltonian, repeatedly switching between the coin and the shift generators. We change the model and consider the case where the Hamiltonian is time-independent,…
We find that the simple coupling of network growth to the position of a random walker on the network generates a traveling wave in the probability distribution of nodes visited by the walker. We argue that the entropy of this probability…
The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. We here discuss a renewal process…
A novel version of the Continuous-Time Random Walk (CTRW) model with memory is developed. This memory means the dependence between arbitrary number of successive jumps of the process, while waiting times between jumps are considered as…
We consider an ensemble of coupled oscillators whose individual states, in addition to the phase, are characterized by an internal variable with autonomous evolution. The time scale of this evolution is different for each oscillator, so…
We consider random walkers that deform the medium as they move, enabling a faster motion in regions which have been recently visited. This induces an effective attraction between walkers mediated by the medium, which can be regarded as a…
This work analyzes fractional continuous-time random walks on two-layer multiplexes. A node-centric dynamics is used, in which it is assumed a Poisson distribution of a walker to become active, while a jump to one of its neighbors depends…
In this paper, we claim that a common underlying structure--a skeleton structure--is present behind discrete-time quantum walks (QWs) on a one-dimensional lattice with a homogeneous coin matrix. This skeleton structure is independent of the…
Random walks of particles on a lattice are a classical paradigm for the microscopic mechanism underlying diffusive processes. In deterministic walks, the role of space and time can be reversed, and the microscopic dynamics can produce quite…
Quantum walks are powerful tools not only to construct the quantum speedup algorithms but also to describe specific models in physical processes. Furthermore, the discrete time quantum walk has been experimentally realized in various…
We study discrete quantum dynamics where single evolution step consists of unitary system transformation followed by decoherence via coupling to an environment. Often non-Markovian memory effects are attributed to structured environments…
Can a closed quantum system generate persistent time-crystal-like dynamics without external driving? Within the Bateman dual oscillator framework, we show that the answer is affirmative. We consider a nonrelativistic (2+1)-dimensional…
We present here a system of self-propelled particles that follow a very simple motion law in continuous space in a deterministic and asynchronous way. This system of particles is capable of producing, depending on the particle density in…
We study the phenomenon of weak ergodicity breaking for a class of globally correlated random walk dynamics defined over a finite set of states. The persistence in a given state or the transition to another one depends on the whole previous…
Using both numerical simulations and scaling arguments, we study the behavior of a random walker on a one-dimensional small-world network. For the properties we study, we find that the random walk obeys a characteristic scaling form. These…
We present the single-particle sector of a quantum cellular automaton, namely a quantum walk, on a simple dynamical triangulated $2-$manifold. The triangulation is changed through Pachner moves, induced by the walker density itself,…
We study a family of weighted random walks on complete graphs. These `democratic walks' turn out to be explicitly solvable, and we find the hierarchy window for which the characteristic time scale saturates the so-called fast scrambling…