Related papers: Finite-State Classical Mechanics
Models of quantum and classical particles on the d-dimensional cubic lattice with pair interparticle interactions are considered. The classical model is obtained from the corresponding quantum one when the reduced physical mass of the…
Dynamical universality is the observation that the dynamical properties of different systems might exhibit universal behavior that are independent of the system details. In this paper, we study the long-time dynamics of an one-dimensional…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
The quantum dynamics of a single particle in a discrete two-dimensional tilted lattice is analyzed from the perspective of the classical-quantum correspondence. Utilizing the fact that tilting the lattice results in oscillatory dynamics, we…
The rounding of first order phase transitions by quenched randomness is stated in a form which is applicable to both classical and quantum systems: The free energy, as well as the ground state energy, of a spin system on a $d$-dimensional…
Time dependent dynamics of the chaotic quantum-mechanical system has been studied. Irreversibility of the dynamics is shown. It is shown, that being in the initial moment in pure quantum-mechanical state, system makes irreversible…
Lattice molecule models are proposed in order to study statistical mechanics of glass transition in finite dimensions. Molecules in the models are represented by hard Wang tiles and their density is controlled by a chemical potential. An…
In this work we analyse the structure of the thermodynamic arrow of time, defined by transformations that leave the thermal equilibrium state unchanged, in classical (incoherent) and quantum (coherent) regimes. We note that in the…
We numerically analyze the dynamical generation of quantum entanglement in a system of 2 interacting particles, started in a coherent separable state, for decreasing values of $\hbar$. As $\hbar\to 0$ the entanglement entropy, computed at…
We study reversible deterministic dynamics of classical charged particles on a lattice with hard-core interaction. It is rigorously shown that the system exhibits three types of transport phenomena, ranging from ballistic, through diffusive…
We extend a previously studied lattice model of particles with infinite repulsions to the case of finite energy interactions. The phase diagram is studied using grand canonical Monte Carlo simulation. Simulations of dynamical phenomena are…
A new class of lattice gas models with trivial interactions but constrained dynamics are introduced. These are proven to exhibit a dynamical glass transition: above a critical density, rho_c, ergodicity is broken due to the appearance of an…
We attempt to characterize irreversibility of a dynamical system from the existence of different forward and backward mathematical representations depending on the direction of the time arrow. Such different representations have been…
Classical cellular automata represent a class of explicit discrete spacetime lattice models in which complex large-scale phenomena emerge from simple deterministic rules. With the goal to uncover different physically distinct classes of…
Dynamics of systems of structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The…
We use the system of p-adic numbers for the description of information processes. Basic objects of our models are so called transformers of information, basic processes are information processes, the statistics are information statistics…
The relationship between classical and quantum mechanics is usually understood via the limit $\hbar \rightarrow 0$. This is the underlying idea behind the quantization of classical objects. The apparent incompatibility of general relativity…
In a quantum mechanical description of the free-electron laser (FEL) the electrons jump on discrete momentum ladders, while they follow continuous trajectories according to the classical description. In order to observe the transition from…
The classical and quantum dynamics for an n-dimensional generalization of the kicked planar (n=1) rotator in an additional effective centrifugal potential. Therefore, typical phenomena like the diffusion in classical phase space are similar…
Classical Electrodynamics in ponderable media remains defined by a century-long debate over force and energy localization. While the prevailing view treats competing formulations (Minkowski, Abraham, etc.) as equivalent conventions, this…