Related papers: Finite-State Classical Mechanics
In the classical stochastic resetting problem, a particle, moving according to some stochastic dynamics, undergoes random interruptions that bring it to a selected domain, and then, the process recommences. Hitherto, the resetting mechanism…
This note presents an attempt to provide a conceptual framework for variational formulations of classical physics. Variational principles of physics have all a common source in the {\it principle of virtual work} well known in statics of…
The irreversibility of the equations of classical dynamics (the Hamilton equations and the Liouville equation) in the space with multifractal time is demonstrated. The time is given on multifractal sets with fractional dimensions. The last…
The multi-wave exact resonance condition is a fundamental principle for understanding energy transfer in condensed matter systems, yet the dynamical evolution of waves satisfying this condition remains unexplored. Here, we reveal that the…
We have studied the emergence of classical states in the perturbative interaction model. The states which interact with many other degrees of freedom, such as the center of mass of a macro-object, play important role. Although the random…
This thesis addresses whether it is possible to build a robust memory device for quantum information. A three-dimensional gapped lattice spin model is found which demonstrates for the first time that a reliable quantum memory at finite…
Classical reversible cellular automata (CAs), which describe the discrete-time dynamics of classical degrees of freedom in a finite state-space, can exhibit exact, nonthermal quantum eigenstates despite being classically chaotic. We show…
Quantum to classical crossover is a fundamental question in dynamics of quantum many-body systems. In frustrated magnets, for example, it is highly non-trivial to describe the crossover from the classical spin liquid with a…
A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
In classical mechanics the complexity of a dynamical system is characterized by the rate of local exponential instability which effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum…
We simulate static memory materials on a two-dimensional lattice. The bulk properties of such materials depend on boundary conditions. Considerable information can be stored in various local patterns. We observe local probabilities…
A kinetic equation is derived for the phase density of a system of point particles, generating a system of integro-differential equations for distribution functions that have a deterministic meaning. The derivation took into account the…
We observe that a wide class of higher-derivative systems admits a bounded integral of motion that ensures the classical stability of dynamics, while the canonical energy is unbounded. We use the concept of a Lagrange anchor to demonstrate…
The exact equations of motion for microscopic density of classical many-body system with account of inter-particle retarded interactions are derived. It is shown that interactions retardation leads to irreversible behaviour of many-body…
In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests…
We study the classical mechanics and dynamics of particles that retains some memory of quantum statistics. Our work builds on earlier work on the statistical mechanics and thermodynamics of such particles. Starting from the effective…
We show that the usefulness of the thermal state of a specific spin-lattice model for measurement-based quantum computing exhibits a transition between two distinct "phases" - one in which every state is a universal resource for quantum…
The concept of determinism for a classical system is interpreted as the requirement that the solution to the Cauchy problem for the equations of motion governing this system be unique. This requirement is generally assumed to hold for all…
A new model is studied which describes the quantum behavior of transitions through an isotropic quantum cosmological bounce in loop quantum cosmology sourced by a free and massless scalar field. As an exactly solvable model even at the…