Related papers: Finite-State Classical Mechanics
In statistical mechanics, it is well known that finite-state classical lattice models can be recast as quantum models, with distinct classical configurations identified with orthogonal basis states. This mapping makes classical statistical…
We define, as local quantities, the least energy and momentum allowed by quantum mechanics and special relativity for physical realizations of some classical lattice dynamics. These definitions depend on local rates of finite-state change.…
Finite physical systems have only a finite amount of distinct state. This finiteness is fundamental in statistical mechanics, where the maximum number of distinct states compatible with macroscopic constraints defines entropy. Here we show…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
The article is dedicated to discussion of irreversibility and foundation of statistical mechanics "from the first principles". Taking into account infinitesimal and, as it seems, neglectful for classical mechanics fluctuations of the…
Considering deterministic classical lattice systems with continuous variables, we show that, if the initial conditions are sampled according to a probability distribution in which the dynamical variables are statistically independent, 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…
We shall show that the abstract and formal rules which govern the quantum kinematic and dynamics can be derived from a law of change of the information content or the degree of uncertainty that the system has a certain configuration in a…
A tradition handed down among physicists maintains that classical physics is a perfectly deterministic theory capable of predicting the future with absolute certainty, independently of any interpretations. It also tells that it was quantum…
The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…
Using the supersymmetry approach, we study spectral statistical properties of a two-dimensional quantum particle subject to a non-uniform magnetic field. We focus mainly on the problem of regularisation of the field theory. Our analysis…
Globally-constrained classical fields provide a unexplored framework for modeling quantum phenomena, including apparent particle-like behavior. By allowing controllable constraints on unknown past fields, these models are retrocausal but…
The question of how irreversibility can emerge as a generic phenomena when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the…
We present a comprehensive comparison of spin and energy dynamics in quantum and classical spin models on different geometries, ranging from one-dimensional chains, over quasi-one-dimensional ladders, to two-dimensional square lattices.…
Uncertainty in the initial conditions of dynamical systems can cause exponentially fast divergence of trajectories, a signature of deterministic chaos. Here, we derive a classical uncertainty relation that sets a speed limit on the rates of…
The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since…
It is well known that, due to the uncertainty principle, the Planck constant sets a resolution boundary in phase space and the resulting trade-off in resolution between incompatible measurements has been thoroughly investigated. It is also…
The limited distinctness of physical systems is roughly expressed by uncertainty relations. Here we show distinctness is a finite resource we can exactly count to define basic physical quantities, limits to the resolution of space and time,…
For a periodically shaken optical lattice, effective time-reversal is investigated numerically. For interacting ultra-cold atoms, the scheme of [J. Phys. B 45, 021002 (2012)] involves a quasi-instantaneous change of both the…
The gap between classical mechanics and quantum mechanics has an important interpretive implication: the Universe must have an irreducible fundamental level, which determines the properties of matter at higher levels of organization. We…