Related papers: Finite-State Classical Mechanics
Coherent states provide a natural connection of quantum systems to their classical limit and are employed in various fields of physics. Here we derive general systematic expansions, with respect to quantum parameters, of expectation values…
Using semiclassical methods, it is possible to construct very accurate approximations in the short wavelength limit of quantum dynamics that rely exclusively on classical dynamical input. For systems whose classical realization is strongly…
Classical statistical particle mechanics in the configuration space can be represented by a nonlinear Schrodinger equation. Even without assuming the existence of deterministic particle trajectories, the resulting quantum-like statistical…
Fisher information is a lower bound on the uncertainty in the statistical estimation of classical and quantum mechanical parameters. While some deterministic dynamical systems are not subject to random fluctuations, they do still have a…
The statistical mechanics of particles that populate indistinguishable energy sub-states is explored. In particular, the mathematical treatment of the microstates differs from conventional statistical mechanics where for a given degeneracy,…
In the statistical description of dynamical systems, an indication of the irreversibility of a given state change is given geometrically by means of a (pre-)ordering of state pairs. Reversible state changes of classical and quantum systems…
The irreversibility of the dynamics of the conservative systems on example of hard disks and potentially of interacting elements is investigated in terms of laws of classical mechanics. The equation of the motion of interacting systems and…
We consider classical models of the kicked rotor type, with piecewise linear kicking potentials designed so that momentum changes only by multiples of a given constant. Their dynamics display quasi-localization of momentum, or quadratic…
Classical $\phi^4$ theory in weak and strong thermal gradients is studied on the lattice in (1+1) dimensions. Classical $\phi^4$ theory in weak and strong thermal gradients is studied on the lattice in (1+1) dimensions. The steady state…
The richness of quantum theory's reversible dynamics is one of its unique operational characteristics, with recent results suggesting deep links between the theory's reversible dynamics, its local state space and the degree of non-locality…
Using the mapping of the Fokker-Planck description of classical stochastic dynamics onto a quantum Hamiltonian, we argue that a dynamical glass transition in the former must have a precise definition in terms of a quantum phase transition…
The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in classical mechanics there is…
An explanation of the mechanism of irreversible dynamics was offered. The explanation was obtained within the framework of laws of classical mechanics by the expansion of Hamilton formalism. Such expansion consisted in adaptation of it to…
Hybrid classical-quantum models are computational schemes that investigate the time evolution of systems, where some degrees of freedom are treated classically, while others are described quantum-mechanically. First, we present the…
The aim of this work is to show that particle mechanics, both classical and quantum, Hamiltonian and Lagrangian, can be derived from few simple physical assumptions. Assuming deterministic and reversible time evolution will give us a…
We study the dynamics of an infinite regular lattice of classical charged oscillators. Each individual oscillator is described as a point particle subject to a harmonic restoring potential, to the retarded electromagnetic field generated by…
While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the…
A mechanism describing state reduction dynamics in relativistic quantum field theory is outlined. The mechanism involves nonlinear stochastic modifications to the standard description of unitary state evolution and the introduction of a…
We study the back-reaction of quantum systems onto classical ones. Taking the starting point that semi-classical physics should be described at all times by a point in classical phase space and a quantum state in Hilbert space, we consider…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…