Related papers: The classical harmonic chain: solution via Laplace…
We develop a classical theoretical description for nonlinear many-body dynamics that incorporates the back-action of a continuous measurement process. The classical approach is compared with the exact quantum solution in an example with an…
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…
This paper provides a new mathematical axiom system for classical harmony, which is a prescriptive rule system for composing music, introduced in the second half of the 18th century. The clearest model of classical harmony is given by the…
The method of restricted path integrals allows one to effectively consider continuous (prolonged in time) measurements of quantum systems. Monitoring of the system coordinates is such a continuous measurement that allows one to describe a…
A filtering problem for a class of quantum systems disturbed by a classical stochastic process is investigated in this paper. The classical disturbance process, which is assumed to be described by a linear stochastic differential equation,…
Electromagnetic properties of quark-like particles are examined in a classical field model involving extended dual electromagnetic fields. These can have fractional charges and a confining potential that derives essentially completely from…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
A large toolbox of numerical schemes for dispersive equations has been established, based on different discretization techniques such as discretizing the variation-of-constants formula (e.g., exponential integrators) or splitting the full…
In a recent letter ({\it{EPL}}, {\bf{104}} (2013) 60003; see also {\it {arXiv:1309.5645}}), Plastino and Rocca suggest that the divergences inherent to the formulation of nonextensive statistical mechanics can be eliminated {\it {via}} the…
The dynamics of hybrid systems -- i.e. ones in which classical and quantum degrees of freedom co-exist and interact -- feature both diffusion in the classical sector and decoherence in the quantum state. In this article, we will consider…
As known all physical properties of solids are described well by the system of quantum linear harmonic oscillators. It is shown in the present paper that the system consisting of classical linear harmonic oscillators having temperature…
We extract the information of a quantum motion and decode it into a certain orbit via a single measurable quantity. Such that a quantum chaotic system can be reconstructed as a chaotic attractor. Two configurations for reconstructing this…
An initial local excitation in a confined quantum system evolves exploring the whole system, returning to the initial position as a mesoscopic echo at the Heisenberg time. We consider a two weakly coupled spin chains, a spin ladder, where…
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose…
Problems concerning with application of quantum rules on classical phenomena have been widely studied, for which lifted up the idea about quantization and uncertainty principle. Energy quantization on classical example of simple harmonic…
The origin of classical predictability is investigated for the one dimensional harmonic chain considered as a closed quantum mechanical system. By comparing the properties of a family of coarse-grained descriptions of the chain, we conclude…
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…
Coherently displaced harmonic oscillator number states of a harmonically bound ion can be coupled to two internal states of the ion by a laser-induced motional sideband interaction. The internal states can subsequently be read out in a…
A well known description of superradiance from pointlike collections of many atoms involves the dissipative motion of a large spin. The pertinent ``superradiance master equation'' allows for a formally exact solution which we subject to a…
In this paper we consider classical point particles in full interaction with an arbitrary number of dynamical scalar and (abelian) vector fields. It is shown that the requirement of stability ---vanishing self-force--- is sufficient to…