Related papers: Classical long-range interacting N-particle config…
The Dirac method is used to analyze the classical and quantum dynamics of a particle constrained on a circle. The method of Lagrange multipliers is scrutinized, in particular in relation to the quantization procedure. Ordering problems are…
It is first shown that when the Schr\"{o}dinger equation for a wave function is written in the polar form, complete information about the system's {\em quantum-ness} is separated out in a single term $Q$, the so called `quantum potential'.…
The two-particle models in de Sitter space-time with time-asymmetric retarded-advanced interactions are constructed. Particular cases of the field-type electromagnetic and scalar interactions are considered. The manifestly covariant…
The non-commutativity of the position and momentum operators is formulated as an effective potential in classical phase space and expanded as a series of successive many-body terms, with the pair term being dominant. A non-linear partial…
We consider the time evolution of nonequilibrium quantum scalar fields in the O(N) model, using the next-to-leading order 1/N expansion of the 2PI effective action. A comparison with exact numerical simulations in 1+1 dimensions in the…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
We provide the differential equations that generalize the Newtonian N-body problem of celestial mechanics to spaces of constant Gaussian curvature, k, for all k real. In previous studies, the equations of motion made sense only for k…
There are known problems of Lorentz-Dirac equation for moving with acceleration charged particle in classical electrodynamics. The model of extended in one dimension particle is proposed and shown that electromagnetic self-interaction can…
In the first quarter of the 20th century, physicists were not aware of the existence of classical electromagnetic zero-point radiation nor of the importance of special relativity. Inclusion of these aspects allows classical electron theory…
On the basis of extensive numerical studies it is argued that there are strong analogies between the probabilistic behavior of quantum systems defined by Hermitian Hamiltonians and the deterministic behavior of classical mechanical systems…
A quantum system of N Coulomb charges confined within a harmonic trap is considered over a wide range of densities and temperatures. A recently described construction of an equivalent classical system is applied in order to exploit the…
An algebraic treatment of shape-invariant potentials in supersymmetric quantum mechanics is discussed. By introducing an operator which reparametrizes wave functions, the shape-invariance condition can be related to a oscillator-like…
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…
In classical physics, there is a basic principle, namely "A particle cannot be located at the position of another one on the same time". Which consequences can be derived if this principle is transferred into quantum physics? For doing…
Euclidean quantum fields obtained as solutions of stochastic partial pseudo differential equations driven by a Poisson white noise have paths given by locally integrable functions. This makes it possible to define a class of ultra-violet…
p-Mechanics is a consistent physical theory which describes both quantum and classical mechanics simultaneously. We continue the development of p-mechanics by introducing the concept of states. The set of coherent states we introduce allow…
Systems with long-range interactions often relax towards statistical equilibrium over timescales that diverge with $N$, the number of particles. A recent work [S. Gupta and D. Mukamel, J. Stat. Mech.: Theory Exp. P03015 (2011)] analyzed a…
The long-standing challenge to describing charged particle dynamics in strong classical electromagnetic fields is how to incorporate classical radiation, classical radiation reaction and quantized photon emission into a consistent unified…
Coulomb integrals, i.e., matrix elements of bare or screened Coulomb interaction between one-electron orbitals, are fundamental objects in many approaches developed to tackle the challenging problem of calculating the electronic structure…
The spatio-temporally periodic (STP) potential is interesting in Physics due to the intimate coupling between its time and spatial components. In this paper we begin with a brief discussion of the dynamical behaviors of a single particle in…