Related papers: Two-particle model with noncommuting operators of …
In the present report, a set of theoretical results obtained in the period from 1991 to 2005 are reviewed. The physical systems under study include quark models of hadrons, inert atom clusters, atomic traps, and electrons and excitons…
We study the exactly solvable quantum system of two particles confined in a three-dimensional harmonic trap and interacting via finite-range soft-core interaction by means of the separation of variables and ansatz method. Supposing the…
For Klein-Gordon equation a consistent physical interpretation of wave functions is reviewed as based on a proper modification of the scalar product in Hilbert space. Bound states are then studied in a deep-square-well model where spectrum…
The quantum dynamics of an ultrarelativistic electron in strong counterpropagating laser beams is investigated. In contrast to the stimulated Compton scattering regime, we consider the case when in the electron rest frame the frequency of…
The first-order, infinite-component field equations we proposed before for non-relativistic anyons (identified with particles in the plane with noncommuting coordinates) are generalized to accommodate arbitrary background electromagnetic…
This is the more technical half of a two-part work in which we introduce a robust microlocal framework for analyzing the non-relativistic limit of relativistic wave equations with time-dependent coefficients, focusing on the Klein--Gordon…
We consider a simple one dimensional quantum system consisting of a heavy and a light particle interacting via a point interaction. The initial state is chosen to be a product state, with the heavy particle described by a coherent…
Electromagnetic and Lorentz-scalar form factors are calculated for a bound system of two spin-less particles exchanging a zero-mass scalar particle. Different approaches are considered including solutions of a Bethe-Salpeter equation, a…
In this note we analyse two different models of two interacting conformal Carroll particles that can be obtained as the Carrollian limit of two relativistic conformal particles. The first model describes particles with zero velocity and…
In this work, we study the existence of various classes of standing waves for a nonlinear Schr\"odinger system with quadratic interaction, along with a harmonic or partially harmonic potential. We establish the existence of ground-state…
Solutions of the Schr\"odinger equation by spanning the wave function is a complete basis is a common practice is many-body interacting systems. We shall study the case of a two-dimensional quantum system composed by two interacting…
We present a quantum kinetic theory for spin-$1/2$ particles, including the spin-orbit interaction, retaining particle dispersive effects to all orders in $\hbar$, based on a gauge-invariant Wigner transformation. Compared to previous…
For the models of $N$-body identical harmonic oscillators interacting through potentials of homogeneous degree -2, the unitary operator that transforms a system of time-dependent parameters into that of unit spring constant and unit mass of…
Collective orders and photo-induced phase transitions in quantum matter can evolve on timescales which are orders of magnitude slower than the femtosecond processes related to electronic motion in the solid. Quantum Boltzmann equations can…
We construct a nonrelativistic wave equation for spinning particles in the noncommutative space (in a sense, a $\theta$-modification of the Pauli equation). To this end, we consider the nonrelativistic limit of the $\theta$-modified Dirac…
We initiate a research program for the systematic investigation of quantum superintegrable systems involving the interaction of two non-relativistic particles with spin $1/2$ moving in the three-dimensional Euclidean space. In this paper,…
We review recent interest in the relativistic Riemann problem as a method for generating a non-equilibrium steady state. In the version of the problem under con- sideration, the initial conditions consist of a planar interface between two…
We find that the momentum conjugate to the relative distance between two gravitating particles in their center of mass frame is a hyperbolic angle. This fact strongly suggests that momentum space should be taken to be a hyperboloid. We…
The Foldy-Wouthuysen transformation for relativistic spin-1 particles interacting with nonuniform electric and uniform magnetic fields is performed. The Hamilton operator in the Foldy-Wouthuysen representation is determined. It agrees with…
Plasma physics give an example of physical system of particles with the long range interaction. At small velocity of particles we can consider the plasma approximately as a system of particles with the Coulomb interaction. The Coulomb…