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Variational wavefunctions that introduce zeros (vortices) to screen repulsive interactions are typically difficult to verify in unbiased microscopic calculations. An approach is constructed to insert vortices into ansatz wavefunctions using…
State-dependent time-impulsive perturbations to a two-dimensional autonomous flow with stable and unstable manifolds are analysed by posing in terms of an integral equation which is valid in both forwards- and backwards-time. The impulses…
Dynamics, the physical change in time and a pillar of natural sciences, can be regarded as an emergent phenomenon when the system of interest is part of a larger, static one. This "relational approach to time", in which the system's…
The equilibrium behavior of vortices in the classical two-dimensional (2D) XY model with uncorrelated random phase shifts is investigated. The model describes Josephson-Junction arrays with positional disorder, and has ramifications in a…
Dynamical systems associated with a q-deformed two dimensional phase space are studied as effective dynamical systems described by ordinary variables. In quantum theory, the momentum operator in such a deformed phase space becomes a…
We conduct a theoretical study of the creation and dynamics of vortices in a two-dimensional binary Bose-Einstein condensate with a mass imbalance between the species. To initiate the dynamics, we use one or two rotating paddle potentials…
In two dimensions the microscopic theory, which provides a basis for the naive analogy between a quantized vortex in a superfluid and an electron in an uniform magnetic field, is presented. A one-to-one correspondence between the rotational…
A phenomenological model describing the time-frequency dependence of the power spectrum of thin plates vibrating in a wave turbulence regime, is introduced. The model equation contains as basic solutions the Rayleigh-Jeans equipartition of…
Pattern forming with externally imposed symmetry is ubiquitous in nature but lightly studied.We present experimental studies of pattern formation and selection by spatial periodic forcing in rapidly rotating convection. We observe symmetric…
Special relativity combined with the stochastic vacuum flux impact model lead to an explicit interpretation of many of the phenomena of elementary quantum mechanics. We examine characteristics of a repetitively impacted submicroscopic…
Deterministic and random fractals, within the framework of Iterated Function Systems, have been used to model and study a wide range of phenomena across many areas of science and technology. However, for many applications deterministic…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
We propose a Poincare-invariant description for the effective dynamics of systems of charged particles by means of intrinsic multipole moments. To achieve this goal we study the effective dynamics of such systems within two frameworks --…
We show the density of eigenvalues for three classes of random matrix ensembles is determinantal. First we derive the density of eigenvalues of product of $k$ independent $n\times n$ matrices with i.i.d. complex Gaussian entries with a few…
The strength functions of quadrupole modes in the unstable oxygen isotopes 22O and 24O are calculated using an extended version of the time-dependent Hartree-Fock theory known as the time-dependent density-matrix theory (TDDM). It is found…
Scattering and electron-positron pair production by a one-dimensional potential is considered in the framework of the $S-$matrix formalism. The solutions of the Dirac equation are classified according to frequency sign. The Bogoliubov…
We reveal that the mechanical pulsation of locally synchronised particles is a generic route to propagate deformation waves. We consider a model of dense repulsive particles whose activity drives periodic change in size of each individual.…
Quantum mechanics is a successful theory that describes the behavior of photons, electrons, and other atomic- and molecular-scale objects. However, it is far from being well understood. In this paper, a new theory - knot physics for…
This works extends the recent study on the dielectric permittivity of crystals within the Hartree model [E. Cances and M. Lewin, Arch. Rational Mech. Anal., 197 (2010) 139--177] to the time-dependent setting. In particular, we prove the…
In the present paper which is a sequel to [N.B. Volkov and A.M. Iskoldsky The dynamics of vortex structures and states of current: 1;[1]], the dynamics of non-equilibrium phase transitions and states of current in electrophysical systems…