1,254 research outputs found
Quantum dynamics of a hydrogen-like atom in a time-dependent box: non-adiabatic regime
We consider a hydrogen atom confined in time-dependent trap created by a
spherical impenetrable box with time-dependent radius. For such model we study
the behavior of atomic electron under the (non-adiabatic) dynamical confinement
caused by the rapidly moving wall of the box. The expectation values of the
total and kinetic energy, average force, pressure and coordinate are analyzed
as a function of time for linearly expanding, contracting and harmonically
breathing boxes. It is shown that linearly extending box leads to de-excitation
of the atom, while the rapidly contracting box causes the creation of very high
pressure on the atom and transition of the atomic electron into the unbound
state. In harmonically breathing box diffusive excitation of atomic electron
may occur in analogy with that for atom in a microwave field
Topological phase transition in non-Hermitian quasicrystals
The discovery of topological phases in non-Hermitian open classical and
quantum systems challenges our current understanding of topological order.
Non-Hermitian systems exhibit unique features with no counterparts in
topological Hermitian models, such as failure of the conventional bulk-boundary
correspondence and non-Hermitian skin effect. Advances in the understanding of
the topological properties of non-Hermitian lattices with translational
invariance have been reported in several recent studies, however little is
known about non-Hermitian quasicrystals. Here we disclose topological phases in
a quasicrystal with parity-time () symmetry, described by a
non-Hermitian extension of the Aubry-Andr\'e-Harper model. It is shown that the
metal-insulating phase transition, observed at the symmetry
breaking point, is of topological nature and can be expressed in terms of a
winding number. A photonic realization of a non-Hermitian quasicrystal is also
suggested.Comment: 11 pages, 5 figures, to appear in Phys Rev Let
Duality Between Dirac Fermions in Curved Spacetime and Optical solitons in Non-Linear Schrodinger Model: Magic of -Dimensional Bosonization
Bosonization in curved spacetime maps massive Thirring model
(self-interacting Dirac fermions) to a generalized sine-Gordon model, both
living in -dimensional curved spacetime. Applying this duality we have
shown that the Thirring model fermion, in non-relativistic limit, gets
identified with the soliton of non-linear Scrodinger model with Kerr form of
non-linearity. We discuss one particular optical soliton in the latter model
and relate it with the Thirring model fermion.Comment: New reference and related discussion added, some equations corrected,
no change in major results, to appear in EPJ
Theoretical studies of bright solitons in trapped atomic Bose-Einstein condensates
Bright solitary-waves may be created in dilute Bose-Einstein condensates of at tractively interacting atoms in one dimensional regimes. In integrable systems, such solitary waves are particle-like objects called solitons. We investigate the consequences of non-integrability on the solitary waves in trapped Bose-Einstein condensates caused by an axial harmonic trap, and non-integrability caused by three dimensional effects. To analyse the soliton-like nature of the solitary-waves in an axial harmonic trap, a particle analogy for the solitary-waves is formulated. Exact Soliton solutions exist in the absence of an external trapping potential, which behave in a particle-like manner, and we find the particle analogy we employ to be a good model also when a harmonic trapping potential is present up to a gradual shift in the trajectories when the harmonic trap period is short compared with the, collision time of the solitons. We find that the collision time of the solions is dependent on the relative phase of the solitons as they collide. In the case of two solitons, the particle model is integrable, and the dynamics are completely regular. In the case of a system of two solitary waves of equal norm, the solitons are shown to retain their phase difference for repeated collisions. The extension to three particles supports both regular and chaotic regimes. The trajectory shift observed for two solitons carrier over to the case of three solitons. This shift aside, the agreement between the particle model and the wave dynamics remains good, even in chaotic regimes. We predict that these chaotic regimes will be an indicator of rapid depletion of the condensate due to quantum transitions of the condensate particles into non-condensate modes. To analyse the residual effects of the three dimensional nature of the solitary waves, we use a nonlinear Schrödinger equation with an additional quintic term. We perform variational calculations, and confirm the collapse of a soliton when the number of particles contained therein is increased past a critical number. We investigate the effects of varying the axial trap frequency and scattering length on the critical number. We propose a method to model particle exchange between solitons by extending the variational treatment to two solitons
Bifurcations and stability of gap solitons in periodic potentials
We analyze the existence, stability, and internal modes of gap solitons in
nonlinear periodic systems described by the nonlinear Schrodinger equation with
a sinusoidal potential, such as photonic crystals, waveguide arrays,
optically-induced photonic lattices, and Bose-Einstein condensates loaded onto
an optical lattice. We study bifurcations of gap solitons from the band edges
of the Floquet-Bloch spectrum, and show that gap solitons can appear near all
lower or upper band edges of the spectrum, for focusing or defocusing
nonlinearity, respectively. We show that, in general, two types of gap solitons
can bifurcate from each band edge, and one of those two is always unstable. A
gap soliton corresponding to a given band edge is shown to possess a number of
internal modes that bifurcate from all band edges of the same polarity. We
demonstrate that stability of gap solitons is determined by location of the
internal modes with respect to the spectral bands of the inverted spectrum and,
when they overlap, complex eigenvalues give rise to oscillatory instabilities
of gap solitons.Comment: 18 pages, 11 figures; updated bibliograph
Completely integrable models of non-linear optics
The models of the non-linear optics in which solitons were appeared are
considered. These models are of paramount importance in studies of non-linear
wave phenomena. The classical examples of phenomena of this kind are the
self-focusing, self-induced transparency, and parametric interaction of three
waves. At the present time there are a number of the theories based on
completely integrable systems of equations, which are both generations of the
original known models and new ones. The modified Korteweg-de Vries equation,
the non- linear Schrodinger equation, the derivative non-linear Schrodinger
equation, Sine-Gordon equation, the reduced Maxwell-Bloch equation, Hirota
equation, the principal chiral field equations, and the equations of massive
Thirring model are gradually putting together a list of soliton equations,
which are usually to be found in non-linear optics theory.Comment: Latex, 17 pages, no figures, submitted to Pramana
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