40 research outputs found
Rogue solitons in Heisenberg spin chain
Following the connection of the non-linear Schr\"{o}dinger equation with the
continuum Heisenberg spin chain, we find the rogue soliton equivalent in the
spin system. The breathers are also mapped to the corresponding space or time
localized oscillatory modes, through the moving curve analogy. The
spatio-temporal evolution of the curvature and torsion of the curve, underlying
these dynamical systems, are explicated to illustrate the localization property
of the rogue waves
On Berezinskii-Kosterlitz-Thouless phase transition and universal breathing mode in two dimensional photon gas
A system of two dimensional photon gas has recently been realized
experimentally. It is pointed out that this setup can be used to observe a
universal breathing mode of photon gas. It is shown that a modification in the
experimental setup would open up a possibility of observing the
Berezinskii-Kosterlitz-Thouless (BKT) phase transition in such a system. It is
shown that the universal jump in the superfluid density of light in the output
channel can be used as an unambiguous signature for the experimental
verification of the BKT transition.Comment: 5 pages, 2 figure
Light-matter interaction and Bose-Einstein condensation of light
The atom - electromagnetic field interaction is studied in the Dicke model,
wherein a single field mode is interacting with a collection of two level atoms
at thermal equilibrium. It is found that in the superradiant phase of the
system, wherein the Bose-Einstein condensation of photons takes place, the
notion of photon as an elementary electromagnetic excitation ceases to exist.
The phase and intensity excitations of the condensate are found to be the true
excitations of electromagnetic field. It is found that in this phase, the atom
interacts with these excitations in a distinct coherent transition process,
apart from the known stimulated emission/absorption and spontaneous emission
processes. In the coherent transition it is found that while the atomic state
changes in course of the transition process, the state of electromagnetic field
remains unaffected. It is found that the transition probability of such
coherent transition process is macroscopically large compared to other
stimulated emission/absorption and spontaneous emission processes.Comment: 7 pages, no figure
On Berezinskii-Kosterlitz-Thouless Phase Transition in Quasi-One Dimensional Bose-Einstein Condensate
We show that quasi-one dimensional Bose-Einstein condensate under suitable
conditions can exhibit a Berezinskii-Kosterlitz-Thouless phase transition. The
role played by quantized vortices in two dimensional case, is played in this
case by dark solitons. We find that the critical temperature for this
transition lies in nano Kelvin range and below, for a wide range of
experimentally accessible parameters. It is seen that the high temperature
(disordered) phase differs from low temperature (ordered) phase in terms of
phase coherence, which can be used as an experimental signature for observing
this transition.Comment: Minor changes, few references added. REVTEX 4, 10 pages, 1 figur
Some results on topological currents in field theory
A few exact results concerning topological currents in field theories are
obtained. It is generally shown that, a topological charge can not generate any
kind of symmetry transformation on the fields. It is also proven that, the
existence of a charge that does not generate any kind of symmetry
transformation on the fields, has to be of topological origin. As a
consequence, it is found that in a given theory, superconductivity via
Anderson-Higgs route can only occur if the gauge coupling with other fields is
minimal. Several physical implications of these results are studied.Comment: LaTeX2e, 20 pages, no figures. To appear in IJMP
Possible Realization of non-BCS type Superconductivity in Graphene
We show that the gauge field induced due to non-uniform hopping, in gapped
graphene, can give rise to a non-BCS type of superconductivity. Unlike the
conventional mechanisms, this superconductivity phenomena does not require any
pairing. We estimate the critical temperature for superconducting-to-normal
transition via Berezinskii-Kosterlitz-Thouless mechanism. Possibility of
observing the same in ultra cold atomic gases is also pointed out.Comment: Major Revision, 4 pages, no figure
Soliton solutions of driven non-linear and higher order non-linear Schr\"odinger equations
We analyse the structure of the exact, dark and bright soliton solutions of
the driven non-linear Schr\"odinger equation. It is found that, a wide class of
solutions of the higher order non-linear Schr\"odinger equation with a source
can also be obtained through the above procedure. Distinct parameter ranges,
allowing the existence of these solutions, phase locked with their respective
sources, are delineated. Conditions for obtaining non-propagating solutions are
found to be quite different for both the equations. A special case, where the
scale of the soliton emerges as a free parameter, is obtained and the condition
under which solitons can develop singularity is pointed out. We also study the
highly restrictive structure of the localised solutions, when the phase and
amplitude get coupled.Comment: 10 pages, 2 figure
Chirped chiral solitons in nonlinear Schr\"odinger equation with self-steepening and self-frequency shift
We find exact solutions to nonlinear Schr\"odinger equation in the presence
of self-steepening and self-frequency shift. These include periodic solutions
and localized solutions of dark-bright type which can be {\emph{chiral}}, and
chirality being controlled by sign of self steepening term. A new form of self
phase modulation, which can be tuned by higher order nonlinearities as also by
the initial conditions, distinct from nonlinear Schr\"odinger equation,
characterizes these solutions. In certain nontrivial parameter domain solutions
are found to satisfy {\emph{linear}} Schr\"odinger equation, indicating
possiblity of linear superposition in this nonlinear system. Dark and bright
solitons exist in both anomalous and normal dispersion regimes and a duality
between dark-bright type of solution and kinematic-higher order chirping is
also seen. Localized kink solutions similar to NLSE solitons, but with very
different self phase modulation, are identified.Comment: 4 pages, ReVTeX format with two figure
Travelling wave solutions to nonlinear Schrodinger equation with self-steepening and self-frequency shift
We investigate exact travelling wave solutions of higher order nonlinear
Schrodinger equation in the absence of third order dispersion, which exhibit
non-trivial self phase modulation. It is shown that, the corresponding
dynamical equation, governing the evolution of intensity in the femtosecond
regime, is that of non-linear Schrodinger equation with a source. The exact
localized solutions to this system can have both super and subluminal
propagation belonging to two distinct class. A number of these solitons exhibit
chirality, thereby showing preferential propagation behavior determined by
group velocity dispersion. Both localized bright and dark solitons are found in
complementary velocity and experimental parameter domains, which can exist for
anomalous and normal dispersion regimes. It is found that, dark solitons in
this system propagate with non-zero velocity, unlike their counterpart in
nanosecond regime. Interestingly, subluminal propagation is observed for
solitons having a nontrivial Pade type intensity profile.Comment: REVTEX 4, 8 pages, 2 figure
A method to solve nonlinear Schr\"odinger equation using Riccati equation
A method to find exact solutions to nonlinear Schr\"odinger equation, defined
on a line and on a plane, is found by connecting it with second order linear
ordinary differential equation. The connection is essentially made using
Riccati equation. Generalisation of several known solutions is found using this
method, in case of nonlinear Schr\"odinger equation defined on a line. This
method also yields non-singular and singular vortex solutions, when applied to
nonlinear Schr\"odinger equation on a plane.Comment: LaTeX2e, 6 pages, no figure