99 research outputs found
Quantum Integrability and Chaos in periodic Toda Lattice with Balanced Loss-Gain
We consider equal-mass quantum Toda lattice with balanced loss-gain for two
and three particles. The two-particle Toda lattice is integrable and two
integrals of motion which are in involution have been found. The bound-state
energy and the corresponding eigenfunctions have been obtained numerically for
a few low-lying states. The three-particle quantum Toda lattice with balanced
loss-gain and velocity mediated coupling admits mixed phases of integrability
and chaos depending on the value of the loss-gain parameter. We have obtained
analytic expressions for two integrals of motion which are in involution.
Although an analytic expression for the third integral has not been found, the
numerical investigation suggests integrability below a critical value of the
loss-gain strength and chaos above this critical value. The level spacing
distribution changes from the Wigner-Dyson to the Poisson distribution as the
loss-gain parameter passes through this critical value and approaches zero. An
identical behaviour is seen in terms of the gap-ratio distribution of the
energy levels. The existence of mixed phases of quantum integrability and chaos
in the specified ranges of the loss-gain parameter has also been confirmed
independently via the study of level repulsion and complexity in higher order
excited states.Comment: 12 pages, 12 figures, two colum
Solvable Limits of a class of generalized Vector Nonlocal Nonlinear Schr\"odinger equation with balanced loss-gain
We consider a class of one dimensional Vector Nonlocal Non-linear
Schr\"odinger Equation (VNNLSE) in an external complex potential with
time-modulated Balanced Loss-Gain(BLG) and Linear Coupling(LC) among the
components of Schr\"odinger fields, and space-time dependent nonlinear
strength. The system admits Lagrangian and Hamiltonian formulations under
certain conditions. It is shown that various dynamical variables like total
power, -symmetric Hamiltonian, width of the wave-packet and its speed
of growth, etc. are real-valued despite the Hamiltonian density being
complex-valued. We study the exact solvability of the generic VNNLSE with or
without a Hamiltonian formulation. In the first part, we study time-evolution
of moments which are analogous to space-integrals of Stokes variables and find
condition for existence of solutions which are bounded in time. In the second
part, we use a non-unitary transformation followed by a coordinate
transformation to map the VNNLSE to various solvable equations. The cordinate
transformation is not required at all for the limiting case when non-unitary
transformation reduces to pseudo-unitary transformation. The exact solutions
are bounded in time for the same condition which is obtained through the study
of time-evolution of moments. Various exact solutions of the VNNLSE are
presented.Comment: To appear in Physica Script
Non-linear Schrdinger equation with time-dependent balanced loss-gain and space-time modulated non-linear interaction
We consider a class of one dimensional vector Non-linear Schrdinger
Equation(NLSE) in an external complex potential with Balanced Loss-Gain(BLG)
and Linear Coupling(LC) among the components of the Schrdinger field.
The solvability of the generic system is investigated for various combinations
of time modulated LC and BLG terms, space-time dependent strength of the
nonlinear interaction and complex potential. We use a non-unitary
transformation followed by a reformulation of the differential equation in a
new coordinate system to map the NLSE to solvable equations. Several physically
motivated examples of exactly solvable systems are presented for various
combinations of LC and BLG, external complex potential and nonlinear
interaction. Exact localized nonlinear modes with spatially constant phase may
be obtained for any real potential for which the corresponding linear
Schrdinger equation is solvable. A method based on supersymmetric
quantum mechanics is devised to construct exact localized nonlinear modes for a
class of complex potentials. The real superpotential corresponding to any
exactly solved linear Schrdinger equation may be used to find a
complex-potential for which exact localized nonlinear modes for the NLSE can be
obtained. The solutions with singular phases are obtained for a few complex
potentials.Comment: Two column, 15 pages,No figur
Entanglement dynamics following a sudden quench: an exact solution
We present an exact and fully analytical treatment of the entanglement
dynamics for an isolated system of coupled oscillators following a sudden
quench of the system parameters. The system is analyzed using the solutions of
the time dependent Schrodinger's equation, which are obtained by solving the
corresponding nonlinear Ermakov equations. The entanglement entropies exhibit a
multi-oscillatory behaviour, where the number of dynamically generated time
scales increases with . The harmonic chains exhibit entanglement revival and
for larger values of , we find near-critical logarithmic scaling for
the entanglement entropy, which is modulated by a time dependent factor. The
case is equivalent to the two site Bose-Hubbard model in the tunneling
regime, which is amenable to empirical realization in cold atom systems.Comment: Figure for large N added, discussion related with near critical
scaling behavior adde
Particles with selective wetting affect spinodal decomposition microstructures
We have used mesoscale simulations to study the effect of immobile particles
on microstructure formation during spinodal decomposition in ternary mixtures
such as polymer blends. Specifically, we have explored a regime of
interparticle spacings (which are a few times the characteristic spinodal
length scale) in which we might expect interesting new effects arising from
interactions among wetting, spinodal decomposition and coarsening. In this
paper, we report three new effects for systems in which the particle phase has
a strong preference for being wetted by one of the components (say, A). In the
presence of particles, microstructures are not bicontinuous in a symmetric
mixture. An asymmetric mixture, on the other hand, first forms a
non-bicontinuous microstructure which then evolves into a bicontinuous one at
intermediate times. Moreover, while wetting of the particle phase by the
preferred component (A) creates alternating A-rich and B-rich layers around the
particles, curvature-driven coarsening leads to shrinking and disappearance of
the first A-rich layer, leaving a layer of the non-preferred component in
contact with the particle. At late simulation times, domains of the matrix
components coarsen following the Lifshitz-Slyozov-Wagner law, .Comment: Accepted for publication in PCCP on 24th May 201
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