3,217 research outputs found
Dynamics of multi-kinks in the presence of wells and barriers
Sine-Gordon kinks are a much studied integrable system that possesses
multi-soliton solutions. Recent studies on sine-Gordon kinks with
space-dependent square-well-type potentials have revealed interesting dynamics
of a single kink interacting with wells and barriers. In this paper, we study a
class of smooth space-dependent potentials and discuss the dynamics of one kink
in the presence of different wells. We also present values for the critical
velocity for different types of barriers. Furthermore, we study two kinks
interacting with various wells and describe interesting trajectories such as
double-trapping, kink knock-out and double-escape.Comment: 17 pages, 7 figure
Iterative Solutions for Low Lying Excited States of a Class of Schroedinger Equation
The convergent iterative procedure for solving the groundstate Schroedinger
equation is extended to derive the excitation energy and the wave function of
the low-lying excited states. The method is applied to the one-dimensional
quartic potential problem. The results show that the iterative solution
converges rapidly when the coupling is not too small.Comment: 14 pages, 4 figure
A New Superintegrable Hamiltonian
We identify a new superintegrable Hamiltonian in 3 degrees of freedom,
obtained as a reduction of pure Keplerian motion in 6 dimensions. The new
Hamiltonian is a generalization of the Keplerian one, and has the familiar 1/r
potential with three barrier terms preventing the particle crossing the
principal planes. In 3 degrees of freedom, there are 5 functionally independent
integrals of motion, and all bound, classical trajectories are closed and
strictly periodic. The generalisation of the Laplace-Runge-Lenz vector is
identified and shown to provide functionally independent isolating integrals.
They are quartic in the momenta and do not arise from separability of the
Hamilton-Jacobi equation. A formulation of the system in action-angle variables
is presented.Comment: 11 pages, 4 figures, submitted to The Journal of Mathematical Physic
Macroscopic quantum many-body tunneling of attractive Bose-Einstein condensate in anharmonic trap
We study the stability of attractive atomic Bose-Einstein condensate and the
macroscopic quantum many-body tunneling (MQT) in the anharmonic trap. We
utilize correlated two-body basis function which keeps all possible two-body
correlations. The anharmonic parameter () is slowly tuned from
harmonic to anharmonic. For each choice of the many-body equation is
solved adiabatically. The use of the van der Waals interaction gives realistic
picture which substantially differs from the mean-field results. For weak
anharmonicity, we observe that the attractive condensate gains stability with
larger number of bosons compared to that in the pure harmonic trap. The
transition from resonances to bound states with weak anharmonicity also differs
significantly from the earlier study of Moiseyev {\it et.al.}[J. Phys. B: At.
Mol. Opt. Phys. {\bf{37}}, L193 (2004)]. We also study the tunneling of the
metastable condensate very close to the critical number of collapse
and observe that near collapse the MQT is the dominant decay mechanism compared
to the two-body and three-body loss rate. We also observe the power law
behavior in MQT near the critical point. The results for pure harmonic trap are
in agreement with mean-field results. However we fail to retrieve the power law
behavior in anharmonic trap although MQT is still the dominant decay mechanism.Comment: Accepted in Eur. Phys. J. D (2013
The Order of Phase Transitions in Barrier Crossing
A spatially extended classical system with metastable states subject to weak
spatiotemporal noise can exhibit a transition in its activation behavior when
one or more external parameters are varied. Depending on the potential, the
transition can be first or second-order, but there exists no systematic theory
of the relation between the order of the transition and the shape of the
potential barrier. In this paper, we address that question in detail for a
general class of systems whose order parameter is describable by a classical
field that can vary both in space and time, and whose zero-noise dynamics are
governed by a smooth polynomial potential. We show that a quartic potential
barrier can only have second-order transitions, confirming an earlier
conjecture [1]. We then derive, through a combination of analytical and
numerical arguments, both necessary conditions and sufficient conditions to
have a first-order vs. a second-order transition in noise-induced activation
behavior, for a large class of systems with smooth polynomial potentials of
arbitrary order. We find in particular that the order of the transition is
especially sensitive to the potential behavior near the top of the barrier.Comment: 8 pages, 6 figures with extended introduction and discussion; version
accepted for publication by Phys. Rev.
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