2,569 research outputs found
Geometric Phase and Classical-Quantum Correspondence
We study the geometric phase factors underlying the classical and the
corresponding quantum dynamics of a driven nonlinear oscillator exhibiting
chaotic dynamics. For the classical problem, we compute the geometric phase
factors associated with the phase space trajectories using Frenet-Serret
formulation. For the corresponding quantum problem, the geometric phase
associated with the time evolution of the wave function is computed. Our
studies suggest that the classical geometric phase may be related to the the
difference in the quantum geometric phases between two neighboring eigenstates.Comment: Copy with higher resolution figures can be obtained from
http://physics.gmu.edu/~isatija by clicking on publications. to appear in the
Yukawa Institute conference proceedings, {\it Quantum Mechanics and Chaos:
From Fundamental Problems through Nano-Science} (2003
Solitons in a hard-core bosonic system: Gross-Pitaevskii type and beyond
A unified formulation that obtains solitary waves for various background
densities in the Bose-Einstein condensate of a system of hard-core bosons with
nearest neighbor attractive interactions is presented.
In general, two species of solitons appear: A nonpersistent (NP) type that
fully delocalizes at its maximum speed, and a persistent (P) type that survives
even at its maximum speed, and transforms into a periodic train of solitons
above this speed. When the background condensate density is nonzero, both
species coexist, the soliton is associated with a constant intrinsic frequency,
and its maximum speed is the speed of sound. In contrast, when the background
condensate density is zero, the system has neither a fixed frequency, nor a
speed of sound. Here, the maximum soliton speed depends on the frequency, which
can be tuned to lead to a cross-over between the NP-type and the P-type at a
certain critical frequency, determined by the energy parameters of the system.
We provide a single functional form for the soliton profile, from which diverse
characteristics for various background densities can be obtained. Using the
mapping to spin systems enables us to characterize the corresponding class of
magnetic solitons in
Heisenberg spin chains with different types of anisotropy, in a unified
fashion
Other incarnations of the Gross-Pitaevskii dark soliton
We show that the dark soliton of the Gross-Pitaevskii equation (GPE) that
describes the Bose-Einstein condensate (BEC) density of a system of weakly
repulsive bosons, also describes that of a system of strongly repulsive hard
core bosons at half filling. As a consequence of this, the GPE soliton gets
related to the magnetic soliton in an easy-plane ferromagnet, where it
describes the square of the in-plane magnetization of the system. These
relationships are shown to be useful in understanding various characteristics
of solitons in these distinct many-body systems
Stochastically perturbed flows: Delayed and interrupted evolution
We present analytical expressions for the time-dependent and stationary
probability distributions corresponding to a stochastically perturbed
one-dimensional flow with critical points, in two physically relevant
situations: delayed evolution, in which the flow alternates with a quiescent
state in which the variate remains frozen at its current value for random
intervals of time; and interrupted evolution, in which the variate is also
re-set in the quiescent state to a random value drawn from a fixed
distribution. In the former case, the effect of the delay upon the first
passage time statistics is analyzed. In the latter case, the conditions under
which an extended stationary distribution can exist as a consequence of the
competition between an attractor in the flow and the random re-setting are
examined. We elucidate the role of the normalization condition in eliminating
the singularities arising from the unstable critical points of the flow, and
present a number of representative examples. A simple formula is obtained for
the stationary distribution and interpreted physically. A similar
interpretation is also given for the known formula for the stationary
distribution in a full-fledged dichotomous flow.Comment: 27 pages; no figures. Submitted to Stochastics and Dynamic
Ladder operators for isospectral oscillators
We present, for the isospectral family of oscillator Hamiltonians, a
systematic procedure for constructing raising and lowering operators satisfying
any prescribed `distorted' Heisenberg algebra (including the
-generalization). This is done by means of an operator transformation
implemented by a shift operator. The latter is obtained by solving an
appropriate partial isometry condition in the Hilbert space. Formal
representations of the non-local operators concerned are given in terms of
pseudo-differential operators. Using the new annihilation operators, new
classes of coherent states are constructed for isospectral oscillator
Hamiltonians. The corresponding Fock-Bargmann representations are also
considered, with specific reference to the order of the entire function family
in each case.Comment: 13 page
Particle-Hole Asymmetry and Brightening of Solitons in A Strongly Repulsive BEC
We study solitary wave propagation in the condensate of a system of hard-core
bosons with nearest-neighbor interactions. For this strongly repulsive system,
the evolution equation for the condensate order parameter of the system,
obtained using spin coherent state averages is different from the usual
Gross-Pitaevskii equation (GPE). The system is found to support two kinds of
solitons when there is a particle-hole imbalance: a dark soliton that dies out
as the velocity approaches the sound velocity, and a new type of soliton which
brightens and persists all the way up to the sound velocity, transforming into
a periodic wave train at supersonic speed. Analogous to the GPE soliton, the
energy-momentum dispersion for both solitons is characterized by Lieb II modes.Comment: Accepted for publication in PRL, Nov 12, 200
Self-assembly of iron nanoclusters on the Fe3O4(111) superstructured surface
We report on the self-organized growth of a regular array of Fe nanoclusters
on a nanopatterned magnetite surface. Under oxidizing preparation conditions
the (111) surface of magnetite exhibits a regular superstructure with
three-fold symmetry and a 42 A periodicity. This superstructure represents an
oxygen terminated (111) surface, which is reconstructed to form a periodically
strained surface. This strain patterned surface has been used as a template for
the growth of an ultrathin metal film. A Fe film of 0.5 A thickness was
deposited on the substrate at room temperature. Fe nanoclusters are formed on
top of the surface superstructure creating a regular array with the period of
the superstructure. We also demonstrate that at least the initial stage of Fe
growth occurs in two-dimensional mode. In the areas of the surface where the
strain pattern is not formed, random nucleation of Fe was observed.Comment: 6 pages, 3 figure
Symmetry-Breaking and Symmetry-Restoring Dynamics of a Mixture of Bose-Einstein Condensates in a Double Well
We study the coherent nonlinear tunneling dynamics of a binary mixture of
Bose-Einstein condensates in a double-well potential. We demonstrate the
existence of a new type of mode associated with the "swapping" of the two
species in the two wells of the potential. In contrast to the symmetry breaking
macroscopic quantum self-trapping (MQST) solutions, the swapping modes
correspond to the tunneling dynamics that preserves the symmetry of the double
well potential. As a consequence of two distinct types of broken symmetry MQST
phases where the two species localize in the different potential welils or
coexist in the same well, the corresponding symmetry restoring swapping modes
result in dynamics where the the two species either avoid or chase each other.
In view of the possibility to control the interaction between the species, the
binary mixture offers a very robust system to observe these novel effects as
well as the phenomena of Josephson oscillations and pi-mode
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