21 research outputs found
Simultaneous eigenstates of the number-difference operator and a bilinear interaction Hamiltonian derived by solving a complex differential equation
As a continuum work of Bhaumik et al who derived the common eigenvector of
the number-difference operator Q and pair-annihilation operator ab (J. Phys. A9
(1976) 1507) we search for the simultaneous eigenvector of Q and
(ab-a^{+}b^{+}) by setting up a complex differential equation in the bipartite
entangled state representation. The differential equation is then solved in
terms of the two-variable Hermite polynomials and the formal hypergeometric
functions. The work is also an addendum to Mod. Phys. Lett. A 9 (1994) 1291 by
Fan and Klauder, in which the common eigenkets of Q and pair creators are
discussed
Strong-field dipole resonance. I. Limiting analytical cases
We investigate population dynamics in N-level systems driven beyond the
linear regime by a strong external field, which couples to the system through
an operator with nonzero diagonal elements. As concrete example we consider the
case of dipolar molecular systems. We identify limiting cases of the
Hamiltonian leading to wavefunctions that can be written in terms of ordinary
exponentials, and focus on the limits of slowly and rapidly varying fields of
arbitrary strength. For rapidly varying fields we prove for arbitrary that
the population dynamics is independent of the sign of the projection of the
field onto the dipole coupling. In the opposite limit of slowly varying fields
the population of the target level is optimized by a dipole resonance
condition. As a result population transfer is maximized for one sign of the
field and suppressed for the other one, so that a switch based on flopping the
field polarization can be devised. For significant sign dependence the
resonance linewidth with respect to the field strength is small. In the
intermediate regime of moderate field variation, the integral of lowest order
in the coupling can be rewritten as a sum of terms resembling the two limiting
cases, plus correction terms for N>2, so that a less pronounced sign-dependence
still exists.Comment: 34 pages, 1 figur
Spatial distribution of persistent sites
We study the distribution of persistent sites (sites unvisited by particles
) in one dimensional reaction-diffusion model. We define
the {\it empty intervals} as the separations between adjacent persistent sites,
and study their size distribution as a function of interval length
and time . The decay of persistence is the process of irreversible
coalescence of these empty intervals, which we study analytically under the
Independent Interval Approximation (IIA). Physical considerations suggest that
the asymptotic solution is given by the dynamic scaling form
with the average interval size . We show
under the IIA that the scaling function as and
decays exponentially at large . The exponent is related to the
persistence exponent through the scaling relation .
We compare these predictions with the results of numerical simulations. We
determine the two-point correlation function under the IIA. We find
that for , where , in agreement
with our earlier numerical results.Comment: 15 pages in RevTeX, 5 postscript figure
Thermal Casimir effect for neutrino and electromagnetic fields in closed Friedmann cosmological model
We calculate the total internal energy, total energy density and pressure,
and the free energy for the neutrino and electromagnetic fields in Einstein and
closed Friedmann cosmological models. The Casimir contributions to all these
quantities are separated. The asymptotic expressions for both the total
internal energy and free energy, and for the Casimir contributions to them are
found in the limiting cases of low and high temperatures. It is shown that the
neutrino field does not possess a classical limit at high temperature. As for
the electromagnetic field, we demonstrate that the total internal energy has
the classical contribution and the Casimir internal energy goes to the
classical limit at high temperature. The respective Casimir free energy
contains both linear and logarithmic terms with respect to the temperature. The
total and Casimir entropies for the neutrino and electromagnetic fields at low
temperature are also calculated and shown to be in agreement with the Nernst
heat theorem.Comment: 23 pages, to appear in Phys. Rev.
Shell Model for Time-correlated Random Advection of Passive Scalars
We study a minimal shell model for the advection of a passive scalar by a
Gaussian time correlated velocity field. The anomalous scaling properties of
the white noise limit are studied analytically. The effect of the time
correlations are investigated using perturbation theory around the white noise
limit and non-perturbatively by numerical integration. The time correlation of
the velocity field is seen to enhance the intermittency of the passive scalar.Comment: Replaced with final version + updated figure
Fractional Langevin Equation: Over-Damped, Under-Damped and Critical Behaviors
The dynamical phase diagram of the fractional Langevin equation is
investigated for harmonically bound particle. It is shown that critical
exponents mark dynamical transitions in the behavior of the system. Four
different critical exponents are found. (i) marks a
transition to a non-monotonic under-damped phase, (ii)
marks a transition to a resonance phase when an external oscillating field
drives the system, (iii) and (iv)
marks transition to a double peak phase of the
"loss" when such an oscillating field present. As a physical explanation we
present a cage effect, where the medium induces an elastic type of friction.
Phase diagrams describing over-damped, under-damped regimes, motion and
resonances, show behaviors different from normal.Comment: 18 pages, 15 figure
Continuous Limit of Discrete Systems with Long-Range Interaction
Discrete systems with long-range interactions are considered. Continuous
medium models as continuous limit of discrete chain system are defined.
Long-range interactions of chain elements that give the fractional equations
for the medium model are discussed. The chain equations of motion with
long-range interaction are mapped into the continuum equation with the Riesz
fractional derivative. We formulate the consistent definition of continuous
limit for the systems with long-range interactions. In this paper, we consider
a wide class of long-range interactions that give fractional medium equations
in the continuous limit. The power-law interaction is a special case of this
class.Comment: 23 pages, LaTe