2,183 research outputs found
Orientational relaxation in a dispersive dynamic medium : Generalization of the Kubo-Ivanov-Anderson jump diffusion model to include fractional environmental dynamics
Ivanov-Anderson (IA) model (and an earlier treatment by Kubo) envisages a
decay of the orientational correlation by random but large amplitude molecular
jumps, as opposed to infinitesimal small jumps assumed in Brownian diffusion.
Recent computer simulation studies on water and supercooled liquids have shown
that large amplitude motions may indeed be more of a rule than exception.
Existing theoretical studies on jump diffusion mostly assume an exponential
(Poissonian) waiting time distribution for jumps, thereby again leading to an
exponential decay. Here we extend the existing formalism of Ivanov and Anderson
to include an algebraic waiting time distribution between two jumps. As a
result, the first and second rank orientational time correlation functions show
the same long time power law, but their short time decay behavior is quite
different. The predicted Cole-Cole plot of dielectric relaxation reproduces
various features of non-Debye behaviour observed experimentally. We also
developed a theory where both unrestricted small jumps and large angular jumps
coexist simultaneously. The small jumps are shown to have a large effect on the
long time decay, particularly in mitigating the effects of algebraic waiting
time distribution, and in giving rise to an exponential-like decay, with a time
constant, surprisingly, less than the time constant that arises from small
amplitude decay alone.Comment: 14 figure
Orientational relaxation in a discotic liquid crystal
We investigate orientational relaxation of a model discotic liquid crystal,
consists of disc-like molecules, by molecular dynamics simulations along two
isobars starting from the high temperature isotropic phase. The two isobars
have been so chosen that (A) the phase sequence isotropic (I)-nematic
(N)-columnar (C) appears upon cooling along one of them and (B) the sequence
isotropic (I)-columnar (C) along the other. While the orientational relaxation
in the isotropic phase near the I-N phase transition in system (A) shows a
power law decay at short to intermediate times, such power law relaxation is
not observed in the isotropic phase near the I-C phase boundary in system (B).
In order to understand this difference (the existence or the absence of the
power law decay), we calculated the the growth of the orientational pair
distribution functions (OPDF) near the I-N phase boundary and also near the I-C
phase boundary. We find that OPDF shows a marked growth in long range
correlation as the I-N phase boundary is approached in the I-N-C system (A),
but such a growth is absent in the I-C system, which appears to be consistent
with the result that I-N phase transition in the former is weakly first order
while the the I-C phase transition in the later is not weak. As the system
settles into the nematic phase, the decay of the single-particle second-rank
orientational OTCF follows a pattern that is similar to what is observed with
calamitic liquid crystals and supercooled molecular liquids.Comment: 16 pages and 4 figure
Competing PT potentials and re-entrant PT symmetric phase for a particle in a box
We investigate the effects of competition between two complex,
-symmetric potentials on the -symmetric phase of a
"particle in a box". These potentials, given by and
, represent long-range and localized
gain/loss regions respectively. We obtain the -symmetric phase in
the plane, and find that for locations near the edge of the
box, the -symmetric phase is strengthened by additional losses to
the loss region. We also predict that a broken -symmetry will be
restored by increasing the strength of the localized potential. By
comparing the results for this problem and its lattice counterpart, we show
that a robust -symmetric phase in the continuum is consistent
with the fragile phase on the lattice. Our results demonstrate that systems
with multiple, -symmetric potentials show unique, unexpected
properties.Comment: 7 pages, 3 figure
Entropy of three-dimensional asymptotically flat cosmological solutions
The thermodynamics of three-dimensional asymptotically flat cosmological
solutions that play the same role than the BTZ black holes in the anti-de
Sitter case is derived and explained from holographic properties of flat space.
It is shown to coincide with the flat-space limit of the thermodynamics of the
inner black hole horizon on the one hand and the semi-classical approximation
to the gravitational partition function associated to the entropy of the outer
horizon on the other. This leads to the insight that it is the Massieu function
that is universal in the sense that it can be computed at either horizon.Comment: 16 pages Latex file, v2: references added, cosmetic changes, v3: 1
reference adde
Inductive algebras and homogeneous shifts
Inductive algebras for the irreducible unitary representations of the
universal cover of the group of unimodular two by two matrices are classified.
The classification of homogeneous shift operators is obtained as a direct
consequence. This gives a new approach to the results of Bagchi and Misra
Pseudo-Hermiticity and some consequences of a generalized quantum condition
We exploit the hidden symmetry structure of a recently proposed non-Hermitian
Hamiltonian and of its Hermitian equivalent one. This sheds new light on the
pseudo-Hermitian character of the former and allows access to a generalized
quantum condition. Special cases lead to hyperbolic and Morse-like potentials
in the framework of a coordinate-dependent mass model.Comment: 10 pages, no figur
Pseudo-Hermitian Interactions in Dirac Theory: Examples
We consider a couple of examples to study the pseudo-Hermitian interaction in
relativistic quantum mechanics. Rasbha interaction, commonly used to study the
spin Hall effect, is considered with imaginary coupling. The corresponding
Dirac Hamiltonian is shown to be parity pseudo-Hermitian. In the other example
we consider parity pseudo-Hermitian scalar interaction with arbitrary parameter
in Dirac theory. In both the cases we show that the energy spectrum is real and
all the other features of non-relativistic pseudo-Hermitian formulation are
present. Using the spectral method the positive definite metric operator
() has been calculated explicitly for both the models to ensure positive
definite norms for the state vectors.Comment: 13 pages, Latex, No figs, Revised version to appear in MPL
Mean field baryon magnetic moments and sumrules
New developments have spurred interest in magnetic moments (-s) of
baryons. The measurement of some of the decuplet -s and the findings of
new sumrules from various methods are partly responsible for this renewed
interest. Our model, inspired by large colour approximation, is a relativistic
self consistent mean field description with a modified Richardson potential and
is used to describe the -s and masses of all baryons with up (u), down (d)
and strange (s) quarks. We have also checked the validity of the Franklin
sumrule (referred to as CGSR in the literature) and sumrules of Luty,
March-Russell and White. We found that our result for sumrules matches better
with experiment than the non-relativistic quark model prediction. We have also
seen that quark magnetic moments depend on the baryon in which they belong
while the naive quark model expects them to be constant.Comment: 7 pages, no figure, uses epl.cl
Shape-invariant quantum Hamiltonian with position-dependent effective mass through second order supersymmetry
Second order supersymmetric approach is taken to the system describing motion
of a quantum particle in a potential endowed with position-dependent effective
mass. It is shown that the intertwining relations between second order partner
Hamiltonians may be exploited to obtain a simple shape-invariant condition.
Indeed a novel relation between potential and mass functions is derived, which
leads to a class of exactly solvable model. As an illustration of our
procedure, two examples are given for which one obtains whole spectra
algebraically. Both shape-invariant potentials exhibit harmonic-oscillator-like
or singular-oscillator-like spectra depending on the values of the
shape-invariant parameter.Comment: 16 pages, 5 figs; Present e-mail of AG: [email protected]
- …