2,489 research outputs found
Generalized Continuity Equation and Modified Normalization in PT-Symmetric Quantum Mechanics
The continuity equation relating the change in time of the position
probability density to the gradient of the probability current density is
generalized to PT-symmetric quantum mechanics. The normalization condition of
eigenfunctions is modified in accordance with this new conservation law and
illustrated with some detailed examples.Comment: 16 pages, amssy
PT-symmetric square well and the associated SUSY hierarchies
The PT-symmetric square well problem is considered in a SUSY framework. When
the coupling strength lies below the critical value
where PT symmetry becomes spontaneously broken, we find a hierarchy of SUSY
partner potentials, depicting an unbroken SUSY situation and reducing to the
family of -like potentials in the limit. For above
, there is a rich diversity of SUSY hierarchies, including
some with PT-symmetry breaking and some with partial PT-symmetry restoration.Comment: LaTeX, 18 pages, no figure; broken PT-symmetry case added (Sec. 6
Bridging the Gap Between the Mode Coupling and the Random First Order Transition Theories of Structural Relaxation in Liquids
A unified treatment of structural relaxation in a deeply supercooled glassy
liquid is developed which extends the existing mode coupling theory (MCT) by
incorporating the effects of activated events by using the concepts from the
random first order transition (RFOT) theory. We show how the decay of the
dynamic structure factor is modified by localized activated events (called
instantons) which lead to the spatial reorganization of molecules in the region
where the instanton pops up. The instanton vertex added to the usual MCT
depicts the probability and consequences of such an event which can be derived
from the random first order transition theory. The vertex is proportional to
where is the configurational entropy. Close to the
glass transition temperature, , since is diminishing, the
activated process slows beyond the time window and this eventually leads to an
arrest of the structural relaxation as expected for glasses. The combined
treatment describes the dynamic structure factor in deeply supercooled liquid
fairly well, with a hopping dominated decay following the MCT plateau.Comment: 11 pages, 5 figures, 1 tabl
Dynamical Heterogeneity and the interplay between activated and mode coupling dynamics in supercooled liquids
We present a theoretical analysis of the dynamic structure factor (DSF) of a
liquid at and below the mode coupling critical temperature , by developing
a self-consistent theoretical treatment which includes the contributions both
from continuous diffusion, described using general two coupling parameter
() mode coupling theory (MCT), and from the activated hopping,
described using the random first order transition (RFOT) theory, incorporating
the effect of dynamical heterogeneity. The theory is valid over the whole
temperature plane and shows correct limiting MCT like behavior above
and goes over to the RFOT theory near the glass transition temperature,
. Between and , the theory predicts that neither the
continuous diffusion, described by pure mode coupling theory, nor the hopping
motion alone suffices but both contribute to the dynamics while interacting
with each other. We show that the interplay between the two contributions
conspires to modify the relaxation behavior of the DSF from what would be
predicted by a theory with a complete static Gaussian barrier distribution in a
manner that may be described as a facilitation effect. Close to , coupling
between the short time part of MCT dynamics and hopping reduces the stretching
given by the F-MCT theory significantly and accelerates structural
relaxation. As the temperature is progressively lowered below , the
equations yield a crossover from MCT dominated regime to the hopping dominated
regime. In the combined theory the dynamical heterogeneity is modified because
the low barrier components interact with the MCT dynamics to enhance the
relaxation rate below and reduces the stretching that would otherwise
arise from an input static barrier height distribution.Comment: 7 pages, 4 figure
New approach to (quasi)-exactly solvable Schrodinger equations with a position-dependent effective mass
By using the point canonical transformation approach in a manner distinct
from previous ones, we generate some new exactly solvable or quasi-exactly
solvable potentials for the one-dimensional Schr\"odinger equation with a
position-dependent effective mass. In the latter case, SUSYQM techniques
provide us with some additional new potentials.Comment: 11 pages, no figur
Universal power law in the orientational relaxation in thermotropic liquid crystals
We observe a surprisingly general power law decay at short to intermediate
times in orientational relaxation in a variety of model systems (both calamitic
and discotic, and also discrete) for thermotropic liquid crystals. As all these
systems transit across the isotropic-nematic phase boundary, two power law
relaxation regimes, separated by a plateau, emerge giving rise to a step-like
feature (well-known in glassy liquids) in the single-particle second-rank
orientational time correlation function. In contrast to its probable dynamical
origin in supercooled liquids, we show that the power law here can originate
from the thermodynamic fluctuations of the orientational order parameter,
driven by the rapid growth in the second-rank orientational correlation length.Comment: Submitted to Physical Review Letter
Comparison of the effects of three different (-)-hydroxycitric acid preparations on food intake in rats: response
A response to Louter-van de Haar J, Wielinga PY, Scheurink AJ, Nieuwenhuizen AG: Comparison of the effects of three different (-)-hydroxycitric acid preparations on food intake in rats. Nutr Metabol 2005, 2:2
Generating Complex Potentials with Real Eigenvalues in Supersymmetric Quantum Mechanics
In the framework of SUSYQM extended to deal with non-Hermitian Hamiltonians,
we analyze three sets of complex potentials with real spectra, recently derived
by a potential algebraic approach based upon the complex Lie algebra sl(2, C).
This extends to the complex domain the well-known relationship between SUSYQM
and potential algebras for Hermitian Hamiltonians, resulting from their common
link with the factorization method and Darboux transformations. In the same
framework, we also generate for the first time a pair of elliptic partner
potentials of Weierstrass type, one of them being real and the other
imaginary and PT symmetric. The latter turns out to be quasiexactly solvable
with one known eigenvalue corresponding to a bound state. When the Weierstrass
function degenerates to a hyperbolic one, the imaginary potential becomes PT
non-symmetric and its known eigenvalue corresponds to an unbound state.Comment: 20 pages, Latex 2e + amssym + graphics, 2 figures, accepted in Int.
J. Mod. Phys.
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