26,469 research outputs found
Supersymmetric analysis for the Dirac equation with spin-symmetric and pseudo-spin-symmetric interactions
A supersymmetric analysis is presented for the d-dimensional Dirac equation
with central potentials under spin-symmetric
(S(r) = V(r)) and pseudo-spin-symmetric (S(r) = - V(r)) regimes. We construct
the explicit shift operators that are required to factorize the Dirac
Hamiltonian with the Kratzer potential. Exact solutions are provided for both
the Coulomb and Kratzer potentials.Comment: 12 page
Collective Oscillations of Vortex Lattices in Rotating Bose-Einstein Condensates
The complete low-energy collective-excitation spectrum of vortex lattices is
discussed for rotating Bose-Einstein condensates (BEC) by solving the
Bogoliubov-de Gennes (BdG) equation, yielding, e.g., the Tkachenko mode
recently observed at JILA. The totally symmetric subset of these modes includes
the transverse shear, common longitudinal, and differential longitudinal modes.
We also solve the time-dependent Gross-Pitaevskii (TDGP) equation to simulate
the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair
of breathing modes. Combining both the BdG and TDGP approaches allows one to
unambiguously identify every observed mode.Comment: 5 pages, 4 figure
Dynamic facilitation explains democratic particle motion of metabasin transitions
Transitions between metabasins in supercooled liquids seem to occur through
rapid "democratic" collective particle rearrangements. Here we show that this
apparent homogeneous particle motion is a direct consequence of dynamic
facilitation. We do so by studying metabasin transitions in facilitated spin
models and constrained lattice gases. We find that metabasin transitions occur
through a sequence of locally facilitated events taking place over a relatively
short time frame. When observed on small enough spatial windows these events
appear sudden and homogeneous. Our results indicate that metabasin transitions
are essentially "non-democratic" in origin and yet another manifestation of
dynamical heterogeneity in glass formers.Comment: 6 pages, 6 figure
Tradeoff between short-term and long-term adaptation in a changing environment
We investigate the competition dynamics of two microbial or viral strains
that live in an environment that switches periodically between two states. One
of the strains is adapted to the long-term environment, but pays a short-term
cost, while the other is adapted to the short-term environment and pays a cost
in the long term. We explore the tradeoff between these alternative strategies
in extensive numerical simulations, and present a simple analytic model that
can predict the outcome of these competitions as a function of the mutation
rate and the time scale of the environmental changes. Our model is relevant for
arboviruses, which alternate between different host species on a regular basis.Comment: 9 pages, 3 figures, PRE in pres
Phases of a fermionic model with chiral condensates and Cooper pairs in 1+1 dimensions
We study the phase structure of a 4-fermi model with three bare coupling
constants, which potentially has three types of bound states. This model is a
generalization of the model discussed previously by A. Chodos et al. [Phys.
Rev. D 61, 045011 (2000)], which contained both chiral condensates and Cooper
pairs. For this generalization we find that there are two independent
renormalized coupling constants which determine the phase structure at finite
density and temperature. We find that the vacuum can be in one of three
distinct phases depending on the value of these two renormalized coupling
constants
Association Between Measures of Body Composition and Functional Movement in Cancer Survivors
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Supersymmetric approach to exactly solvable systems with position-dependent effective masses
We discuss the relationship between exact solvability of the Schr\"{o}dinger
equation with a position-dependent mass and the ordering ambiguity in the
Hamiltonian operator within the frame of supersymmetric quantum mechanics. The
one-dimensional Schr\"{o}dinger equation, derived from the general form of the
effective mass Hamiltonian, is solved exactly for a system with exponentially
changing mass in the presence of a potential with similar behaviour, and the
corresponding supersymmetric partner Hamiltonians are related to the
effective-mass Hamiltonians proposed in the literature.Comment: 12 pages article in LaTEX (uses standard article.sty). Please check
http://www1.gantep.edu.tr/~ozer for other studies of Nuclear Physics Group at
University of Gaziantep. [arXiv admin note: excessive overlap with
quant-ph/0306065 and "Supersymmetric approach to quantum systems with
position-dependent effective mass" by A. R. Plastino, A. Rigo, M. Casas, F.
Garcias, and A. Plastino - Phys. Rev. A 60, 4318 - 4325 (1999)
Operator Transformations Between Exactly Solvable Potentials and Their Lie Group Generators
One may obtain, using operator transformations, algebraic relations between
the Fourier transforms of the causal propagators of different exactly solvable
potentials. These relations are derived for the shape invariant potentials.
Also, potentials related by real transformation functions are shown to have the
same spectrum generating algebra with Hermitian generators related by this
operator transformation.Comment: 13 pages with one Postscript figure, uses LaTeX2e with revte
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