16 research outputs found
Reconstruction of Rb-Rb inter-atomic potential from ultracold Bose-gas collision
Scattering phase shifts obtained from 87Rb Bose-gas collision experiments are
used to reconstruct effective potentials resulting, self-consistently, in the
same scattering events observed in the experiments at a particular energy. We
have found that the interaction strength close to the origin suddenly changes
from repulsion to attraction when the collision energy crosses, from below, the
l=2 shape resonance position at E = 275 mikroK. This observation may be
utilized in outlining future Bose-gas collision experiments.Comment: 4 pages, 4 figure
Simplified solutions of the Cox-Thompson inverse scattering method at fixed energy
Simplified solutions of the Cox-Thompson inverse quantum scattering method at
fixed energy are derived if a finite number of partial waves with only even or
odd angular momenta contribute to the scattering process. Based on new formulae
various approximate methods are introduced which also prove applicable to the
generic scattering events.Comment: 9 pages, 3 figure
Geometric scaling in the spectrum of an electron captured by a stationary finite dipole
We examine the energy spectrum of a charged particle in the presence of a
{\it non-rotating} finite electric dipole. For {\emph{any}} value of the dipole
moment above a certain critical value p_{\mathrm{c}}$ an infinite series of
bound states arises of which the energy eigenvalues obey an Efimov-like
geometric scaling law with an accumulation point at zero energy. These
properties are largely destroyed in a realistic situation when rotations are
included. Nevertheless, our analysis of the idealised case is of interest
because it may possibly be realised using quantum dots as artificial atoms.Comment: 5 figures; references added, outlook section reduce
Assessment of interspecies scattering lengths from stability of two-component Bose-Einstein condensates
A stability method is used to assess possible values of interspecies
scattering lengths a_12 in two-component Bose-Einstein condensates described
within the Gross-Pitaevskii approximation. The technique, based on a recent
stability analysis of solitonic excitations in two-component Bose-Einstein
condensates, is applied to ninety combinations of atomic alkali pairs with
given singlet and triplet intraspecies scattering lengths as input parameters.
Results obtained for values of a_12 are in a reasonable agreement with the few
ones available in the literature and with those obtained from a Painleve
analysis of the coupled Gross-Pitaevskii equations.Comment: (8 pages, 4 figures, 3 tables
Is the Riemann zeta function in a short interval a 1-RSB spin glass ?
Fyodorov, Hiary & Keating established an intriguing connection between the
maxima of log-correlated processes and the ones of the Riemann zeta function on
a short interval of the critical line. In particular, they suggest that the
analogue of the free energy of the Riemann zeta function is identical to the
one of the Random Energy Model in spin glasses. In this paper, the connection
between spin glasses and the Riemann zeta function is explored further. We
study a random model of the Riemann zeta function and show that its two-overlap
distribution corresponds to the one of a one-step replica symmetry breaking
(1-RSB) spin glass. This provides evidence that the local maxima of the zeta
function are strongly clustered.Comment: 20 pages, 1 figure, Minor corrections, References update
Matter-Wave Solitons in an F=1 Spinor Bose-Einstein Condensate
Following our previous work [J. Ieda, T. Miyakawa, M. Wadati,
cond-mat/0404569] on a novel integrable model describing soliton dynamics of an
F=1 spinor Bose--Einstein condensate, we discuss in detail the properties of
the multi-component system with spin-exchange interactions. The exact multiple
bright soliton solutions are obtained for the system where the mean-field
interaction is attractive (c_0 < 0) and the spin-exchange interaction is
ferromagnetic (c_2 < 0). A complete classification of the one-soliton solution
with respect to the spin states and an explicit formula of the two-soliton
solution are presented. For solitons in polar state, there exists a variety of
different shaped solutions including twin peaks. We show that a "singlet pair"
density can be used to distinguish those energetically degenerate solitons. We
also analyze collisional effects between solitons in the same or different spin
state(s) by computing the asymptotic forms of their initial and final states.
The result reveals that it is possible to manipulate the spin dynamics by
controlling the parameters of colliding solitons.Comment: 12 pages, 9 figures, to appear in J. Phys. Soc. Jpn. Vol.73 No.11
(2004
Physics of the Riemann Hypothesis
Physicists become acquainted with special functions early in their studies.
Consider our perennial model, the harmonic oscillator, for which we need
Hermite functions, or the Laguerre functions in quantum mechanics. Here we
choose a particular number theoretical function, the Riemann zeta function and
examine its influence in the realm of physics and also how physics may be
suggestive for the resolution of one of mathematics' most famous unconfirmed
conjectures, the Riemann Hypothesis. Does physics hold an essential key to the
solution for this more than hundred-year-old problem? In this work we examine
numerous models from different branches of physics, from classical mechanics to
statistical physics, where this function plays an integral role. We also see
how this function is related to quantum chaos and how its pole-structure
encodes when particles can undergo Bose-Einstein condensation at low
temperature. Throughout these examinations we highlight how physics can perhaps
shed light on the Riemann Hypothesis. Naturally, our aim could not be to be
comprehensive, rather we focus on the major models and aim to give an informed
starting point for the interested Reader.Comment: 27 pages, 9 figure
Scattering theory and ground-state energy of Dirac fermions in graphene with two Coulomb impurities
We study the physics of Dirac fermions in a gapped graphene monolayer containing two Coulomb impurities. For the case of equal impurity charges, we discuss the ground-state energy using the linear combination of atomic orbitals (LCAO) approach. For opposite charges of the Coulomb centers, an electric dipole potential results at large distances. We provide a nonperturbative analysis of the corresponding low-energy scattering problem