776 research outputs found
Phases of a rotating Bose-Einstein condensate with anharmonic confinement
We examine an effectively repulsive Bose-Einstein condensate of atoms that
rotates in a quadratic-plus-quartic potential. With use of a variational method
we identify the three possible phases of the system (multiple quantization,
single quantization, and a mixed phase) as a function of the rotational
frequency of the gas and of the coupling constant. The derived phase diagram is
shown to be universal and the continuous transitions to be exact in the limit
of weak coupling and small anharmonicity. The variational results are found to
be consistent with numerical solutions of the Gross-Pitaevskii equation.Comment: 8 pages, 6 figure
Automating Security Analysis: Symbolic Equivalence of Constraint Systems
We consider security properties of cryptographic protocols, that are either trace properties (such as confidentiality or authenticity) or equivalence properties (such as anonymity or strong secrecy). Infinite sets of possible traces are symbolically represented using deducibility constraints. We give a new algorithm that decides the trace equivalence for the traces that are represented using such constraints, in the case of signatures, symmetric and asymmetric encryptions. Our algorithm is implemented and performs well on typical benchmarks. This is the first implemented algorithm, deciding symbolic trace equivalence
Relating two standard notions of secrecy
Two styles of definitions are usually considered to express that a security
protocol preserves the confidentiality of a data s. Reachability-based secrecy
means that s should never be disclosed while equivalence-based secrecy states
that two executions of a protocol with distinct instances for s should be
indistinguishable to an attacker. Although the second formulation ensures a
higher level of security and is closer to cryptographic notions of secrecy,
decidability results and automatic tools have mainly focused on the first
definition so far.
This paper initiates a systematic investigation of the situations where
syntactic secrecy entails strong secrecy. We show that in the passive case,
reachability-based secrecy actually implies equivalence-based secrecy for
digital signatures, symmetric and asymmetric encryption provided that the
primitives are probabilistic. For active adversaries, we provide sufficient
(and rather tight) conditions on the protocol for this implication to hold.Comment: 29 pages, published in LMC
Multiply quantized vortices in trapped Bose-Einstein condensates
Vortex configurations in rotating Bose-Einstein condensed gases trapped in
power-law and anharmonic potentials are studied. When the confining potential
is steeper than harmonic in the plane perpendicular to the axis of rotation,
vortices with quantum numbers larger than one are energetically favorable if
the interaction is weak enough. Features of the wave function for small and
intermediate rotation frequencies are investigated numerically.Comment: 9 pages, 6 figures. Revised and extended article following referee
repor
A developmentally descriptive method for quantifying shape in gastropod shells
The growth of snail shells can be described by simple mathematical rules. Variation in a few parameters can explain much of the diversity of shell shapes seen in nature. However, empirical studies of gastropod shell shape variation typically use geometric morphometric approaches, which do not capture this growth pattern. We have developed a way to infer a set of developmentally descriptive shape parameters based on three-dimensional logarithmic helicospiral growth and using landmarks from two-dimensional shell images as input. We demonstrate the utility of this approach, and compare it to the geometric morphometric approach, using a large set of Littorina saxatilis shells in which locally adapted populations differ in shape. Our method can be modified easily to make it applicable to a wide range of shell forms, which would allow for investigations of the similarities and differences between and within many different species of gastropods
Phase diagram of quantized vortices in a trapped Bose-Einstein condensed gas
We investigate the thermodynamic stability of quantized vortices in a dilute
Bose gas confined by a rotating harmonic trap at finite temperature.
Interatomic forces play a crucial role in characterizing the resulting phase
diagram, especially in the large Thomas-Fermi regime. We show that the
critical temperature for the creation of stable vortices exhibits a maximum as
a function of the frequency of the rotating trap and that the corresponding
transition is associated with a discontinuity in the number of atoms in the
condensate. Possible strategies for approaching the vortical region are
discussed.Comment: Revtex, 4 pages, 2 figure
Laser-driven plasma waves in capillary tubes
The excitation of plasma waves over a length of up to 8 centimeters is, for
the first time, demon- strated using laser guiding of intense laser pulses
through hydrogen filled glass capillary tubes. The plasma waves are diagnosed
by spectral analysis of the transmitted laser radiation. The dependence of the
spectral redshift, measured as a function of filling pressure, capillary tube
length and incident laser energy, is in excellent agreement with simulation
results. The longitudinal accelerating field inferred from the simulations is
in the range 1 -10 GV/m
Vortex nucleation in Bose-Einstein condensates in time-dependent traps
Vortex nucleation in a Bose-Einstein condensate subject to a stirring
potential is studied numerically using the zero-temperature, two-dimensional
Gross-Pitaevskii equation. It is found that this theory is able to describe the
creation of vortices, but not the crystallization of a vortex lattice. In the
case of a rotating, slightly anisotropic harmonic potential, the numerical
results reproduce experimental findings, thereby showing that finite
temperatures are not necessary for vortex excitation below the quadrupole
frequency. In the case of a condensate subject to stirring by a narrow rotating
potential, the process of vortex excitation is described by a classical model
that treats the multitude of vortices created by the stirrer as a continuously
distributed vorticity at the center of the cloud, but retains a potential flow
pattern at large distances from the center.Comment: 22 pages, 7 figures. Changes after referee report: one new figure,
new refs. No conclusions altere
Shape deformations and angular momentum transfer in trapped Bose-Einstein condensates
Angular momentum can be transferred to a trapped Bose-Einstein condensate by
distorting its shape with an external rotating field, provided the rotational
frequency is larger than a critical frequency fixed by the energy and angular
momentum of the excited states of the system. By using the Gross-Pitaevskii
equation and sum rules, we explore the dependence of such a critical frequency
on the multipolarity of the excitations and the asymmetry of the confining
potential. We also discuss its possible relevance for vortex nucleation in
rotating traps.Comment: 4 pages revtex, 2 figures include
Stability of rotating states in a weakly-interacting Bose-Einstein condensate
We investigate the lowest state of a rotating, weakly-interacting
Bose-Einstein condensate trapped in a harmonic confining potential that is
driven by an infinitesimally asymmetric perturbation. Although in an
axially-symmetric confining potential the gas has an axially-symmetric
single-particle density distribution, we show that in the presence of the small
asymmetric perturbation its lowest state is the one given by the mean-field
approximation, which is a broken-symmetric state. We also estimate the rate of
relaxation of angular momentum when the gas is no longer driven by the
asymmetric perturbation and identify two regimes of "slow" and "fast"
relaxation. States of certain symmetry are found to be more robust.Comment: 6 pages, RevTe
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