854 research outputs found
Small-amplitude normal modes of a vortex in a trapped Bose-Einstein condensate
We consider a cylindrically symmetric trap containing a small Bose-Einstein
condensate with a singly quantized vortex on the axis of symmetry. A
time-dependent variational Lagrangian analysis yields the small-amplitude
dynamics of the vortex and the condensate, directly determining the equations
of motion of the coupled normal modes. As found previously from the Bogoliubov
equations, there are two rigid dipole modes and one anomalous mode with a
negative frequency when seen in the laboratory frame.Comment: 4 pages, no figures, Revte
OpenSwarm: an event-driven embedded operating system for miniature robots
This paper presents OpenSwarm, a lightweight easy-to-use open-source operating system. To our knowledge, it is the first operating system designed for and deployed on miniature robots. OpenSwarm operates directly on a robotâs microcontroller. It has a memory footprint of 1 kB RAM and 12 kB ROM. OpenSwarm enables a robot to execute multiple processes simultaneously. It provides a hybrid kernel that natively supports preemptive and cooperative scheduling, making it suitable for both computationally intensive and swiftly responsive robotics tasks. OpenSwarm provides hardware abstractions to rapidly develop and test platformindependent code. We show how OpenSwarm can be used to solve a canonical problem in swarm roboticsâclustering a collection of dispersed objects. We report experiments, conducted with five e-puck mobile robots, that show that an OpenSwarm implementation performs as good as a hardware-near implementation. The primary goal of OpenSwarm is to make robots with severely constrained hardware more accessible, which may help such systems to be deployed in real-world applications
The role of caretakers in disease dynamics
One of the key challenges in modeling the dynamics of contagion phenomena is
to understand how the structure of social interactions shapes the time course
of a disease. Complex network theory has provided significant advances in this
context. However, awareness of an epidemic in a population typically yields
behavioral changes that correspond to changes in the network structure on which
the disease evolves. This feedback mechanism has not been investigated in
depth. For example, one would intuitively expect susceptible individuals to
avoid other infecteds. However, doctors treating patients or parents tending
sick children may also increase the amount of contact made with an infecteds,
in an effort to speed up recovery but also exposing themselves to higher risks
of infection. We study the role of these caretaker links in an adaptive network
models where individuals react to a disease by increasing or decreasing the
amount of contact they make with infected individuals. We find that pure
avoidance, with only few caretaker links, is the best strategy for curtailing
an SIS disease in networks that possess a large topological variability. In
more homogeneous networks, disease prevalence is decreased for low
concentrations of caretakers whereas a high prevalence emerges if caretaker
concentration passes a well defined critical value.Comment: 8 pages, 9 figure
Self-Trapping, Quantum Tunneling and Decay Rates for a Bose Gas with Attractive Nonlocal Interaction
We study the Bose-Einstein condensation for a cloud of Li atoms with
attractive nonlocal (finite-range) interaction in a harmonic trap. In addition
to the low-density metastable branch, that is present also in the case of local
interaction, a new stable branch appears at higher densities. For a large
number of atoms, the size of the cloud in the stable high-density branch is
independent of the trap size and the atoms are in a macroscopic quantum
self-trapped configuration. We analyze the macroscopic quantum tunneling
between the low-density metastable branch and the high-density one by using the
istanton technique. Moreover we consider the decay rate of the Bose condensate
due to inelastic two- and three-body collisions.Comment: 5 pages, 4 figures, submitted to Phys. Rev.
Vortex states in binary mixture of Bose-Einstein condensates
The vortex configurations in the Bose-Einstein condensate of the mixture of
two different spin states |F=1,m_f=-1> and |2,1> of ^{87}Rb atoms corresponding
to the recent experiments by Matthews et. al. (Phys. Rev. Lett. 83, 2498
(1999)) are considered in the framework of the Thomas-Fermi approximation as
functions of N_2/N_1, where N_1 is the number of atoms in the state |1,-1> and
N_2 - in the state |2,1>. It is shown that for nonrotating condensates the
configuration with the |1,-1> fluid forming the shell about the |2,1> fluid
(configuration "a") has lower energy than the opposite configuration
(configuration "b") for all values of N_2/N_1. When the |1,-1> fluid has net
angular momentum and forms an equatorial ring around the resting central
condensate |2,1>, the total energy of the system is higher than the ground
energy, but the configuration "a" has lower energy than the configuration "b"
for all N_2/N_1. On the other hand, when the |2> fluid has the net angular
momentum, for the lowest value of the angular momentum \hbar l (l=1) there is
the range of the ratio N_2/N_1 where the configuration "b" has lower energy
than the configuration "a". For higher values of the angular momentum the
configuration "b" is stable for all values of N_2/N_1.Comment: minor changes, references adde
Hydrodynamic Approach to Vortex Lifetime in Trapped Bose Condensates
We study a vortex in a two-dimensional, harmonically trapped Bose-Einstein
condensate at zero temperature. Through a variational calculation using a trial
condensate wave function and a nonlinear Schroedinger Lagrangian, we obtain the
effective potential experienced by a vortex at an arbitrary position in the
condensate, and find that an off-center vortex will move in a circular
trajectory around the trap center. We find the frequency of this precession to
be smaller than the elementary excitation frequencies in the cloud.
We also study the radiation of sound from a moving vortex in an infinite,
uniform system, and discuss the validity of this as an approximation for the
trapped case. Furthermore, we estimate the lifetime of a vortex due to
imperfections in the trapping potential.Comment: 10 pages, 1 eps figure, submitted to PRA, adjustments in response to
referee, one refernce adde
Condensate Heating by Atomic Losses
Atomic Bose-Einstein condensate is heated by atomic losses. Predicted
depletion ranges from 1% for a uniform 3D condensate to around 10% for a
quasi-1D condensate in a harmonic trap.Comment: 4 pages in RevTex, 1 eps figur
Analyticity of The Ground State Energy For Massless Nelson Models
We show that the ground state energy of the translationally invariant Nelson
model, describing a particle coupled to a relativistic field of massless
bosons, is an analytic function of the coupling constant and the total
momentum. We derive an explicit expression for the ground state energy which is
used to determine the effective mass.Comment: 33 pages, 1 figure, added a section on the calculation of the
effective mas
Free expansion of Bose-Einstein condensates with quantized vortices
The expansion of Bose-Einstein condensates with quantized vortices is studied
by solving numerically the time-dependent Gross-Pitaevskii equation at zero
temperature. For a condensate initially trapped in a spherical harmonic
potential, we confirm previous results obtained by means of variational methods
showing that, after releasing the trap, the vortex core expands faster than the
radius of the atomic cloud. This could make the detection of vortices feasible,
by observing the depletion of the density along the axis of rotation. We find
that this effect is significantly enhanced in the case of anisotropic
disc-shaped traps. The results obtained as a function of the anisotropy of the
initial configuration are compared with the analytic solution for a
noninteracting gas in 3D as well as with the scaling law predicted for an
interacting gas in 2D.Comment: 5 pages, 6 postscript figure
A particle-number-conserving Bogoliubov method which demonstrates the validity of the time-dependent Gross-Pitaevskii equation for a highly condensed Bose gas
The Bogoliubov method for the excitation spectrum of a Bose-condensed gas is
generalized to apply to a gas with an exact large number of particles.
This generalization yields a description of the Schr\"odinger picture field
operators as the product of an annihilation operator for the total number
of particles and the sum of a ``condensate wavefunction'' and a phonon
field operator in the form when the field operator acts on the N particle subspace. It
is then possible to expand the Hamiltonian in decreasing powers of ,
an thus obtain solutions for eigenvalues and eigenstates as an asymptotic
expansion of the same kind. It is also possible to compute all matrix elements
of field operators between states of different N.Comment: RevTeX, 11 page
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