1,111 research outputs found
Bosons in anisotropic traps: ground state and vortices
We solve the Gross-Pitaevskii equations for a dilute atomic gas in a magnetic
trap, modeled by an anisotropic harmonic potential. We evaluate the wave
function and the energy of the Bose Einstein condensate as a function of the
particle number, both for positive and negative scattering length. The results
for the transverse and vertical size of the cloud of atoms, as well as for the
kinetic and potential energy per particle, are compared with the predictions of
approximated models. We also compare the aspect ratio of the velocity
distribution with first experimental estimates available for Rb. Vortex
states are considered and the critical angular velocity for production of
vortices is calculated. We show that the presence of vortices significantly
increases the stability of the condensate in the case of attractive
interactions.Comment: 22 pages, REVTEX, 8 figures available upon request or at
http://anubis.science.unitn.it/~dalfovo/papers/papers.htm
Improved numerical approach for time-independent Gross-Pitaevskii nonlinear Schroedinger equation
In the present work, we improve a numerical method, developed to solve the
Gross-Pitaevkii nonlinear Schroedinger equation. A particular scaling is used
in the equation, which permits to evaluate the wave-function normalization
after the numerical solution. We have a two point boundary value problem, where
the second point is taken at infinity. The differential equation is solved
using the shooting method and Runge-Kutta integration method, requiring that
the asymptotic constants, for the function and its derivative, are equal for
large distances. In order to obtain fast convergence, the secant method is
used.Comment: 2 figure
Optimal Hypercontractivity for Fermi Fields and Related Non-Commutative Integration
Optimal hypercontractivity bounds for the fermion oscillator semigroup are
obtained. These are the fermion analogs of the optimal hypercontractivity
bounds for the boson oscillator semigroup obtained by Nelson. In the process,
several results of independent interest in the theory of non-commutative
integration are established. {}.Comment: 18 p., princeton/ecel/7-12-9
Interaction of pulses in nonlinear Schroedinger model
The interaction of two rectangular pulses in nonlinear Schroedinger model is
studied by solving the appropriate Zakharov-Shabat system. It is shown that two
real pulses may result in appearance of moving solitons. Different limiting
cases, such as a single pulse with a phase jump, a single chirped pulse,
in-phase and out-of-phase pulses, and pulses with frequency separation, are
analyzed. The thresholds of creation of new solitons and multi-soliton states
are found.Comment: 9 pages, 7 figures. Accepted to Phys. Rev. E, 200
Fermion Mixing Renormalization and Gauge Invariance
We study the renormalization of the fermion mixing matrix in the Standard
Model and derive the constraints that must be satisfied to respect gauge
invariance to all orders. We demonstrate that the prescription based on the
{\it on-shell} renormalization conditions is not consistent with the
Ward-Takahashi Identities and leads to gauge dependent physical amplitudes. A
simple scheme is proposed that satisfies all theoretical requirements and is
very convenient for practical calculations.Comment: 10 pages, LaTex; Revised version accepted for publication in Phys.
Lett.
The Dirac equation in Taub-NUT space
Using chiral supersymmetry, we show that the massless Dirac equation in the
Taub-NUT gravitational instanton field is exactly soluble and explain the
arisal and the use of the dynamical (super) symmetry.Comment: An importatn misprint in a reference is corrected. Plain Tex. 8 page
Instantons and radial excitations in attractive Bose-Einstein condensates
Imaginary- and real-time versions of an equation for the condensate density
are presented which describe dynamics and decay of any spherical Bose-Einstein
condensate (BEC) within the mean field appraoch. We obtain quantized energies
of collective finite amplitude radial oscillations and exact numerical
instanton solutions which describe quantum tunneling from both the metastable
and radially excited states of the BEC of 7Li atoms. The mass parameter for the
radial motion is found different from the gaussian value assumed hitherto, but
the effect of this difference on decay exponents is small. The collective
breathing states form slightly compressed harmonic spectrum, n=4 state lying
lower than the second Bogolyubov (small amplitude) mode. The decay of these
states, if excited, may simulate a shorter than true lifetime of the metastable
state. By scaling arguments, results extend to other attractive BEC-s.Comment: 6 pages, 3 figure
Steady-State Visual Evoked Potentials Can Be Explained by Temporal Superposition of Transient Event-Related Responses
<p><b>Background:</b> One common criterion for classifying electrophysiological brain responses is based on the distinction between transient (i.e. event-related potentials, ERPs) and steady-state responses (SSRs). The generation of SSRs is usually attributed to the entrainment of a neural rhythm driven by the stimulus train. However, a more parsimonious account suggests that SSRs might result from the linear addition of the transient responses elicited by each stimulus. This study aimed to investigate this possibility.</p>
<p><b>Methodology/Principal Findings::</b> We recorded brain potentials elicited by a checkerboard stimulus reversing at different rates. We modeled SSRs by sequentially shifting and linearly adding rate-specific ERPs. Our results show a strong resemblance between recorded and synthetic SSRs, supporting the superposition hypothesis. Furthermore, we did not find evidence of entrainment of a neural oscillation at the stimulation frequency.</p>
<p><b>Conclusions/Significance:</b> This study provides evidence that visual SSRs can be explained as a superposition of transient ERPs. These findings have critical implications in our current understanding of brain oscillations. Contrary to the idea that neural networks can be tuned to a wide range of frequencies, our findings rather suggest that the oscillatory response of a given neural network is constrained within its natural frequency range.</p>
Disorder Effects in Two-Dimensional d-wave Superconductors
Influence of weak nonmagnetic impurities on the single-particle density of
states of two-dimensional electron systems with a conical
spectrum is studied. We use a nonperturbative approach, based on replica trick
with subsequent mapping of the effective action onto a one-dimensional model of
interacting fermions, the latter being treated by Abelian and non-Abelian
bosonization methods. It is shown that, in a d-wave superconductor, the density
of states, averaged over randomness, follows a nontrivial power-law behavior
near the Fermi energy: . The exponent
is calculated for several types of disorder. We demonstrate that the
property is a direct consequence of a {\it continuous} symmetry
of the effective fermionic model, whose breakdown is forbidden in two
dimensions. As a counter example, we consider another model with a conical
spectrum - a two-dimensional orbital antiferromagnet, where static disorder
leads to a finite due to breakdown of a {\it discrete}
(particle-hole) symmetry.Comment: 24 pages, 3 figures upon request, RevTe
Adler Function, DIS sum rules and Crewther Relations
The current status of the Adler function and two closely related Deep
Inelastic Scattering (DIS) sum rules, namely, the Bjorken sum rule for
polarized DIS and the Gross-Llewellyn Smith sum rule are briefly reviewed. A
new result is presented: an analytical calculation of the coefficient function
of the latter sum rule in a generic gauge theory in order O(alpha_s^4). It is
demonstrated that the corresponding Crewther relation allows to fix two of
three colour structures in the O(alpha_s^4) contribution to the singlet part of
the Adler function.Comment: Talk presented at 10-th DESY Workshop on Elementary Particle Theory:
Loops and Legs in Quantum Field Theory, W\"orlitz, Germany, 25-30 April 201
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