264 research outputs found

### Spin-charge separation in cold Fermi-gases: a real time analysis

Using the adaptive time-dependent density-matrix renormalization group method
for the 1D Hubbard model, the splitting of local perturbations into separate
wave packets carrying charge and spin is observed in real-time. We show the
robustness of this separation beyond the low-energy Luttinger liquid theory by
studying the time-evolution of single particle excitations and density wave
packets. A striking signature of spin-charge separation is found in 1D cold
Fermi gases in a harmonic trap at the boundary between liquid and
Mott-insulating phases. We give quantitative estimates for an experimental
observation of spin-charge separation in an array of atomic wires

### Phases of Bosons or Fermions in confined optical lattices

Phases of Bose or Fermi atoms in optical lattices confined in harmonic traps
are studied within the Thomas-Fermi approximation. Critical radii and particle
number for onset of Mott insulator states are calculated and phase diagrams
shown in 1D, and estimated for 2 and 3D. Methods to observe these and novel
phases such as d-wave superconductivity is discussed. Specifically the
collective modes are calculated.Comment: Revised and extended. To appear in PR

### Oscillating Casimir force between impurities in one-dimensional Fermi liquids

We study the interaction of two localized impurities in a repulsive
one-dimensional Fermi liquid via bosonization. In a previous paper [Phys. Rev.
A 72, 023616 (2005)], it was shown that at distances much larger than the
interparticle spacing the impurities interact through a Casimir-type force
mediated by the zero sound phonons of the underlying quantum liquid. Here we
extend these results and show that the strength and sign of this Casimir
interaction depend sensitively on the impurities separation. These oscillations
in the Casimir interaction have the same period as Friedel oscillations. Their
maxima correspond to tunneling resonances tuned by the impurities separation.Comment: This paper is a continuation of Phys. Rev. A 72, 023616 (2005). v2:
two appendix adde

### Magnetic Braking and Viscous Damping of Differential Rotation in Cylindrical Stars

Differential rotation in stars generates toroidal magnetic fields whenever an
initial seed poloidal field is present. The resulting magnetic stresses, along
with viscosity, drive the star toward uniform rotation. This magnetic braking
has important dynamical consequences in many astrophysical contexts. For
example, merging binary neutron stars can form "hypermassive" remnants
supported against collapse by differential rotation. The removal of this
support by magnetic braking induces radial fluid motion, which can lead to
delayed collapse of the remnant to a black hole. We explore the effects of
magnetic braking and viscosity on the structure of a differentially rotating,
compressible star, generalizing our earlier calculations for incompressible
configurations. The star is idealized as a differentially rotating, infinite
cylinder supported initially by a polytropic equation of state. The gas is
assumed to be infinitely conducting and our calculations are performed in
Newtonian gravitation. Though highly idealized, our model allows for the
incorporation of magnetic fields, viscosity, compressibility, and shocks with
minimal computational resources in a 1+1 dimensional Lagrangian MHD code. Our
evolution calculations show that magnetic braking can lead to significant
structural changes in a star, including quasistatic contraction of the core and
ejection of matter in the outermost regions to form a wind or an ambient disk.
These calculations serve as a prelude and a guide to more realistic MHD
simulations in full 3+1 general relativity.Comment: 20 pages, 19 figures, 3 tables, AASTeX, accepted by Ap

### Polaron to molecule transition in a strongly imbalanced Fermi gas

A single down spin Fermion with an attractive, zero range interaction with a
Fermi sea of up-spin Fermions forms a polaronic quasiparticle. The associated
quasiparticle weight vanishes beyond a critical strength of the attractive
interaction, where a many-body bound state is formed. From a variational
wavefunction in the molecular limit, we determine the critical value for the
polaron to molecule transition. The value agrees well with the diagrammatic
Monte Carlo results of Prokof'ev and Svistunov and is consistent with recent
rf-spectroscopy measurements of the quasiparticle weight by Schirotzek et. al.
In addition, we calculate the contact coefficient of the strongly imbalanced
gas, using the adiabatic theorem of Tan and discuss the implications of the
polaron to molecule transition for the phase diagram of the attractive Fermi
gas at finite imbalance.Comment: 10 pages, 4 figures, RevTex4, minor changes, references adde

### Commensurate-incommensurate transition of cold atoms in an optical lattice

An atomic gas subject to a commensurate periodic potential generated by an
optical lattice undergoes a superfluid--Mott insulator transition. Confining a
strongly interacting gas to one dimension generates an instability where an
arbitrary weak potential is sufficient to pin the atoms into the Mott state;
here, we derive the corresponding phase diagram. The commensurate pinned state
may be detected via its finite excitation gap and the Bragg peaks in the static
structure factor.Comment: 4 pages, 2 figure

### Gravitational waves from relativistic rotational core collapse

We present results from simulations of axisymmetric relativistic rotational
core collapse. The general relativistic hydrodynamic equations are formulated
in flux-conservative form and solved using a high-resolution shock-capturing
scheme. The Einstein equations are approximated with a conformally flat
3-metric. We use the quadrupole formula to extract waveforms of the
gravitational radiation emitted during the collapse. A comparison of our
results with those of Newtonian simulations shows that the wave amplitudes
agree within 30%. Surprisingly, in some cases, relativistic effects actually
diminish the amplitude of the gravitational wave signal. We further find that
the parameter range of models suffering multiple coherent bounces due to
centrifugal forces is considerably smaller than in Newtonian simulations.Comment: 4 pages, 3 figure

### A learning approach to the detection of gravitational wave transients

We investigate the class of quadratic detectors (i.e., the statistic is a
bilinear function of the data) for the detection of poorly modeled
gravitational transients of short duration. We point out that all such
detection methods are equivalent to passing the signal through a filter bank
and linearly combine the output energy. Existing methods for the choice of the
filter bank and of the weight parameters rely essentially on the two following
ideas: (i) the use of the likelihood function based on a (possibly
non-informative) statistical model of the signal and the noise, (ii) the use of
Monte-Carlo simulations for the tuning of parametric filters to get the best
detection probability keeping fixed the false alarm rate. We propose a third
approach according to which the filter bank is "learned" from a set of training
data. By-products of this viewpoint are that, contrarily to previous methods,
(i) there is no requirement of an explicit description of the probability
density function of the data when the signal is present and (ii) the filters we
use are non-parametric. The learning procedure may be described as a two step
process: first, estimate the mean and covariance of the signal with the
training data; second, find the filters which maximize a contrast criterion
referred to as deflection between the "noise only" and "signal+noise"
hypothesis. The deflection is homogeneous to the signal-to-noise ratio and it
uses the quantities estimated at the first step. We apply this original method
to the problem of the detection of supernovae core collapses. We use the
catalog of waveforms provided recently by Dimmelmeier et al. to train our
algorithm. We expect such detector to have better performances on this
particular problem provided that the reference signals are reliable.Comment: 22 pages, 4 figure

### Scanning gate experiments: from strongly to weakly invasive probes

An open resonator fabricated in a two-dimensional electron gas is used to
explore the transition from strongly invasive scanning gate microscopy to the
perturbative regime of weak tip-induced potentials. With the help of numerical
simulations that faithfully reproduce the main experimental findings, we
quantify the extent of the perturbative regime in which the tip-induced
conductance change is unambiguously determined by properties of the unperturbed
system. The correspondence between the experimental and numerical results is
established by analyzing the characteristic length scale and the amplitude
modulation of the conductance change. In the perturbative regime, the former is
shown to assume a disorder-dependent maximum value, while the latter linearly
increases with the strength of a weak tip potential.Comment: 11 pages, 7 figure

### Differential Rotation in Neutron Stars: Magnetic Braking and Viscous Damping

Diffferentially rotating stars can support significantly more mass in
equilibrium than nonrotating or uniformly rotating stars, according to general
relativity. The remnant of a binary neutron star merger may give rise to such a
``hypermassive'' object. While such a star may be dynamically stable against
gravitational collapse and bar formation, the radial stabilization due to
differential rotation is likely to be temporary. Magnetic braking and viscosity
combine to drive the star to uniform rotation, even if the seed magnetic field
and the viscosity are small. This process inevitably leads to delayed collapse,
which will be accompanied by a delayed gravitational wave burst and, possibly,
a gamma-ray burst. We provide a simple, Newtonian, MHD calculation of the
braking of differential rotation by magnetic fields and viscosity. The star is
idealized as a differentially rotating, infinite cylinder consisting of a
homogeneous, incompressible conducting gas. We solve analytically the simplest
case in which the gas has no viscosity and the star resides in an exterior
vacuum. We treat numerically cases in which the gas has internal viscosity and
the star is embedded in an exterior, low-density, conducting medium. Our
evolution calculations are presented to stimulate more realistic MHD
simulations in full 3+1 general relativity. They serve to identify some of the
key physical and numerical parameters, scaling behavior and competing
timescales that characterize this important process.Comment: 11 pages. To appear in ApJ (November 20, 2000

- â€¦