54 research outputs found
Persistent Currents in Ferromagnetic Condensates
Persistent currents in Bose condensates with a scalar order parameter are
stabilized by the topology of the order parameter manifold. In condensates with
multicomponent order parameters it is topologically possible for supercurrents
to `unwind' without leaving the manifold. We study the energetics of this
process in the case of ferromagnetic condensates using a long wavelength energy
functional that includes both the superfluid and spin stiffnesses. Exploiting
analogies to an elastic rod and rigid body motion, we show that the current
carrying state in a 1D ring geometry transitions between a spin helix in the
energy minima and a soliton-like configuration at the maxima. The relevance to
recent experiments in ultracold atoms is briefly discussed.Comment: 10 pages, 7 figures. Accepted versio
Noise and Counting Statistics of Insulating Phases in One-Dimensional Optical Lattices
We discuss the correlation properties of current carrying states of
one-dimensional insulators, which could be realized by applying an impulse to
atoms loaded onto an optical lattice. While the equilibrium noise has a gapped
spectrum, the quantum uncertainty encoded in the amplitudes for the Zener
process gives a zero frequency contribution out of equilibrium. We derive a
general expression for the generating function of the full counting statistics
and find that the particle transport obeys binomial statistics with doubled
charge, resulting in super-Poissonian noise that originates from the bosonic
nature of particle-hole pairs
Noise correlations in the expansion of an interacting 1D Bose gas from a regular array
We consider the one dimensional expansion of a system of interacting bosons,
starting from a regular array. Without interactions the familiar Hanbury Brown
and Twiss effect for bosons gives rise to a series of peaks in the
density-density correlations of the expanded system. Infinitely repulsive
particles likewise give a series of dips, a signature of the underlying
description in terms of free fermions. In the intermediate case of finite
interaction the noise correlations consist of a set of Fano resonance
lineshapes, with an asymmetry parameter determined by the scattering phase
shift of a pair of particles, and a width depending on the initial momentum
spread of the particles
Diffractive scattering of three particles in one dimension: a simple result for weak violations of the Yang--Baxter equation
We study scattering of three equal mass particles in one dimension.
Integrable interactions are synonymous with non-diffractive scattering, meaning
that the set of incoming momenta for any scattering event coincides with the
set of outgoing momenta. A system is integrable if the two particle scattering
matrix obeys the Yang--Baxter equation. Nonintegrable interactions correspond
to diffractive scattering, where the set of outgoing momenta may take on all
values consistent with energy and momentum conservation. Such processes play a
vital role in the kinetics of one dimensional gases, where binary collisions
are unable to alter the distribution function.
When integrability is broken weakly, the result is a small diffractive
scattering amplitude. Our main result is a simple formula for the diffractive
part of the scattering amplitude, when the violation of the Yang--Baxter
equation is small. Although the derivation is given for delta-function
interactions, the result depends only on the two-particle scattering matrix,
and should therefore also apply to finite-range interactions close to
integrable.Comment: 11 pages, 7 figure
Unitary circuits of finite depth and infinite width from quantum channels
We introduce an approach to compute reduced density matrices for local
quantum unitary circuits of finite depth and infinite width. Suppose the
time-evolved state under the circuit is a matrix-product state with bond
dimension ; then the reduced density matrix of a half-infinite system has
the same spectrum as an appropriate matrix acting on an ancilla
space. We show that reduced density matrices at different spatial cuts are
related by quantum channels acting on the ancilla space. This quantum channel
approach allows for efficient numerical evaluation of the entanglement spectrum
and R\'enyi entropies and their spatial fluctuations at finite times in an
infinite system. We benchmark our numerical method on random unitary circuits,
where many analytic results are available, and also show how our approach
analytically recovers the behaviour of the kicked Ising model at the self-dual
point. We study various properties of the spectra of the reduced density
matrices and their spatial fluctuations in both the random and
translation-invariant cases.Comment: 16 pages, 12 figures, such Tik
Quantum Hydrodynamics in One Dimension beyond the Luttinger Liquid
Recent years have seen the development of a rich phenomenology beyond the
Luttinger Liquid model of one dimensional quantum fluids, arising from
interactions between the elementary phonon excitations. It has been known for
some time, however, that the straightforward inclusion of these interactions
presents technical difficulties that have necessitated approaches based on
refermionization or effective impurity models.
In this work we show that the nonlinear extensions of the Luttinger model are
tractable in the phonon basis. We present a calculation of the singularities
present in the zero temperature dynamical structure factor in the semiclassical
limit where the phonon dispersion is strong.
A unitary transformation decouples interactions between left-- and
right--moving phonons, leaving a nonlinear chiral Hamiltonian. At low momenta,
this Hamiltonian has a spectrum bounded above and below by thresholds
identified with phonon and soliton excitations in the semiclassical limit. The
chiral dynamical structure factor therefore has support only in this region,
with power law singularities at the thresholds originating in the Anderson
orthogonality catastrophe, which we calculate analytically. The dynamical
structure factor for the original nonchiral Hamiltonian is a convolution of
this chiral correlator with a power law arising from the left--right
decoupling.Comment: 17 pages, 7 figure
From GPE to KPZ: finite temperature dynamical structure factor of the 1D Bose gas
We study the finite temperature dynamical structure factor of a
1D Bose gas using numerical simulations of the Gross--Pitaevskii equation
appropriate to a weakly interacting system. The lineshape of the phonon peaks
in has a width at low wavevectors. This
anomalous width arises from resonant three-phonon interactions, and reveals a
remarkable connection to the Kardar--Parisi--Zhang universality class of
dynamical critical phenomena
The Fine Structure of the Phonon in One Dimension from Quantum Hydrodynamics
We show that the resonant interactions between phonons in one dimension may
be treated consistently within Quantum Hydrodynamics by the introduction of
phonon dispersion. In this way the physics of a nonlinear Luttinger liquid may
be described in terms of hydrodynamic (i.e. bosonized) variables without
recourse to refermionization or the introduction of fictitious impurities.
We focus on the calculation of the dynamic structure factor for a model with
quadratic dispersion, which has the Benjamin--Ono equation of fluid dynamics as
its equation of motion. We find singular behavior in the vicinity of upper and
lower energetic thresholds corresponding to phonon and soliton branches of the
classical theory, which may be benchmarked against known results for the
Calogero--Sutherland model.Comment: 5 pages, 1 figur
Dispersion relation and spectral function of an impurity in a one-dimensional quantum liquid
We consider the motion of an impurity particle in a general one-dimensional
quantum fluid at zero temperature. The dispersion relation of the
impurity is strongly affected by interactions with the fluid as the momentum
approaches , where is the density.
This behavior is caused by singular scattering processes and
can be understood by analogy to the Kondo effect, both at strong and weak
coupling, with the possibility of a quantum phase transition where jumps to zero with increasing coupling. The low energy singularities in
the impurity spectral function can be understood on the same footing.Comment: Published versio
Potential insights into non-equilibrium behavior from atomic physics
This chapter seeks to outline a few basic problems in quantum statistical
physics where recent experimental advances from the atomic physics community
offer the hope of dramatic progress. The focus is on nonequilibrium situations
where the powerful concepts and methods of equilibrium statistical physics and
"linear response" theory (for small deviations from equilibrium) are not
applicable. The problems discussed here are chosen in part because they have a
high degree of "universality" or generality across different microscopic
situations, as the major challenge in nonequilibrium statistical physics, both
quantum and classical, has been to find principles as general as the basic
principles of equilibrium statistical physics or linear response.Comment: Chapter to appear in the forthcoming volume "Ultracold Bosonic and
Fermionic Gases", (Contemporary Concepts of Condensed Matter Science
(Elsevier)), edited by Alexander Fetter, Katherine Levin, and Dan
Stamper-Kur
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