161 research outputs found
Correlations in an expanding gas of hard-core bosons
We consider a longitudinal expansion of a one-dimensional gas of hard-core
bosons suddenly released from a trap. We show that the broken translational
invariance in the initial state of the system is encoded in correlations
between the bosonic occupation numbers in the momentum space. The correlations
are protected by the integrability and exhibit no relaxation during the
expansion
Quantum decay of dark solitons in one dimensional Bose systems
Unless protected by the exact integrability, solitons are subject to
dissipative forces, originating from a thermally fluctuating background. At low
enough temperatures background fluctuations should be considered as being
quantized which enables us to calculate finite lifetime of the solitons
. We also find that the coherent nature of the quantum
fluctuations leads to long-range interactions between the solitons mediated by
the superradiation. Our results are of relevance to current experiments with
ultracold atoms, while the approach may be extended to solitons in other media.Comment: 5 pages, 1 figure. Accepted for publication in PRL
Localization of eigenstates in a modified Tomonaga-Luttinger model
We study the localization in the Hilbert space of a modified
Tomonaga-Luttinger model. For the standard version of this model, the states
are found to be extended in the basis of Slater determinants, representing the
eigenstates of the non-interacting system. The linear dispersion which leads to
the fact that these eigenstates are extended in the modified model is replaced
by one with random level spacings modeling the complicated one-particle spectra
of realistic models. The localization properties of the eigenstates are
studied. The interactions are simplified and an effective one-dimensional Lloyd
model is obtained. The effects of many-body energy correlations are studied
numerically. The eigenstates of the system are found to be localized in Fock
space for any strength of the interactions, but the localization is not
exponential.Comment: 19 pages, 7 figure
Replica Treatment of the Calogero-Sutherland Model
Employing Forrester-Ha method of Jack polynomials, we derive an integral
identity connecting certain N-fold coordinate average of the
Calogero-Sutherland model with the n-fold replica integral. Subsequent
analytical continuation to non-integer n leads to asymptotic expressions for
the (static and dynamic) density-density correlation function of the model as
well as the Green's function for an arbitrary coupling constant .Comment: 15 pages, 3 figures, revised version, section 5 corrected, submitted
to Nucl.Phys.
Mobile impurities in integrable models
We use a mobile impurity or depleton model to study elementary excitations in
one-dimensional integrable systems. For Lieb-Liniger and bosonic Yang-Gaudin
models we express two phenomenological parameters characterising renormalised
inter- actions of mobile impurities with superfluid background: the number of
depleted particles, and the superfluid phase drop in terms of the
corresponding Bethe Ansatz solution and demonstrate, in the leading order, the
absence of two-phonon scattering resulting in vanishing rates of inelastic
processes such as viscosity experienced by the mobile impuritiesComment: 25 pages, minor corrections made to the manuscrip
Kinetics of mobile impurities and correlation functions in one-dimensional superfluids at finite temperature
We scrutinize the hydrodynamic approach for calculating dynamical
correlations in one-dimensional superfluids near integrability and calculate
the characteristic time scale {\tau} beyond which this approach is valid. For
time scales shorter than {\tau} hydrodynamics fails and we develop an approach
based on kinetics of fermionic quasiparticles described as mobile impurities.
New universal results for the dynamical structure factor relevant to
experiments in ultracold atomic gases are obtained.Comment: 5 pages, 2 figures. Supplemental material included. Version 3: Minor
typos correcte
Comment on "Kinetic theory for a mobile impurity in a degenerate Tonks-Girardeau gas"
In a recent paper, arxiv:1402.6362, Gamayun, Lychkovskiy, and Cheianov
studied the dynamics of a mobile impurity embedded into a one-dimensional
Tonks-Girardeau gas of strongly interacting bosons. Employing the Boltzmann
equation approach, they arrived at the following main conclusions: (i) a light
impurity, being accelerated by a constant force does not exhibit Bloch
oscillations; (ii) a heavy impurity does undergo Bloch oscillations,
accompanied by a drift with the velocity proportional to the square root of
force. In this comment we argue that the result (i) is an artifact of the
classical Boltzmann approximation, which misses the formation of the (quasi)
bound-state between the impurity and a hole. Result (ii), while not valid at
asymptotically small force, indeed reflects an interesting intermediate-force
behavior. Here we clarify its limits of applicability and extend beyond the
Tonks-Girardeau limit.Comment: 2 pages, 1 figur
Sudden Expansion of a One-Dimensional Bose Gas from Power-Law Traps
We analyze free expansion of a trapped one-dimensional Bose gas after a
sudden release from the confining trap potential. By using the stationary phase
and local density approximations, we show that the long-time asymptotic density
profile and the momentum distribution of the gas are determined by the initial
distribution of Bethe rapidities (quasimomenta) and hence can be obtained from
the solutions to the Lieb-Liniger equations in the thermodynamic limit. For
expansion from a harmonic trap, and in the limits of very weak and very strong
interactions, we recover the self-similar scaling solutions known from the
hydrodynamic approach. For all other power-law traps and arbitrary interaction
strengths, the expansion is not self-similar and shows strong dependence of the
density profile evolution on the trap anharmonicity. We also characterize
dynamical fermionization of the expanding cloud in terms of correlation
functions describing phase and density fluctuations.Comment: Final published version with modified title and a couple of other
minor changes. 5 pages, 2 figures, and Supplemental Materia
Fluctuational susceptibility of ultracold bosons in the vicinity of condensation
We study the behaviour of ultracold bosonic gas in the critical region above
the Bose-Einstein condensation in the presence of an artificial magnetic field,
. We show that the condensate fluctuations above the critical
temperature cause the fluctuational susceptibility, ,
of a uniform gas to have a stronger power-law divergence than in an analogous
superconducting system. Measuring such a divergence opens new ways of exploring
critical properties of the ultracold gas and an opportunity of an accurate
determination of . We describe a method of measuring
which requires a constant gradient in and suggest a way of
creating such a field in experiment.Comment: 5 pages, 3 figures, 5 pages of Supplement; the text is rewritten and
rearranged, and the figures are modifie
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