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Metastable states and macroscopic quantum tunneling in a cold atom Josephson ring
We study macroscopic properties of a system of weakly interacting neutral
bosons confined in a ring-shaped potential with a Josephson junction. We derive
an effective low energy action for this system and evaluate its properties. In
particular we find that the system possesses a set of metastable
current-carrying states and evaluate the rates of transitions between these
states due to macroscopic quantum tunneling. Finally we discuss signatures of
different metastable states in the time-of-flight images and argue that the
effect is observable within currently available experimental technique.Comment: 4 pages, 2 figure
Comparison of LZ77-type Parsings
We investigate the relations between different variants of the LZ77 parsing
existing in the literature. All of them are defined as greedily constructed
parsings encoding each phrase by reference to a string occurring earlier in the
input. They differ by the phrase encodings: encoded by pairs (length + position
of an earlier occurrence) or by triples (length + position of an earlier
occurrence + the letter following the earlier occurring part); and they differ
by allowing or not allowing overlaps between the phrase and its earlier
occurrence. For a given string of length over an alphabet of size ,
denote the numbers of phrases in the parsings allowing (resp., not allowing)
overlaps by (resp., ) for "pairs", and by (resp.,
) for "triples". We prove the following bounds and provide series of
examples showing that these bounds are tight:
and
;
and .Comment: 6 page
Nonlinear magnetic response of the magnetized vacuum to applied electric field
We find first nonlinear correction to the field, produced by a static charge
at rest in a background constant magnetic field. It is quadratic in the charge
and purely magnetic. The third-rank polarization tensor - the nonlinear
response function - is written within the local approximation of the effective
action in an otherwise model- and approximation-independent way within any
P-invariant nonlinear electrodynamics, QED included.Comment: 11 pages without figures or tables. Numerical coefficients and some
signs in Version I corrected, three new references and two equations adde
Brownian dynamics of a microswimmer
We report on dynamic properties of a simple model microswimmer composed of
three spheres and propelling itself in a viscous fluid by spinning motion of
the spheres under zero net torque constraint. At a fixed temperature and
increasing the spinning frequency, the swimmer demonstrates a transition from
dissipation-dominated to a pumping-dominated motion regime characterized by
negative effective friction coefficient. In the limit of high frequencies, the
diffusion of the swimmer can be described by a model of an active particle with
constant velocity.Comment: Submitte
Kinetics of the Phase Separation Transition in Cold-Atom Boson-Fermion Mixtures
We study the kinetics of the first order phase separation transition in
boson-fermion cold-atom mixtures. At sufficiently low temperatures such a
transition is driven by quantum fluctuations responsible for the formation of
critical nuclei of a stable phase. Based on a microscopic description of
interacting boson-fermion mixtures we derive an effective action for the
critical droplet and obtain an asymptotic expression for the nucleation rate in
the vicinity of the phase transition and near the spinodal instability of the
mixed phase. We also discuss effects of dissipation which play a dominant role
close to the transition point, and identify the regimes where quantum
nucleation can be experimentally observed in cold-atom systems.Comment: 4 pages 1 figure, typos correcte
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