11 research outputs found
Casimir-like force arising from quantum fluctuations in a slow-moving dilute Bose-Einstein condensate
We calculate a force due to zero-temperature quantum fluctuations on a
stationary object in a moving superfluid flow. We model the object by a
localized potential varying only in the flow direction and model the flow by a
three-dimensional weakly interacting Bose-Einstein condensate at zero
temperature. We show that this force exists for any arbitrarily small flow
velocity and discuss the implications for the stability of superfluid flow.Comment: v3: revised discussion of toroidal geometry; replotted figure; minor
editorial changes; quantitative and qualitative conclusions remain unchange
Casimir forces in Bose-Einstein condensates: finite size effects in three-dimensional rectangular cavities
The Casimir force due to {\it thermal} fluctuations (or pseudo-Casimir force)
was previously calculated for the perfect Bose gas in the slab geometry for
various boundary conditions. The Casimir pressure due to {\it quantum}
fluctuations in a weakly-interacting dilute Bose-Einstein condensate (BEC)
confined to a parallel plate geometry was recently calculated for Dirichlet
boundary conditions. In this paper we calculate the Casimir energy and pressure
due to quantum fluctuations in a zero-temperature homogeneous
weakly-interacting dilute BEC confined to a parallel plate geometry with
periodic boundary conditions and include higher-order corrections which we
refer to as Bogoliubov corrections. The leading order term is identified as the
Casimir energy of a massless scalar field moving with wave velocity equal to
the speed of sound in the BEC. We then obtain the leading order Casimir
pressure in a general three-dimensional rectangular cavity of arbitrary lengths
and obtain the finite-size correction to the parallel plate scenario.Comment: 12 pages; no figures; v.2: version accepted for publication in JSTAT
v.3: references adde
Casimir Energy of a BEC: From Moderate Interactions to the Ideal Gas
Considering the Casimir effect due to phononic excitations of a weakly
interacting dilute {BEC}, we derive a re-normalized expression for the zero
temperature Casimir energy of a {BEC} confined to a parallel
plate geometry with periodic boundary conditions. Our expression is formally
equivalent to the free energy of a bosonic field at finite temperature, with a
nontrivial density of modes that we compute analytically. As a function of the
interaction strength, smoothly describes the transition from
the weakly interacting Bogoliubov regime to the non-interacting ideal {BEC}.
For the weakly interacting case, reduces to leading order to
the Casimir energy due to zero-point fluctuations of massless phonon modes. In
the limit of an ideal Bose gas, our result correctly describes the Casimir
energy going to zero.Comment: 12 pages, 3 figures, accepted for publication in JPA. New version
with corrected typos and an additional appendi
Multidimensional cut-off technique, odd-dimensional Epstein zeta functions and Casimir energy of massless scalar fields
Quantum fluctuations of massless scalar fields represented by quantum
fluctuations of the quasiparticle vacuum in a zero-temperature dilute
Bose-Einstein condensate may well provide the first experimental arena for
measuring the Casimir force of a field other than the electromagnetic field.
This would constitute a real Casimir force measurement - due to quantum
fluctuations - in contrast to thermal fluctuation effects. We develop a
multidimensional cut-off technique for calculating the Casimir energy of
massless scalar fields in -dimensional rectangular spaces with large
dimensions and dimensions of length and generalize the technique to
arbitrary lengths. We explicitly evaluate the multidimensional remainder and
express it in a form that converges exponentially fast. Together with the
compact analytical formulas we derive, the numerical results are exact and easy
to obtain. Most importantly, we show that the division between analytical and
remainder is not arbitrary but has a natural physical interpretation. The
analytical part can be viewed as the sum of individual parallel plate energies
and the remainder as an interaction energy. In a separate procedure, via
results from number theory, we express some odd-dimensional homogeneous Epstein
zeta functions as products of one-dimensional sums plus a tiny remainder and
calculate from them the Casimir energy via zeta function regularization.Comment: 42 pages, 3 figures. v.2: typos corrected to match published versio
Casimir force on interacting Bose-Einstein condensate
We have presented an analytic theory for the Casimir force on a Bose-Einstein
condensate (BEC) which is confined between two parallel plates. We have
considered Dirichlet boundary conditions for the condensate wave function as
well as for the phonon field. We have shown that, the condensate wave function
(which obeys the Gross-Pitaevskii equation) is responsible for the mean field
part of Casimir force, which usually dominates over the quantum (fluctuations)
part of the Casimir force.Comment: Accepted in Journal of Physics B: Atomic, Molecular and Optical
Physic
The Cerenkov effect revisited: from swimming ducks to zero modes in gravitational analogs
We present an interdisciplinary review of the generalized Cerenkov emission
of radiation from uniformly moving sources in the different contexts of
classical electromagnetism, superfluid hydrodynamics, and classical
hydrodynamics. The details of each specific physical systems enter our theory
via the dispersion law of the excitations. A geometrical recipe to obtain the
emission patterns in both real and wavevector space from the geometrical shape
of the dispersion law is discussed and applied to a number of cases of current
experimental interest. Some consequences of these emission processes onto the
stability of condensed-matter analogs of gravitational systems are finally
illustrated.Comment: Lecture Notes at the IX SIGRAV School on "Analogue Gravity" in Como,
Italy from May 16th-21th, 201