12,128 research outputs found
Gapless Hartree-Fock-Bogoliubov Approximation for Bose Gases
A dilute Bose system with Bose-Einstein condensate is considered. It is shown
that the Hartree-Fock-Bogolubov approximation can be made both conserving as
well as gapless. This is achieved by taking into account all physical
normalization conditions, that is, the normalization condition for the
condensed particles and that for the total number of particles. Two Lagrange
multipliers, introduced for preserving these normalization conditions, make the
consideration completely self-consistent.Comment: Latex file, 22 pages, 2 figure
Josephson and proximity effects on the surface of a topological insulator
We investigate Josephson and proximity effects on the surface of a
topological insulator on which superconductors and a ferromagnet are deposited.
The superconducting regions are described by the conventional BCS Hamiltonian,
rather than the superconducting Dirac Hamiltonian. Junction interfaces are
assumed to be dirty. We obtain analytical expressions of the Josephson current
and the proximity-induced anomalous Green's function on the topological
insulator. The dependence of the Josephson effect on the junction length, the
temperature, the chemical potential and the magnetization is discussed. It is
also shown that the proximity-induced pairing on the surface of a topological
insulator includes even and odd frequency triplet pairings as well as a
conventional s-wave one.Comment: 7 pages, 5 figure
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Modeling the effects of combining diverse software fault detection techniques
The software engineering literature contains many studies of the efficacy of fault finding techniques. Few of these, however, consider what happens when several different techniques are used together. We show that the effectiveness of such multitechnique approaches depends upon quite subtle interplay between their individual efficacies and dependence between them. The modelling tool we use to study this problem is closely related to earlier work on software design diversity. The earliest of these results showed that, under quite plausible assumptions, it would be unreasonable even to expect software versions that were developed ‘truly independently’ to fail independently of one another. The key idea here was a ‘difficulty function’ over the input space. Later work extended these ideas to introduce a notion of ‘forced’ diversity, in which it became possible to obtain system failure behaviour better even than could be expected if the versions failed independently. In this paper we show that many of these results for design diversity have counterparts in diverse fault detection in a single software version. We define measures of fault finding effectiveness, and of diversity, and show how these might be used to give guidance for the optimal application of different fault finding procedures to a particular program. We show that the effects upon reliability of repeated applications of a particular fault finding procedure are not statistically independent - in fact such an incorrect assumption of independence will always give results that are too optimistic. For diverse fault finding procedures, on the other hand, things are different: here it is possible for effectiveness to be even greater than it would be under an assumption of statistical independence. We show that diversity of fault finding procedures is, in a precisely defined way, ‘a good thing’, and should be applied as widely as possible. The new model and its results are illustrated using some data from an experimental investigation into diverse fault finding on a railway signalling application
Ab initio methods for finite temperature two-dimensional Bose gases
The stochastic Gross-Pitaevskii equation and modified Popov theory are shown
to provide an ab initio description of finite temperature, weakly-interacting
two-dimensional Bose gas experiments. Using modified Popov theory, a systematic
approach is developed in which the momentum cut-off inherent to classical field
methods is removed as a free parameter. This is shown to yield excellent
agreement with the recent experiment of Hung et al. [Nature, 470, 236 (2011)],
verifying that the stochastic Gross-Pitaevskii equation captures the observed
universality and scale-invariance.Comment: 5 pages, 4 figure
Vortex mass in a superfluid at low frequencies
An inertial mass of a vortex can be calculated by driving it round in a
circle with a steadily revolving pinning potential. We show that in the low
frequency limit this gives precisely the same formula that was used by Baym and
Chandler, but find that the result is not unique and depends on the force field
used to cause the acceleration. We apply this method to the Gross-Pitaevskii
model, and derive a simple formula for the vortex mass. We study both the long
range and short range properties of the solution. We agree with earlier results
that the non-zero compressibility leads to a divergent mass. From the
short-range behavior of the solution we find that the mass is sensitive to the
form of the pinning potential, and diverges logarithmically when the radius of
this potential tends to zero.Comment: 4 page
Multidimensional Worldline Instantons
We extend the worldline instanton technique to compute the vacuum pair
production rate for spatially inhomogeneous electric background fields, with
the spatial inhomogeneity being genuinely two or three dimensional, both for
the magnitude and direction of the electric field. Other techniques, such as
WKB, have not been applied to such higher dimensional problems. Our method
exploits the instanton dominance of the worldline path integral expression for
the effective action.Comment: 22 pages, 13 figure
Vortex-Phonon Interaction in the Kosterlitz-Thouless Theory
The "canonical" variables of the Kosterlitz-Thouless theory--fields
and , generally believed to stand for vortices
and phonons (or their XY equivalents, like spin waves, etc.) turn out to be
neither vortices and phonons, nor, strictly speaking, {\it canonical}
variables. The latter fact explains paradoxes of (i) absence of interaction
between and , and (ii) non-physical contribution of small vortex
pairs to long-range phase correlations. We resolve the paradoxes by explicitly
relating and to canonical vortex-pair and phonon variables.Comment: 4 pages, RevTe
Improved Approximations for Fermion Pair Production in Inhomogeneous Electric Fields
Reformulating the instantons in a complex plane for tunneling or transmitting
states, we calculate the pair-production rate of charged fermions in a
spatially localized electric field, illustrated by the Sauter electric field
E_0 sech^2 (z/L), and in a temporally localized electric field such as E_0
sech^2 (t/T). The integration of the quadratic part of WKB instanton actions
over the frequency and transverse momentum leads to the pair-production rate
obtained by the worldline instanton method, including the prefactor, of Phys.
Rev. D72, 105004 (2005) and D73, 065028 (2006). It is further shown that the
WKB instanton action plus the next-to-leading order contribution in spinor QED
equals the WKB instanton action in scalar QED, thus justifying why the WKB
instanton in scalar QED can work for the pair production of fermions. Finally
we obtain the pair-production rate in a spatially localized electric field
together with a constant magnetic field in the same direction.Comment: RevTex, 12 pages, two figures; replaced by the version accepted in
Phys. Rev.
Berezinskii-Kosterlitz-Thouless transition in two-dimensional dipole systems
The superfluid to normal fluid transition of dipolar bosons in two dimensions
is studied throughout the whole density range using path integral Monte Carlo
simulations and summarized in the phase diagram. While at low densities, we
find good agreement with the universal results depending only on the scattering
length , at moderate and high densities, the transition temperature is
strongly affected by interactions and the elementary excitation spectrum. The
results are expected to be of relevance to dipolar atomic and molecular systems
and indirect excitons in quantum wells
Mean-field phase diagram of the 1-D Bose gas in a disorder potential
We study the quantum phase transition of the 1D weakly interacting Bose gas
in the presence of disorder. We characterize the phase transition as a function
of disorder and interaction strengths, by inspecting the long-range behavior of
the one-body density matrix as well as the drop in the superfluid fraction. We
focus on the properties of the low-energy Bogoliubov excitations that drive the
phase transition, and find that the transition to the insulator state is marked
by a diverging density of states and a localization length that diverges as a
power-law with power 1. We draw the phase diagram and we observe that the
boundary between the superfluid and the Bose glass phase is characterized by
two different algebraic relations. These can be explained analytically by
considering the limiting cases of zero and infinite disorder correlation
length.Comment: 10 pages, 10 figure
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