89 research outputs found
Finite Size Effect on Correlation Functions of a Bose Gas in a Trap and Destruction of the Order Parameter by Phase Fluctuations
The influence of the finite sizes on the coherent properties of 3D Bose
systems is considered. As is shown, the correlation functions of a Bose gas in
a trap have essential differences from analogous correlation functions in an
infinite system. Thus, the anomalous correlation function vanishes due to the
divergency of phase fluctuations which destruct the order parameter too. The
normal correlation function decays exponentially in time for sufficiently large
time interval.Comment: 10 pages, RevTex4, some references have been added some changes in
text are mad
Magnetic-field-induced Luttinger liquid
It is shown that a strong magnetic field applied to a bulk metal induces a
Luttinger-liquid phase. This phase is characterized by the zero-bias anomaly in
tunneling: the tunneling conductance scales as a power-law of voltage or
temperature. The tunneling exponent increases with the magnetic field as BlnB.
The zero-bias anomaly is most pronounced for tunneling with the field applied
perpendicular to the plane of the tunneling junction.Comment: a reference added, minor typos correcte
The Yangian of sl(n|m) and the universal R-matrix
In this paper we study Yangians of sl(n|m) superalgebras. We derive the
universal R-matrix and evaluate it on the fundamental representation obtaining
the standard Yang R-matrix with unitary dressing factors. For m=0, we directly
recover up to a CDD factor the well-known S-matrices for relativistic
integrable models with su(N) symmetry. Hence, the universal R-matrix found
provides an abstract plug-in formula, which leads to results obeying
fundamental physical constraints: crossing symmetry, unitrarity and the
Yang-Baxter equation. This implies that the Yangian double unifies all desired
symmetries into one algebraic structure. In particular, our analysis is valid
in the case of sl(n|n), where one has to extend the algebra by an additional
generator leading to the algebra gl(n|n). We find two-parameter families of
scalar factors in this case and provide a detailed study for gl(1|1).Comment: 24 pages, 2 figure
Massless particles on supergroups and AdS3 x S3 supergravity
Firstly, we study the state space of a massless particle on a supergroup with
a reparameterization invariant action. After gauge fixing the
reparameterization invariance, we compute the physical state space through the
BRST cohomology and show that the quadratic Casimir Hamiltonian becomes
diagonalizable in cohomology. We illustrate the general mechanism in detail in
the example of a supergroup target GL(1|1). The space of physical states
remains an indecomposable infinite dimensional representation of the space-time
supersymmetry algebra. Secondly, we show how the full string BRST cohomology in
the particle limit of string theory on AdS3 x S3 renders the quadratic Casimir
diagonalizable, and reduces the Hilbert space to finite dimensional
representations of the space-time supersymmetry algebra (after analytic
continuation). Our analysis provides an efficient way to calculate the
Kaluza-Klein spectrum for supergravity on AdS3 x S3. It may also be a step
towards the identification of an interesting and simpler subsector of
logarithmic supergroup conformal field theories, relevant to string theory.Comment: 16 pages, 10 figure
The conformal current algebra on supergroups with applications to the spectrum and integrability
We compute the algebra of left and right currents for a principal chiral
model with arbitrary Wess-Zumino term on supergroups with zero Killing form. We
define primary fields for the current algebra that match the affine primaries
at the Wess-Zumino-Witten points. The Maurer-Cartan equation together with
current conservation tightly constrain the current-current and current-primary
operator product expansions. The Hilbert space of the theory is generated by
acting with the currents on primary fields. We compute the conformal dimensions
of a subset of these states in the large radius limit. The current algebra is
shown to be consistent with the quantum integrability of these models to
several orders in perturbation theory.Comment: 45 pages. Minor correction
Strings on Semisymmetric Superspaces
Several string backgrounds which arise in the AdS/CFT correspondence are
described by integrable sigma-models. Their target space is always a Z(4)
supercoset (a semi-symmetric superspace). Here we list all semi-symmetric
cosets which have zero beta function and central charge c<=26 at one loop in
perturbation theory.Comment: 25 pages, 1 figur
Functional methods in the theory of magnetoimpurity states of electrons in quantum wires
Functional methods are used to study magnetoimpurity states of electrons in
nanostructures. The Keldysh formalism is applied to these states. The theory is
illustrated using a quantum wire sample with impurity atoms capable of
localizing electrons in a magnetic field. The characteristics of
magnetoimpurity states of electrons in the wire are calculated using the model
of a Gaussian separable potential.Comment: 15 pages, 1 figur
Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux
We study superstrings on AdS_3 x S^3 x T^4 supported by a combination of
Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz three form fluxes, and construct
a set of finite-gap equations that describe the classical string spectrum.
Using the recently proposed all-loop S-matrix we write down the all-loop Bethe
ansatz equations for the massive sector. In the thermodynamic limit the Bethe
ansatz reproduces the finite-gap equations. As part of this derivation we
propose expressions for the leading order dressing phases. These phases differ
from the well-known Arutyunov-Frolov-Staudacher phase that appears in the pure
Ramond-Ramond case. We also consider the one-loop quantization of the algebraic
curve and determine the one-loop corrections to the dressing phases. Finally we
consider some classical string solutions including finite size giant magnons
and circular strings.Comment: 44 pages, 3 figures. v2: references and a discussion about
perturbative results adde
Kaluza-Klein gauge and minimal integrable extension of OSp(4|6)/(SO(1,3) x U(3)) sigma-model
Basing upon experience from performing double-dimensional reduction of the
D=11 supermembrane on AdS_4 x S^7 background to Type IIA superstring on AdS_4 x
CP^3 we introduce Kaluza-Klein (partial) kappa-symmetry gauge as a vanishing
condition of the contribution to the D=11 supervielbein components tangent to
D=10 space-time proportional to the differential of the coordinate
parametrizing compact 11-th space-time dimension, that is identified with the
supermembrane world-volume compact dimension. For AdS_4 x S^7 supermembrane
Kaluza-Klein gauge removes half Grassmann coordinates associated with 8
space-time supersymmetries, broken by the AdS_4 x CP^3 superbackground, by
imposing D=3 (anti-)Majorana condition on them. The consideration relies on the
realization of osp(4|8) isometry superalgebra of the AdS_4 x S^7
superbackground as D=3 N=8 superconformal algebra. Requiring further vanishing
of the D=10 dilaton leaves in the sector of broken supersymmetries just two
Grassmann coordinates organized into D=3 (anti-)Majorana spinor that defines
minimal SL(2,R)-covariant extension of the OSp(4|6)/(SO(1,3)x U(3))
sigma-model. Among 4 possibilities of such a minimal extension we consider in
detail one, that corresponds to picking out D=3 Majorana coordinate related to
broken Poincare supersymmetry, and show that the AdS_4 x CP^3 superstring
equations of motion in this partial kappa-symmetry gauge are integrable. Also
the relation between the OSp(4|6)/(SO(1,3) x U(3)) sigma-model and the AdS_4 x
CP^3 superstring is revisited.Comment: LaTeX, 22 pages; v2: minor improvements in the text, typos corrected,
references adde
Do attractive bosons condense?
Motivated by experiments on bose atoms in traps which have attractive
interactions (e.g. ^7Li), we consider two models which may be solved exactly.
We construct the ground states subject to the constraint that the system is
rotating with angular momentum proportional to the number of atoms. In a
conventional system this would lead to quantised vortices; here, for attractive
interactions, we find that the angular momentum is absorbed by the centre of
mass motion. Moreover, the state is uncondensed and is an example of a
`fragmented' condensate discussed by Nozi\`eres and Saint James. The same
models with repulsive interactions are fully condensed in the thermodynamic
limit.Comment: 4 pages, Latex, RevTe
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