49 research outputs found
Thermally fluctuating superconductors in two dimensions
We describe the different regimes of finite temperature dynamics in the
vicinity of a zero temperature superconductor to insulator quantum phase
transition in two dimensions. New results are obtained for a low temperature
phase-only hydrodynamics, and for the intermediate temperature quantum-critical
region. In the latter case, we obtain a universal relationship between the
frequency-dependence of the conductivity and the value of the d.c. resistance.Comment: Presentation completely revised; 4 pages, 2 figure
Dissipative superfluid dynamics from gravity
Charged asymptotically AdS black branes in five dimensions are sometimes
unstable to the condensation of charged scalar fields. For fields of infinite
charge and squared mass -4 Herzog was able to analytically determine the phase
transition temperature and compute the endpoint of this instability in the
neighborhood of the phase transition. We generalize Herzog's construction by
perturbing away from infinite charge in an expansion in inverse charge and use
the solutions so obtained as input for the fluid gravity map. Our tube wise
construction of patched up locally hairy black brane solutions yields a one to
one map from the space of solutions of superfluid dynamics to the long
wavelength solutions of the Einstein Maxwell system. We obtain explicit
expressions for the metric, gauge field and scalar field dual to an arbitrary
superfluid flow at first order in the derivative expansion. Our construction
allows us to read off the the leading dissipative corrections to the perfect
superfluid stress tensor, current and Josephson equations. A general framework
for dissipative superfluid dynamics was worked out by Landau and Lifshitz for
zero superfluid velocity and generalized to nonzero fluid velocity by Clark and
Putterman. Our gravitational results do not fit into the 13 parameter
Clark-Putterman framework. Purely within fluid dynamics we present a consistent
new generalization of Clark and Putterman's equations to a set of superfluid
equations parameterized by 14 dissipative parameters. The results of our
gravitational calculation fit perfectly into this enlarged framework. In
particular we compute all the dissipative constants for the gravitational
superfluid.Comment: v1: 58 + 1 pages; v2: 83 + 1 page
Transport in holographic superfluids
We construct a slowly varying space-time dependent holographic superfluid and
compute its transport coefficients. Our solution is presented as a series
expansion in inverse powers of the charge of the order parameter. We find that
the shear viscosity associated with the motion of the condensate vanishes. The
diffusion coefficient of the superfluid is continuous across the phase
transition while its third bulk viscosity is found to diverge at the critical
temperature. As was previously shown, the ratio of the shear viscosity of the
normal component to the entropy density is 1/(4 pi). As a consequence of our
analysis we obtain an analytic expression for the backreacted metric near the
phase transition for a particular type of holographic superfluid.Comment: 45 pages + appendice
Spacelike Singularities and Hidden Symmetries of Gravity
We review the intimate connection between (super-)gravity close to a
spacelike singularity (the "BKL-limit") and the theory of Lorentzian Kac-Moody
algebras. We show that in this limit the gravitational theory can be
reformulated in terms of billiard motion in a region of hyperbolic space,
revealing that the dynamics is completely determined by a (possibly infinite)
sequence of reflections, which are elements of a Lorentzian Coxeter group. Such
Coxeter groups are the Weyl groups of infinite-dimensional Kac-Moody algebras,
suggesting that these algebras yield symmetries of gravitational theories. Our
presentation is aimed to be a self-contained and comprehensive treatment of the
subject, with all the relevant mathematical background material introduced and
explained in detail. We also review attempts at making the infinite-dimensional
symmetries manifest, through the construction of a geodesic sigma model based
on a Lorentzian Kac-Moody algebra. An explicit example is provided for the case
of the hyperbolic algebra E10, which is conjectured to be an underlying
symmetry of M-theory. Illustrations of this conjecture are also discussed in
the context of cosmological solutions to eleven-dimensional supergravity.Comment: 228 pages. Typos corrected. References added. Subject index added.
Published versio
Reaction rates and transport in neutron stars
Understanding signals from neutron stars requires knowledge about the
transport inside the star. We review the transport properties and the
underlying reaction rates of dense hadronic and quark matter in the crust and
the core of neutron stars and point out open problems and future directions.Comment: 74 pages; commissioned for the book "Physics and Astrophysics of
Neutron Stars", NewCompStar COST Action MP1304; version 3: minor changes,
references updated, overview graphic added in the introduction, improvements
in Sec IV.A.
Physics of Neutron Star Crusts
The physics of neutron star crusts is vast, involving many different research
fields, from nuclear and condensed matter physics to general relativity. This
review summarizes the progress, which has been achieved over the last few
years, in modeling neutron star crusts, both at the microscopic and macroscopic
levels. The confrontation of these theoretical models with observations is also
briefly discussed.Comment: 182 pages, published version available at
<http://www.livingreviews.org/lrr-2008-10
Motives and periods in Bianchi IX gravity models
In this paper we show that the heat coefficients of the Dirac-Laplacian of SU(2)-invariant Bianchi IX metrics are periods of motives of complements in affine spaces of unions of quadrics and hyperplanes
A theory of first order dissipative superfluid dynamics
We determine the most general form of the equations of relativistic
superfluid hydrodynamics consistent with Lorentz invariance, time-reversal
invariance, the Onsager principle and the second law of thermodynamics at first
order in the derivative expansion. Once parity is violated, either because the
symmetry is anomalous or as a consequence of a different parity-breaking
mechanism, our results deviate from the standard textbook analysis of
superfluids. Our general equations require the specification of twenty
parameters (such as the viscosity and conductivity). In the limit of small
relative superfluid velocities we find a seven parameter set of equations. In
the same limit, we have used the AdS/CFT correspondence to compute the parity
odd contributions to the superfluid equations of motion for a generic
holographic model and have verified that our results are consistent.Comment: v1: 84+1 pages; v2: a sign error corrected, and the assumption of
time-reversal invariance made explici