2,606 research outputs found
Quantum computational complexity, Einstein's equations and accelerated expansion of the Universe
We study the relation between quantum computational complexity and general
relativity. The quantum computational complexity is proposed to be quantified
by the shortest length of geodesic quantum curves. We examine the
complexity/volume duality in a geodesic causal ball in the framework of Fermi
normal coordinates and derive the full non-linear Einstein equation. Using
insights from the complexity/action duality, we argue that the accelerated
expansion of the universe could be driven by the quantum complexity and free
from coincidence and fine-tunning problems.Comment: 1+20 pages, 2 figures, references adde
Shear Viscosity to Entropy Density Ratio in Higher Derivative Gravity with Momentum Dissipation
We investigate in linear scalar fields modified Gauss-Bonnet theory
that breaks translation invariance. We first calculate both
analytically and numerically and show its relationship with temperature in
log-log plot. Our results show that at low temperatures. The
causality is also considered in this work. We then find that causality
violation still happens in the presence of the linear scalar field and we
suggest there is a Gauss-Bonnet coupling dependent lower limit for the
effective mass of the graviton. If the effective mass of the graviton is big
enough, then there will be no causality violation and hence no constraints for
the Gauss-Bonnet coupling.Comment: 21 pages, 5 figures, revised version, references added, to appear in
PR
Sound modes and stability of momentum dissipated black branes in holography
We systematically investigate the sound modes of momentum dissipated
holographic systems. In particular, we focus on the Einstein-linear axions and
the Einstein-Maxwell-dilaton-axion theories in four-dimensional bulk spacetime
dimensions. The sound velocities of the two theories are computed respectively
and the sound attenuation of the Einstein-Maxwell-axion theory is also
calculated analytically. We also obtain numeral dispersion relations in the two
theories which match with our analytical results. Our results show that the
sound velocity of the Einstein-Maxwell-dilaton theory with additional linear
axion fields is equivalent to that of 2 + 1 - dimensional
Banados-Teitelboim-Zanelli black holes. It allowed us to compare our solution
of the Einstein-linear axions theory with that of systems without translational
invariance from another method. After the computation on the sound velocity, we
calculate the quasinormal modes of scalar-type fluctuations in the
Einstein-Maxwell-dilaton-axion theory. The results show that a dynamical
instability is observed under the condition that the null energy condition is
violated.Comment: 22 pages, 6 figure
Observing the inhomogeneity in the holographic models of superconductors
We study the gravity duals of striped holographic superconductors in the AdS
black hole and AdS soliton backgrounds. We show the dependences of the
condensation and the critical temperature/critical chemical potential on the
inhomogeneity in these two different spacetimes. By exploring the dynamics of
the normal phase through the scalar field perturbation, we argue that the pair
susceptibility and the conductivity can be possible phenomenological
indications to disclose the property of inhomogeneity.Comment: 16 page
d-Wave holographic superconductors with backreaction in external magnetic fields
We study the d-wave holographic superconductors (the d-wave model proposed in
[arXiv:1003.2991[hep-th]]) immersed in constant external magnetic fields by
using the analytic matching method and numerical computation. In the probe
limit, we calculate the spatially dependent condensate solution in the presence
of the magnetism and find that the expression for the upper critical magnetic
field satisfies the relation given in the Ginzburg-Landau theory. The result
shows that the upper critical field gradually increases to its maximum value
at absolute zero temperature T=0, while vanishing at the critical
temperature . Moving away from the probe limit, we investigate the
effect of spacetime backreaction on the critical temperature and the upper
critical magnetic field. The magnetic fields as well as the electric fields
acting as gravitational sources reduce the critical temperature of the
superconductor and actually result in a dyonic black hole solution to the
leading order. We obtain the expression for the upper critical magnetic field
up to order. The analytic result is consistent with the
numerical findings.Comment: 23 pages, 7 figures. typos corrected. to appear in JHEP. arXiv admin
note: text overlap with arXiv:1105.433
Holographic RG flow of thermo-electric transports with momentum dissipation
We construct the holographic renormalization group (RG) flow of
thermo-electric conductivities when the translational symmetry is broken. The
RG flow is probed by the intrinsic observers hovering on the sliding radial
membranes. We obtain the RG flow by solving a matrix-form Riccati equation. The
RG flow provides a high-efficient numerical method to calculate the
thermo-electric conductivities of strongly coupled systems with momentum
dissipation. As an illustration, we recover the AC thermo-electric
conductivities in the Einstein-Maxwell-axion model. Moreover, in several
homogeneous and isotropic holographic models which dissipate the momentum and
have the finite density, it is found that the RG flow of a particular
combination of DC thermo-electric conductivities does not run. As a result, the
DC thermal conductivity on the boundary field theory can be derived
analytically, without using the conserved thermal current.Comment: 27 pages, 6 figures, typo corrected, a ref adde
Collective diffusion and quantum chaos in holography
We define a particular combination of charge and heat currents that is
decoupled with the heat current. This `heat-decoupled' (HD) current can be
transported by diffusion at long distances, when some thermo-electric
conductivities and susceptibilities satisfy a simple condition. Using the
diffusion condition together with the Kelvin formula, we show that the HD
diffusivity can be same as the charge diffusivity and also the heat
diffusivity. We illustrate that such mechanism is implemented in a strongly
coupled field theory, which is dual to a Lifshitz gravity with the dynamical
critical index z=2. In particular, it is exhibited that both charge and heat
diffusivities build the relationship to the quantum chaos. Moreover, we study
the HD diffusivity without imposing the diffusion condition. In some
homogeneous holographic lattices, it is found that the diffusivity/chaos
relation holds independently of any parameters, including the strength of
momentum relaxation, chemical potential, or temperature. We also show a counter
example of the relation and discuss its limited universality.Comment: v4: 26 pages, 1 figure, major revisio
On the geometry outside of acoustic black holes in -dimensional spacetime
Analogue black holes, which can mimic the kinetic aspects of real black
holes, have been proposed for many years. The growth of the radial momentum of
test particles toward the acoustic horizon is calculated for acoustic black
holes in flat and curved spacetimes. Surprisingly, for a freely infalling
vortex approaching the acoustic black hole, the Lyapunov exponent of the growth
of the momentum at the horizon saturates the chaos bound . We investigate the orbits of test vortices and sound
wave rays in the -dimensional "curved" spacetime of an acoustic black
hole. We show that the vortices orbit, the sound wave orbit, and the time delay
of sound are similar to those famous effects of general relativity. These
effects can be verified experimentally in future experiments.Comment: major revision, 25 pages, 9 figures, typos correcte
Gravitational thermodynamics and universal holographic duality in dynamical spacetimes
We construct a generalized Smarr formula which could provide a thermodynamic
route to derive the covariant field equation of general theories of gravity in
dynamic spacetimes. Combining some thermodynamic variables and a new chemical
potential conjugated to the number of degree of freedom on the holographic
screen, we find a universal Cardy-Verlinde formula and give its braneworld
interpretation. We demonstrate that the associated AdS-Bekenstein bound is
tighten than the previous expression for multi-charge black holes in the gauged
supergravities. The Cardy-Verlinde formula and the AdS-Bekenstein bound are
derived from the thermodynamics of bulk trapping horizons, which strongly
suggests the underlying holographic duality between dynamical bulk spacetime
and boundary field theory.Comment: 30 pages; presentation improved, clarifications and references adde
Deriving the gravitational field equation and horizon entropy for arbitrary diffeomorphism-invariant gravity from spacetime solid
Motivated by the analogy between the spacetime and the solid with
inhomogeneous elasticity modulus, we present an alternative method to obtain
the field equation of any diffeomorphism-invariant gravity, by extremizing the
constructed entropy function of the displacement vector field of spacetime
solid. In general stationary spacetimes, we show that the Wald entropy of
horizon arises from the on-shell entropy function of spacetime solid.Comment: 19 pages, no figure, to be published in Phys. Rev.
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