88 research outputs found
Thermal out-of-time-order correlators, KMS relations, and spectral functions
We describe general features of thermal correlation functions in quantum
systems, with specific focus on the fluctuation-dissipation type relations
implied by the KMS condition. These end up relating correlation functions with
different time ordering and thus should naturally be viewed in the larger
context of out-of-time-ordered (OTO) observables. In particular, eschewing the
standard formulation of KMS relations where thermal periodicity is combined
with time-reversal to stay within the purview of Schwinger-Keldysh functional
integrals, we show that there is a natural way to phrase them directly in terms
of OTO correlators. We use these observations to construct a natural causal
basis for thermal n-point functions in terms of fully nested commutators. We
provide several general results which can be inferred from cyclic orbits of
permutations, and exemplify the abstract results using a quantum oscillator as
an explicit example.Comment: 36 pages + appendices. v2: minor changes + refs added. v3: minor
changes, published versio
Effect of long range connections on an infinite randomness fixed point associated with the quantum phase transitions in a transverse Ising model
We study the effect of long-range connections on the infinite-randomness
fixed point associated with the quantum phase transitions in a transverse Ising
model (TIM). The TIM resides on a long-range connected lattice where any two
sites at a distance r are connected with a non-random ferromagnetic bond with a
probability that falls algebraically with the distance between the sites as
1/r^{d+\sigma}. The interplay of the fluctuations due to dilutions together
with the quantum fluctuations due to the transverse field leads to an
interesting critical behaviour. The exponents at the critical fixed point
(which is an infinite randomness fixed point (IRFP)) are related to the
classical "long-range" percolation exponents. The most interesting observation
is that the gap exponent \psi is exactly obtained for all values of \sigma and
d. Exponents depend on the range parameter \sigma and show a crossover to
short-range values when \sigma >= 2 -\eta_{SR} where \eta_{SR} is the anomalous
dimension for the conventional percolation problem. Long-range connections are
also found to tune the strength of the Griffiths phase.Comment: 5 pages, 1 figure, To appear in Phys. Rev.
Anomaly/Transport in an Ideal Weyl gas
We study some of the transport processes which are specific to an ideal gas
of relativistic Weyl fermions and relate the corresponding transport
coefficients to various anomaly coefficients of the system. We propose that
these transport processes can be thought of as arising from the continuous
injection of chiral states and their subsequent adiabatic flow driven by
vorticity. This in turn leads to an elegant expression relating the anomaly
induced transport coefficients to the anomaly polynomial of the Ideal Weyl gas.Comment: 35 pages, JHEP forma
Higher Derivative Corrections to Locally Black Brane Metrics
In this paper we generalize the construction of locally boosted black brane
space time to higher derivative gravities. We consider the Gauss-Bonnet term
(with coefficient ) as a toy example. We find the solution to the
corrected Einstein equations to first order in the boundary
derivative expansion. This allows us to find the corrections to the
boundary stress tensor in the presence of the Gauss-Bonnet term in the bulk
action. We therefore obtain the ratio of shear viscosity to entropy which
agrees with other methods of computation in the literature.Comment: 0+17 page
Local Fluid Dynamical Entropy from Gravity
Spacetime geometries dual to arbitrary fluid flows in strongly coupled = 4 super Yang Mills theory have recently been constructed perturbatively in the long wavelength limit. We demonstrate that these geometries all have regular event horizons, and determine the location of the horizon order by order in a boundary derivative expansion. Intriguingly, the derivative expansion allows us to determine the location of the event horizon in the bulk as a local function of the fluid dynamical variables. We define a natural map from the boundary to the horizon using ingoing null geodesics. The area-form on spatial sections of the horizon can then be pulled back to the boundary to define a local entropy current for the dual field theory in the hydrodynamic limit. The area theorem of general relativity guarantees the positivity of the divergence of the entropy current thus constructed
CFT dual of the AdS Dirichlet problem: Fluid/Gravity on cut-off surfaces
We study the gravitational Dirichlet problem in AdS spacetimes with a view to
understanding the boundary CFT interpretation. We define the problem as bulk
Einstein's equations with Dirichlet boundary conditions on fixed timelike
cut-off hypersurface. Using the fluid/gravity correspondence, we argue that one
can determine non-linear solutions to this problem in the long wavelength
regime. On the boundary we find a conformal fluid with Dirichlet constitutive
relations, viz., the fluid propagates on a `dynamical' background metric which
depends on the local fluid velocities and temperature. This boundary fluid can
be re-expressed as an emergent hypersurface fluid which is non-conformal but
has the same value of the shear viscosity as the boundary fluid. The
hypersurface dynamics arises as a collective effect, wherein effects of the
background are transmuted into the fluid degrees of freedom. Furthermore, we
demonstrate that this collective fluid is forced to be non-relativistic below a
critical cut-off radius in AdS to avoid acausal sound propagation with respect
to the hypersurface metric. We further go on to show how one can use this
set-up to embed the recent constructions of flat spacetime duals to
non-relativistic fluid dynamics into the AdS/CFT correspondence, arguing that a
version of the membrane paradigm arises naturally when the boundary fluid lives
on a background Galilean manifold.Comment: 71 pages, 2 figures. v2: Errors in bulk metrics dual to
non-relativistic fluids (both on cut-off surface and on the boundary) have
been corrected. New appendix with general results added. Fixed typos. 82
pages, 2 figure
Relativistic Viscous Fluid Dynamics and Non-Equilibrium Entropy
Fluid dynamics corresponds to the dynamics of a substance in the long
wavelength limit. Writing down all terms in a gradient (long wavelength)
expansion up to second order for a relativistic system at vanishing charge
density, one obtains the most general (causal) equations of motion for a fluid
in the presence of shear and bulk viscosity, as well as the structure of the
non-equilibrium entropy current. Requiring positivity of the divergence of the
non-equilibrium entropy current relates some of its coefficients to those
entering the equations of motion. I comment on possible applications of these
results for conformal and non-conformal fluids.Comment: 25 pages, no figures; v2: matches published versio
Hydrodynamics from charged black branes
We extend the recent work on fluid-gravity correspondence to charged
black-branes by determining the metric duals to arbitrary charged fluid
configuration up to second order in the boundary derivative expansion. We also
derive the energy-momentum tensor and the charge current for these
configurations up to second order in the boundary derivative expansion. We find
a new term in the charge current when there is a bulk Chern-Simons interaction
thus resolving an earlier discrepancy between thermodynamics of charged
rotating black holes and boundary hydrodynamics. We have also confirmed that
all our expressions are covariant under boundary Weyl-transformations as
expected.Comment: 0+ 31 Pages; v2: 0+33 pages, typos corrected and new sections (in
appendix) added; v3:published versio
Thermodynamics, gravitational anomalies and cones
By studying the Euclidean partition function on a cone, we argue that pure
and mixed gravitational anomalies generate a "Casimir momentum" which manifests
itself as parity violating coefficients in the hydrodynamic stress tensor and
charge current. The coefficients generated by these anomalies enter at a lower
order in the hydrodynamic gradient expansion than would be naively expected. In
1+1 dimensions, the gravitational anomaly affects coefficients at zeroth order
in the gradient expansion. The mixed anomaly in 3+1 dimensions controls the
value of coefficients at first order in the gradient expansion.Comment: 37 page
Shear Viscosity to Entropy Density Ratio in Six Derivative Gravity
We calculate shear viscosity to entropy density ratio in presence of four
derivative (with coefficient ) and six derivative (with coefficient
) terms in bulk action. In general, there can be three possible four
derivative terms and ten possible six derivative terms in the Lagrangian. Among
them two four derivative and eight six derivative terms are ambiguous, i.e.,
these terms can be removed from the action by suitable field redefinitions.
Rest are unambiguous. According to the AdS/CFT correspondence all the
unambiguous coefficients (coefficients of unambiguous terms) can be fixed in
terms of field theory parameters. Therefore, any measurable quantities of
boundary theory, for example shear viscosity to entropy density ratio, when
calculated holographically can be expressed in terms of unambiguous
coefficients in the bulk theory (or equivalently in terms of boundary
parameters). We calculate for generic six derivative gravity and find
that apparently it depends on few ambiguous coefficients at order .
We calculate six derivative corrections to central charges and and
express in terms of these central charges and unambiguous coefficients
in the bulk theory.Comment: 29 pages, no figure, V2, results and typos correcte
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