4,792 research outputs found
Diffusion and Butterfly Velocity at Finite Density
We study diffusion and butterfly velocity () in two holographic models,
linear axion and axion-dilaton model, with a momentum relaxation parameter
() at finite density or chemical potential (). Axion-dilaton model
is particularly interesting since it shows linear--resistivity, which may
have something to do with the universal bound of diffusion. At finite density,
there are two diffusion constants describing the coupled diffusion of
charge and energy. By computing exactly, we find that in the incoherent
regime () is identified with the charge
diffusion constant () and is identified with the energy diffusion
constant (). In the coherent regime, at very small density, are
`maximally' mixed in the sense that is identified with ,
which is opposite to the case in the incoherent regime. In the incoherent
regime where or 1 so it is
universal independently of and . However, where or so, in general,
may not saturate to the lower bound in the incoherent regime, which suggests
that the characteristic velocity for charge diffusion may not be the butterfly
velocity. We find that the finite density does not affect the diffusion
property at zero density in the incoherent regime.Comment: 24 pages, 6 figures, v2 minor edits and references adde
Surface Counterterms and Regularized Holographic Complexity
The holographic complexity is UV divergent. As a finite complexity, we
propose a "regularized complexity" by employing a similar method to the
holographic renormalization. We add codimension-two boundary counterterms which
do not contain any boundary stress tensor information. It means that we
subtract only non-dynamic background and all the dynamic information of
holographic complexity is contained in the regularized part. After showing the
general counterterms for both CA and CV conjectures in holographic spacetime
dimension 5 and less, we give concrete examples: the BTZ black holes and the
four and five dimensional Schwarzschild AdS black holes. We propose how to
obtain the counterterms in higher spacetime dimensions and show explicit
formulas only for some special cases with enough symmetries. We also compute
the complexity of formation by using the regularized complexity.Comment: Published version with some small improvement
Universal corner contributions to entanglement negativity
It has been realised that corners in entangling surfaces can induce new
universal contributions to the entanglement entropy and R\'enyi entropy. In
this paper we study universal corner contributions to entanglement negativity
in three- and four-dimensional CFTs using both field theory and holographic
techniques. We focus on the quantity defined by the ratio of the
universal part of the entanglement negativity over that of the entanglement
entropy, which may characterise the amount of distillable entanglement. We find
that for most of the examples takes bigger values for singular
entangling regions, which may suggest increase in distillable entanglement.
However, there also exist counterexamples where distillable entanglement
decreases for singular surfaces. We also explore the behaviour of as the
coupling varies and observe that for singular entangling surfaces, the amount
of distillable entanglement is mostly largest for free theories, while
counterexample exists for free Dirac fermion in three dimensions. For
holographic CFTs described by higher derivative gravity, may increase or
decrease, depending on the sign of the relevant parameters. Our results may
reveal a more profound connection between geometry and distillable
entanglement.Comment: 28 pages, 5 figure
- …