4,456 research outputs found
Modave lectures on bulk reconstruction in AdS/CFT
These lecture notes are based on a series of lectures given at the XIII
Modave summer school in mathematical physics. We review the construction due to
Hamilton, Kabat, Lifschytz and Lowe for reconstructing local bulk operators
from CFT operators in the context of AdS/CFT and show how to recover bulk
correlation functions from this definition. Building on the work of these
authors, it has been noted that the bulk displays quantum error correcting
properties. We will discuss tensor network toy models to exemplify these
remarkable features. We will discuss the role of gauge invariance and of
diffeomorphism symmetry in the reconstruction of bulk operators. Lastly, we
provide another method of bulk reconstruction specified to AdS/CFT in
which bulk operators create cross-cap states in the CFT.Comment: 35 pages, 8 figures, lecture notes, v4: a few minor improvements upon
the published proceedings version (version 3 of these lecture notes in arXiv)
have been implemente
DC-current induced domain wall in a chiral -wave superconductor
We study theoretically the impact of an applied DC-current on a mesoscopic
chiral -wave superconductor. Performing quasiclassical calculations on a
two-dimensional system, with an external magnetic flux to generate a DC
current, we show that the current can trigger a transition to a state with a
domain wall between regions of different chiralities. The system shows an
hysteretic behavior, as different domain wall configurations are possible for a
given current. This domain wall creation mechanism can give new insights on
recent experiments observing anomalous current variations in SrRuO
junctions.Comment: 7 pages, 3 figure
Stochastic bounds for two-layer loss systems
This paper studies multiclass loss systems with two layers of servers, where
each server at the first layer is dedicated to a certain customer class, while
the servers at the second layer can handle all customer classes. The routing of
customers follows an overflow scheme, where arriving customers are
preferentially directed to the first layer. Stochastic comparison and coupling
techniques are developed for studying how the system is affected by packing of
customers, altered service rates, and altered server configurations. This
analysis leads to easily computable upper and lower bounds for the performance
of the system.Comment: Revised conten
Anomalous Hall effects and electron polarizability
A theory of the anomalous and spin Hall effects, based on the space
distribution of the current densities, is presented. Spin-orbit coupling gives
rise to a space separation of the mass centers, as well as a current density
separation of the quasiparticle states having opposite group velocities. It is
shown that this microscopic property is essential for existence of both Hall
effects
Stability of multi-dimensional birth-and-death processes with state-dependent 0-homogeneous jumps
We study the positive recurrence of multi-dimensional birth-and-death
processes describing the evolution of a large class of stochastic systems, a
typical example being the randomly varying number of flow-level transfers in a
telecommunication wire-line or wireless network.
We first provide a generic method to construct a Lyapunov function when the
drift can be extended to a smooth function on , using an
associated deterministic dynamical system. This approach gives an elementary
proof of ergodicity without needing to establish the convergence of the scaled
version of the process towards a fluid limit and then proving that the
stability of the fluid limit implies the stability of the process. We also
provide a counterpart result proving instability conditions.
We then show how discontinuous drifts change the nature of the stability
conditions and we provide generic sufficient stability conditions having a
simple geometric interpretation. These conditions turn out to be necessary
(outside a negligible set of the parameter space) for piece-wise constant
drifts in dimension 2.Comment: 18 pages, 4 figure
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