14,761 research outputs found
Dynamics for holographic codes
We describe how to introduce dynamics for the holographic states and codes
introduced by Pastawski, Yoshida, Harlow and Preskill. This task requires the
definition of a continuous limit of the kinematical Hilbert space which we
argue may be achieved via the semicontinuous limit of Jones. Dynamics is then
introduced by building a unitary representation of a group known as Thompson's
group T, which is closely related to the conformal group in 1+1 dimensions. The
bulk Hilbert space is realised as a special subspace of the semicontinuous
limit Hilbert space spanned by a class of distinguished states which can be
assigned a discrete bulk geometry. The analogue of the group of large bulk
diffeomorphisms is given by a unitary representation of the Ptolemy group Pt,
on the bulk Hilbert space thus realising a toy model of the AdS/CFT
correspondence which we call the Pt/T correspondence.Comment: 40 pages (revised version submitted to journal). See video of related
talk: https://www.youtube.com/watch?v=xc2KIa2LDF
Steady-state thermodynamics of non-interacting transport beyond weak coupling
We investigate the thermodynamics of simple (non-interacting) transport
models beyond the scope of weak coupling. For a single fermionic or bosonic
level -- tunnel-coupled to two reservoirs -- exact expressions for the
stationary matter and energy current are derived from the solutions of the
Heisenberg equations of motion. The positivity of the steady-state entropy
production rate is demonstrated explicitly. Finally, for a configuration in
which particles are pumped upwards in chemical potential by a downward
temperature gradient, we demonstrate that the thermodynamic efficiency of this
process decreases when the coupling strength between system and reservoirs is
increased, as a direct consequence of the loss of a tight coupling between
energy and matter currents.Comment: 6 pages, 2 figures, to appear in EP
Stochastic transport in the presence of spatial disorder: fluctuation-induced corrections to homogenization
Motivated by uncertainty quantification in natural transport systems, we
investigate an individual-based transport process involving particles
undergoing a random walk along a line of point sinks whose strengths are
themselves independent random variables. We assume particles are removed from
the system via first-order kinetics. We analyse the system using a hierarchy of
approaches when the sinks are sparsely distributed, including a stochastic
homogenization approximation that yields explicit predictions for the extrinsic
disorder in the stationary state due to sink strength fluctuations. The
extrinsic noise induces long-range spatial correlations in the particle
concentration, unlike fluctuations due to the intrinsic noise alone.
Additionally, the mean concentration profile, averaged over both intrinsic and
extrinsic noise, is elevated compared with the corresponding profile from a
uniform sink distribution, showing that the classical homogenization
approximation can be a biased estimator of the true mean.Comment: 16 pages, 8 figure
Bistability in the Complex Ginzburg-Landau Equation with Drift
Properties of the complex Ginzburg-Landau equation with drift are studied focusing on the Benjamin-Feir stable regime. On a finite interval with Neumann boundary conditions the equation exhibits bistability between a spatially uniform time-periodic state and a variety of nonuniform states with complex time dependence. The origin of this behavior is identified and contrasted with the bistable behavior present with periodic boundary conditions and no drift
Self-consistent calculation of electric potentials in Hall devices
Using a first-principles classical many-body simulation of a Hall bar, we
study the necessary conditions for the formation of the Hall potential: (i)
Ohmic contacts with metallic reservoirs, (ii) electron-electron interactions,
and (iii) confinement to a finite system. By propagating thousands of
interacting electrons over million time-steps we capture the build-up of the
self-consistent potential, which resembles results obtained by
conformal-mapping methods. As shown by a microscopic model of the current
injection, the Hall effect is linked to specific boundary conditions at the
particle reservoirs.Comment: 6 pages, 7 figure
Weyl superconductors
We study the physics of the superconducting variant of Weyl semimetals, which
may be realized in multilayer structures comprising topological insulators and
superconductors. We show how superconductivity can split each Weyl node into
two. The resulting Bogoliubov Weyl nodes can be pairwise independently
controlled, allowing to access a set of phases characterized by different
numbers of bulk Bogoliubov Weyl nodes and chiral Majorana surface modes. We
analyze the physics of vortices in such systems, which trap zero energy
Majorana modes only under certain conditions. We finally comment on possible
experimental probes, thereby also exploiting the similarities between Weyl
superconductors and 2-dimensional p + ip superconductors.Comment: 13 pages, 5 figure
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