6 research outputs found
Chiral Edge Currents in a Holographic Josephson Junction
We discuss the Josephson effect and the appearance of dissipationless edge
currents in a holographic Josephson junction configuration involving a chiral,
time-reversal breaking, superconductor in 2+1 dimensions. Such a superconductor
is expected to be topological, thereby supporting topologically protected
gapless Majorana-Weyl edge modes. Such modes manifest themselves in chiral
dissipationless edge currents, which we exhibit and investigate in the context
of our construction. The physics of the Josephson current itself, though
expected to be unconventional in some non-equilibrium settings, is shown to be
conventional in our setup which takes place in thermal equilibrium. We comment
on various ways in which the expected Majorana nature of the edge excitations,
and relatedly the unconventional nature of topological Josephson junctions, can
be verified in the holographic context.Comment: 14 pages, 7 figures. Minor change
Dynamics of Holographic Entanglement Entropy Following a Local Quench
We discuss the behaviour of holographic entanglement entropy following a
local quench in 2+1 dimensional strongly coupled CFTs. The entanglement
generated by the quench propagates along an emergent light-cone, reminiscent of
the Lieb-Robinson light-cone propagation of correlations in non-relativistic
systems. We find the speed of propagation is bounded from below by the
entanglement tsunami velocity obtained earlier for global quenches in
holographic systems, and from above by the speed of light. The former is
realized for sufficiently broad quenches, while the latter pertains for well
localized quenches. The non-universal behavior in the intermediate regime
appears to stem from finite-size effects. We also note that the entanglement
entropy of subsystems reverts to the equilibrium value exponentially fast, in
contrast to a much slower equilibration seen in certain spin models.Comment: 27 pages, 12 figures. v2: added refs and fixed typos. v3: added
clarifications, published versio
Numerical investigation of spatial inhomogeneities in gravity and quantum field theory
Many interesting phenomena, such as high-temperature superconductivity and the quark-gluon plasma, still lack a satisfyingly predictive theoretical description. However, recent advances have revealed a curious connection between quantum field theories at strong coupling and classical gravity. This correspondence, known as the gauge/gravity duality or holographic correspondence, offers a promising perspective for investigating strongly correlated systems. In this thesis, we focus on using these new tools to examine the consequences of breaking translational invariance in such systems.
We first use this duality to study the holographic realization of a spatially inhomogeneous condensed matter device known as a Josephson junction. We do so by constructing the gravitational equivalent of two superconductors separated by a weak metallic link, from which we then extract various field-theoretic quantities of interest. These include the spontaneously generated Josephson current, the superconducting order parameter, as well as a novel quantity we refer to as edge currents, which are indicative of gapless chiral modes localized at the interfaces between phases.
We then investigate the more abstract construct of entanglement entropy in holographic theories. We model the fast local injection of energy in a 2+1 dimensional field theory and study the resulting thermalization of quantum entanglement. We achieve this objective by numerically evolving the geometry dual to a local quench from which we then compute the area of various minimal surfaces, the holographic proxy for entanglement entropy. We observe the appearance of a lightcone featuring two distinct regimes of entanglement propagation and provide a phenomenological explanation of the underlying mechanisms at play.
Finally, we turn our attention to spatial inhomogeneities in gravitational systems themselves. We use an approximation of general relativity in which the number of spacetime dimensions is infinite to investigate the Gregory-Laflamme instability of higher-dimensional charged black branes. We argue that charged branes are always unstable in this new language, and push the approximation to next-to-leading order to compute the critical dimension below which the instability results in horizon fragmentation. We also examine the stability properties of two-dimensional black membranes and find that the triangular lattice minimizes brane enthalpy.Science, Faculty ofPhysics and Astronomy, Department ofGraduat