15 research outputs found
Coarse-Graining Can Beat the Rotating Wave Approximation in Quantum Markovian Master Equations
We present a first-principles derivation of the Markovian semi-group master equation without invoking the rotating wave approximation (RWA). Instead we use a time coarse-graining approach which leaves us with a free timescale parameter, which we can optimize. Comparing this approach to the standard RWA-based Markovian master equation, we find that significantly better agreement is possible using the coarse-graining approach, for a three-level model coupled to a bath of oscillators, whose exact dynamics we can solve for at zero temperature. The model has the important feature that the RWA has a non-trivial effect on the dynamics of the populations. We show that the two different master equations can exhibit strong qualitative differences for the population of the energy eigenstates even for such a simple model. The RWA-based master equation misses an important feature which the coarse-graining based scheme does not. By optimizing the coarse-graining timescale the latter scheme can be made to approach the exact solution much more closely than the RWA-based master equation
Holographic Aspects of Fermi Liquids in a Background Magnetic Field
We study the effects of an external magnetic field on the properties of the
quasiparticle spectrum of the class of 2+1 dimensional strongly coupled
theories holographically dual to charged AdS black holes at zero
temperature. We uncover several interesting features. At certain values of the
magnetic field, there are multiple quasiparticle peaks representing a novel
level structure of the associated Fermi surfaces. Furthermore, increasing
magnetic field deforms the dispersion characteristics of the quasiparticle
peaks from non-Landau toward Landau behaviour. At a certain value of the
magnetic field, just at the onset of Landau-like behaviour of the Fermi liquid,
the quasiparticles and Fermi surface disappear.Comment: 18 pages, 10 figures. Revised some of the terminology: changed
non-separable solutions to infinite-sum solution
Holographic Studies of Entanglement Entropy in Superconductors
We present the results of our studies of the entanglement entropy of a
superconducting system described holographically as a fully back-reacted
gravity system, with a stable ground state. We use the holographic prescription
for the entanglement entropy. We uncover the behavior of the entropy across the
superconducting phase transition, showing the reorganization of the degrees of
freedom of the system. We exhibit the behaviour of the entanglement entropy
from the superconducting transition all the way down to the ground state at
T=0. In some cases, we also observe a novel transition in the entanglement
entropy at intermediate temperatures, resulting from the detection of an
additional length scale.Comment: 21 pages, 14 figures. v2:Clarified some remarks concerning stability.
v3: Updated to the version that appears in JHE
Dynamics of Fundamental Matter in N=2* Yang-Mills Theory
We study the dynamics of quenched fundamental matter in
supersymmetric large SU(N) Yang-Mills theory at zero temperature. Our tools
for this study are probe D7-branes in the holographically dual
Pilch-Warner gravitational background. Previous work using
D3-brane probes of this geometry has shown that it captures the physics of a
special slice of the Coulomb branch moduli space of the gauge theory, where the
constituent D3-branes form a dense one dimensional locus known as the
enhancon, located deep in the infrared. Our present work shows how this physics
is supplemented by the physics of dynamical flavours, revealed by the D7-branes
embeddings we find. The Pilch-Warner background introduces new divergences into
the D7-branes free energy, which we are able to remove with a single
counterterm. We find a family of D7-brane embeddings in the geometry and
discuss their properties. We study the physics of the quark condensate,
constituent quark mass, and part of the meson spectrum. Notably, there is a
special zero mass embedding that ends on the enhancon, which shows that while
the geometry acts repulsively on the D7-branes, it does not do so in a way that
produces spontaneous chiral symmetry breaking.Comment: 24 pages, 8 figures. Corrected typos, added comment about
counterterm. To appear in JHE
Thermal Dynamics of Quarks and Mesons in N=2* Yang-Mills Theory
We study the dynamics of quenched fundamental matter in
supersymmetric large Yang-Mills theory, extending our earlier
work to finite temperature. We use probe D7-branes in the holographically dual
thermalized generalization of the Pilch-Warner
gravitational background found by Buchel and Liu. Such a system provides an
opportunity to study how key features of the dynamics are affected by being in
a non-conformal setting where there is an intrinsic scale, set here by the
mass, , of a hypermultiplet. Such studies are motivated by connections to
experimental studies of the quark-gluon plasma at RHIC and LHC, where the
microscopic theory of the constituents, QCD, has a scale, .
We show that the binding energy of mesons in the theory is
increased in the presence of the scale , and that subsequently the
meson-melting temperature is higher than for the conformal case.Comment: 17 pages, 6 figure
Landau Levels, Magnetic Fields and Holographic Fermi Liquids
We further consider a probe fermion in a dyonic black hole background in
anti-de Sitter spacetime, at zero temperature, comparing and contrasting two
distinct classes of solution that have previously appeared in the literature.
Each class has members labeled by an integer n, corresponding to the n-th
Landau level for the fermion. Our interest is the study of the spectral
function of the fermion, interpreting poles in it as indicative of
quasiparticles associated with the edge of a Fermi surface in the
holographically dual strongly coupled theory in a background magnetic field H
at finite chemical potential. Using both analytical and numerical methods, we
explicitly show how one class of solutions naturally leads to an infinite
family of quasiparticle peaks, signaling the presence of a Fermi surface for
each level n. We present some of the properties of these peaks, which fall into
a well behaved pattern at large n, extracting the scaling of Fermi energy with
n and H, as well as the dispersion of the quasiparticles.Comment: 23 pages, 4 figures. Changed some of the terminology: non-separable
-> infinite-sum. Clarified the relationship between our ansatz and the
separable ansat
Quantum Adiabatic Markovian Master Equations
We develop from first principles Markovian master equations suited for
studying the time evolution of a system evolving adiabatically while coupled
weakly to a thermal bath. We derive two sets of equations in the adiabatic
limit, one using the rotating wave (secular) approximation that results in a
master equation in Lindblad form, the other without the rotating wave
approximation but not in Lindblad form. The two equations make markedly
different predictions depending on whether or not the Lamb shift is included.
Our analysis keeps track of the various time- and energy-scales associated with
the various approximations we make, and thus allows for a systematic inclusion
of higher order corrections, in particular beyond the adiabatic limit. We use
our formalism to study the evolution of an Ising spin chain in a transverse
field and coupled to a thermal bosonic bath, for which we identify four
distinct evolution phases. While we do not expect this to be a generic feature,
in one of these phases dissipation acts to increase the fidelity of the system
state relative to the adiabatic ground state.Comment: 31 pages, 9 figures. v2: Generalized Markov approximation bound.
Included a section on thermal equilibration. v3: Added text that appears in
NJP version. Generalized Lindblad ME to include degenerate subspaces. v3.
Corrections made to Appendix E and F. We thank Kabuki Takada and Hidetoshi
Nishimori for pointing out the errors. v4: Corrected a typo in Eqt. B
Evolution of Holographic Entanglement Entropy after Thermal and Electromagnetic Quenches
We study the evolution and scaling of the entanglement entropy after two
types of quenches for a 2+1 field theory, using holographic techniques. We
study a thermal quench, dual to the addition of a shell of uncharged matter to
four dimensional Anti-de Sitter (AdS_4) spacetime, and study the subsequent
formation of a Schwarzschild black hole. We also study an electromagnetic
quench, dual to the addition of a shell of charged sources to AdS_4, following
the subsequent formation of an extremal dyonic black hole. In these backgrounds
we consider the entanglement entropy of two types of geometries, the infinite
strip and the round disc, and find distinct behavior for each. Some of our
findings naturally supply results analogous to observations made in the
literature for lower dimensions, but we also uncover several new phenomena,
such as (in some cases) a discontinuity in the time derivative of the
entanglement entropy as it nears saturation, and for the electromagnetic
quench, a logarithmic growth in the entanglement entropy with time for both the
disc and strip, before settling to saturation.Comment: 30 pages, 19 figures. Corrected typos and added some discussion. To
appear in New J. Phy