43,274 research outputs found
Spectroscopic probes of isolated nonequilibrium quantum matter: Quantum quenches, Floquet states, and distribution functions
We investigate radio-frequency (rf) spectroscopy, metal-to-superconductor
tunneling, and ARPES as probes of isolated out-of-equilibrium quantum systems,
and examine the crucial role played by the nonequilibrium distribution
function. As an example, we focus on the induced topological time-periodic
(Floquet) phase in a 2D superfluid, following an instantaneous quench of
the coupling strength. The post-quench Cooper pairs occupy a linear combination
of "ground" and "excited" Floquet states, with coefficients determined by the
distribution function. While the Floquet bandstructure exhibits a single
avoided crossing relative to the equilibrium case, the distribution function
shows a population inversion of the Floquet bands at low energies. For a
realization in ultracold atoms, these two features compensate, producing a bulk
average rf signal that is well-captured by a quasi-equilibrium approximation.
In particular, the rf spectrum shows a robust gap. The single crossing occurs
because the quench-induced Floquet phase belongs to a particular class of
soliton dynamics for the BCS equation. The population inversion is a
consequence of this, and ensures the conservation of the pseudospin winding
number. As a comparison, we compute the rf signal when only the lower Floquet
band is occupied; in this case, the gap disappears for strong quenches. The
tunneling signal in a solid state realization is ignorant of the distribution
function, and can show wildly different behaviors. We also examine rf,
tunneling, and ARPES for weak quenches, such that the resulting topological
steady-state is characterized by a constant nonequilibrium order parameter. In
a system with a boundary, tunneling reveals the Majorana edge states. However,
the local rf signal due to the edge states is suppressed by a factor of the
inverse system size, and is spatially deconfined throughout the bulk of the
sample.Comment: 22 pages, 15 figures. v2: Added calculated ARPES spectr
Response theory of the ergodic many-body delocalized phase: Keldysh Finkel'stein sigma models and the 10-fold way
We derive the finite temperature Keldysh response theory for interacting
fermions in the presence of quenched disorder, as applicable to any of the 10
Altland-Zirnbauer classes in an Anderson delocalized phase with at least a U(1)
continuous symmetry. In this formulation of the interacting Finkel'stein
nonlinear sigma model, the statistics of one-body wave functions are encoded by
the constrained matrix field, while physical correlations follow from the
hydrodynamic density or spin response field, which decouples the interactions.
Integrating out the matrix field first, we obtain weak (anti)localization and
Altshuler-Aronov quantum conductance corrections from the hydrodynamic response
function. This procedure automatically incorporates the correct infrared
physics, and in particular gives the Altshuler-Aronov-Khmelnitsky (AAK)
equations for dephasing of weak (anti)localization due to electron-electron
collisions. We explicate the method by deriving known quantum corrections in
two dimensions for the symplectic metal class AII, as well as the spin-SU(2)
invariant superconductor classes C and CI. We show that conductance corrections
due to the special modes at zero energy in nonstandard classes are
automatically cut off by temperature, as previously expected, while the
Wigner-Dyson class Cooperon modes that persist to all energies are cut by
dephasing. We also show that for short-ranged interactions, the standard
self-consistent solution for the dephasing rate is equivalent to a diagrammatic
summation via the self-consistent Born approximation. This should be compared
to the AAK solution for long-ranged Coulomb interactions, which exploits the
Markovian noise correlations induced by thermal fluctuations of the
electromagnetic field. We discuss prospects for exploring the many-body
localization transition from the ergodic side as a dephasing catastrophe in
short-range interacting models.Comment: 68 pages, 23 figure
Traveling Dark Solitons in Superfluid Fermi Gases
Families of dark solitons exist in superfluid Fermi gases. The
energy-velocity dispersion and number of depleted particles completely
determines the dynamics of dark solitons on a slowly-varying background
density. For the unitary Fermi gas we determine these relations from general
scaling arguments and conservation of local particle number. We find solitons
to oscillate sinusoidally at the trap frequency reduced by a factor of
. Numerical integration of the time-dependent Bogoliubov-de Gennes
equation determines spatial profiles and soliton dispersion relations across
the BEC-BCS crossover and proves consistent with the scaling relations at
unitarity.Comment: Small changes in response to referee's comments; fig 1 revised and
refs updated. Cross listed to nucl-th due to interest in the unitary Fermi
ga
Precise Formulation of Neutrino Oscillation in the Earth
We give a perturbation theory of neutrino oscillation in the Earth. The
perturbation theory is valid for neutrinos with energy E \gsim 0.5 GeV. It is
formulated using trajectory dependent average potential. Non-adiabatic
contributions are included as the first order effects in the perturbation
theory. We analyze neutrino oscillation with standard matter effect and with
non-standard matter effect. In a three flavor analysis we show that the
perturbation theory gives a precise description of neutrino conversion in the
Earth. Effect of the Earth matter is substantially simplified in this
formulation.Comment: References added, 21 pages, 10 figures, version to appear in PR
WZW action in odd dimensional gauge theories
It is shown that Wess-Zumino-Witten (WZW) type actions can be constructed in
odd dimensional space-times using Wilson line or Wilson loop. WZW action
constructed using Wilson line gives anomalous gauge variations and the WZW
action constructed using Wilson loop gives anomalous chiral transformation. We
show that pure gauge theory including Yang-Mills action, Chern-Simons action
and the WZW action can be defined in odd dimensional space-times with even
dimensional boundaries. Examples in 3D and 5D are given. We emphasize that this
offers a way to generalize gauge theory in odd dimensions. The WZW action
constructed using Wilson line can not be considered as action localized on
boundary space-times since it can give anomalous gauge transformations on
separated boundaries. We try to show that such WZW action can be obtained in
the effective theory when making localized chiral fermions decouple.Comment: 19 pages, text shortened, reference added. Version to appear in PR
Deep learning with 3D and label geometry
A fine-grained understanding of an image is two-fold: visual understanding and semantic understanding. The former strives to understand the intrinsic properties of the object in the image, whereas the latter aims at associating the diverse objects with certain semantics. All of these form the basis of an in-depth understanding of images. Today’s default architectures of deep convolutional networks have already shown a remarkable ability in capturing the 2D visual appearances of images, and mapping visual content to semantic classes thereafter. However, research on fine-grained image understanding, such as inferring the intrinsic 3D information and more structured semantics, is less explored. In this thesis, we look at the problems by asking "How to better utilize geometry for better image understanding?" In the first part, we research visual image understanding with 3D geometry. We show that it is possible to automatically explain a variety of visual contents in the image with texture-free 3D shapes. Furthermore, we develop a deep learning framework to reliably recover a set of 3D geometric attributes, such as the pose of an object and the surface normal of its shape, from a 2D image. In the second part, we explore label geometry for semantic image understanding. We find that a set of image classification problems have geometrically similar probability spaces. Therefore, label geometry is introduced, unifying one-vs.-rest classification, multi-label classification, and out-of-distribution classification in one framework. Moreover, we show that learned hierarchical label geometries can balance the accuracy and specificity of an image classifier
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