301 research outputs found
A flow equation approach to periodically driven quantum systems
We present a theoretical method to generate a highly accurate {\em
time-independent} Hamiltonian governing the finite-time behavior of a
time-periodic system. The method exploits infinitesimal unitary transformation
steps, from which renormalization group-like flow equations are derived to
produce the effective Hamiltonian. Our tractable method has a range of validity
reaching into frequency regimes that are usually inaccessible via high
frequency expansions in the parameter , where is the
upper limit for the strength of local interactions. We demonstrate our approach
on both interacting and non-interacting many-body Hamiltonians where it offers
an improvement over the more well-known Magnus expansion and other high
frequency expansions. For the interacting models, we compare our approximate
results to those found via exact diagonalization. While the approximation
generally performs better globally than other high frequency approximations,
the improvement is especially pronounced in the regime of lower frequencies and
strong external driving. This regime is of special interest because of its
proximity to the resonant regime where the effect of a periodic drive is the
most dramatic. Our results open a new route towards identifying novel
non-equilibrium regimes and behaviors in driven quantum many-particle systems.Comment: 25 pages, 14 figure
Floquet topological transitions in extended Kane-Mele models with disorder
In this work we use Floquet theory to theoretically study the influence of
circularly polarized light on disordered two-dimensional models exhibiting
topological transitions. We find circularly polarized light can induce a
topological transition in extended Kane-Mele models that include additional
hopping terms and on-site disorder. The topological transitions are understood
from the Floquet-Bloch band structure of the clean system at high symmetry
points in the first Brillouin zone. The light modifies the equilibrium band
structure of the clean system in such a way that the smallest gap in the
Brillouin zone can be shifted from the points to the points, the
point, or even other lower symmetry points. The movement of the
minimal gap point through the Brillouin zone as a function of laser parameters
is explained in the high frequency regime through the Magnus expansion. In the
disordered model, we compute the Bott index to reveal topological phases and
transitions. The disorder can induce transitions from topologically non-trivial
states to trivial states or vice versa, both examples of Floquet topological
Anderson transitions. As a result of the movement of the minimal gap point
through the Brillouin zone as a function of laser parameters, the nature of the
topological phases and transitions is laser-parameter dependent--a contrasting
behavior to the Kane-Mele model.Comment: 10 pages, 7 figure
Reinforcement learning in populations of spiking neurons
Population coding is widely regarded as a key mechanism for achieving reliable behavioral responses in the face of neuronal variability. But in standard reinforcement learning a flip-side becomes apparent. Learning slows down with increasing population size since the global reinforcement becomes less and less related to the performance of any single neuron. We show that, in contrast, learning speeds up with increasing population size if feedback about the populationresponse modulates synaptic plasticity in addition to global reinforcement. The two feedback signals (reinforcement and population-response signal) can be encoded by ambient neurotransmitter concentrations which vary slowly, yielding a fully online plasticity rule where the learning of a stimulus is interleaved with the processing of the subsequent one. The assumption of a single additional feedback mechanism therefore reconciles biological plausibility with efficient learning
Many-body theory of the quantum mirage
In recent scanning tunneling microscopy experiments, confinement in an
elliptical corral has been used to project the Kondo effect from one focus to
the other one. I solve the Anderson model at arbitrary temperatures, for an
impurity hybridized with eigenstates of an elliptical corral, each of which has
a resonant level width delta. This width is crucial. If delta < 20 meV, the
Kondo peak disappears, while if delta > 80 meV, the mirage disappears. For
particular conditions, a stronger mirage with the impurity out of the foci is
predicted.Comment: 5 pages, 5 figures. Some clarifications of the method added, and a
reference included to show that the hybridization of the impurity with bulk
states can be neglecte
Singular responses of spin-incoherent Luttinger liquids
When a local potential changes abruptly in time, an electron gas shifts to a
new state which at long times is orthogonal to the one in the absence of the
local potential. This is known as Anderson's orthogonality catastrophe and it
is relevant for the so-called X-ray edge or Fermi edge singularity, and for
tunneling into an interacting one dimensional system of fermions. It often
happens that the finite frequency response of the photon absorption or the
tunneling density of states exhibits a singular behavior as a function of
frequency: where is a
threshold frequency and is an exponent characterizing the singular
response. In this paper singular responses of spin-incoherent Luttinger liquids
are reviewed. Such responses most often do not fall into the familiar form
above, but instead typically exhibit logarithmic corrections and display a much
higher universality in terms of the microscopic interactions in the theory.
Specific predictions are made, the current experimental situation is
summarized, and key outstanding theoretical issues related to spin-incoherent
Luttinger liquids are highlighted.Comment: 21 pages, 3 figures. Invited Topical Review Articl
Floquet Hofstadter Butterfly on the Kagome and Triangular Lattices
In this work we use Floquet theory to theoretically study the influence of
monochromatic circularly and linearly polarized light on the Hofstadter
butterfly---induced by a uniform perpendicular magnetic field--for both the
kagome and triangular lattices. In the absence of the laser light, the
butterfly has fractal structure with inversion symmetry about magnetic flux
, and reflection symmetry about . As the system is exposed
to an external laser, we find circularly polarized light deforms the butterfly
by breaking the mirror symmetry at flux . By contrast, linearly
polarized light deforms the original butterfly while preserving the mirror
symmetry at flux . We find the inversion symmetry is always preserved
for both linear and circular polarized light. For linearly polarized light, the
Hofstadter butterfly depends on the polarization direction. Further, we study
the effect of the laser on the Chern number of lowest band in the off-resonance
regime (laser frequency is larger than the bandwidth). For circularly polarized
light, we find that low laser intensity will not change the Chern number, but
beyond a critical intensity the Chern number will change. For linearly
polarized light, the Chern number depends on the polarization direction. Our
work highlights the generic features expected for the periodically driven
Hofstadter problem on different lattices.Comment: 13 pages, 11 figure
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