19,824 research outputs found
Field Induced Positional Shift of Bloch Electrons and its Dynamical Implications
We derive the field correction to the Berry curvature of Bloch electrons,
which can be traced back to a positional shift due to the interband mixing
induced by external electromagnetic fields. The resulting semiclassical
dynamics is accurate to second order in the fields, in the same form as before,
provided that the wave packet energy is derived up to the same order. As
applications, we discuss the orbital magnetoelectric polarizability and predict
nonlinear anomalous Hall effects
Online Local Learning via Semidefinite Programming
In many online learning problems we are interested in predicting local
information about some universe of items. For example, we may want to know
whether two items are in the same cluster rather than computing an assignment
of items to clusters; we may want to know which of two teams will win a game
rather than computing a ranking of teams. Although finding the optimal
clustering or ranking is typically intractable, it may be possible to predict
the relationships between items as well as if you could solve the global
optimization problem exactly.
Formally, we consider an online learning problem in which a learner
repeatedly guesses a pair of labels (l(x), l(y)) and receives an adversarial
payoff depending on those labels. The learner's goal is to receive a payoff
nearly as good as the best fixed labeling of the items. We show that a simple
algorithm based on semidefinite programming can obtain asymptotically optimal
regret in the case where the number of possible labels is O(1), resolving an
open problem posed by Hazan, Kale, and Shalev-Schwartz. Our main technical
contribution is a novel use and analysis of the log determinant regularizer,
exploiting the observation that log det(A + I) upper bounds the entropy of any
distribution with covariance matrix A.Comment: 10 page
Quantization and Corrections of Adiabatic Particle Transport in a Periodic Ratchet Potential
We study the transport of an overdamped particle adiabatically driven by an
asymmetric potential which is periodic in both space and time. We develop an
adiabatic perturbation theory after transforming the Fokker-Planck equation
into a time-dependent hermitian problem, and reveal an analogy with quantum
adiabatic particle transport. An analytical expression is obtained for the
ensemble average of the particle velocity in terms of the Berry phase of the
Bloch states. Its time average is shown to be quantized as a Chern number in
the deterministic or tight-binding limit, with exponentially small corrections.
In the opposite limit, where the thermal energy dominates the ratchet
potential, a formula for the average velocity is also obtained, showing a
second order dependence on the potential.Comment: 8 page
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