7,384 research outputs found
Sufficient Conditions for Topological Order in Insulators
We prove the existence of low energy excitations in insulating systems at
general filling factor under certain conditions, and discuss in which cases
these may be identified as topological excitations. This proof is based on
previously proven locality results. In the case of half-filling it provides a
significantly shortened proof of the recent higher dimensional
Lieb-Schultz-Mattis theorem.Comment: 7 pages, no figure
Quasi-Adiabatic Continuation in Gapped Spin and Fermion Systems: Goldstone's Theorem and Flux Periodicity
We apply the technique of quasi-adiabatic continuation to study systems with
continuous symmetries. We first derive a general form of Goldstone's theorem
applicable to gapped nonrelativistic systems with continuous symmetries. We
then show that for a fermionic system with a spin gap, it is possible to insert
-flux into a cylinder with only exponentially small change in the energy
of the system, a scenario which covers several physically interesting cases
such as an s-wave superconductor or a resonating valence bond state.Comment: 19 pages, 2 figures, final version in press at JSTA
Systematic Series Expansions for Processes on Networks
We use series expansions to study dynamics of equilibrium and non-equilibrium
systems on networks. This analytical method enables us to include detailed
non-universal effects of the network structure. We show that even low order
calculations produce results which compare accurately to numerical simulation,
while the results can be systematically improved. We show that certain commonly
accepted analytical results for the critical point on networks with a broad
degree distribution need to be modified in certain cases due to
disassortativity; the present method is able to take into account the
assortativity at sufficiently high order, while previous results correspond to
leading and second order approximations in this method. Finally, we apply this
method to real-world data.Comment: 4 pages, 3 figure
Theory of plasma contactors in ground-based experiments and low Earth orbit
Previous theoretical work on plasma contactors as current collectors has fallen into two categories: collisionless double layer theory (describing space charge limited contactor clouds) and collisional quasineutral theory. Ground based experiments at low current are well explained by double layer theory, but this theory does not scale well to power generation by electrodynamic tethers in space, since very high anode potentials are needed to draw a substantial ambient electron current across the magnetic field in the absence of collisions (or effective collisions due to turbulence). Isotropic quasineutral models of contactor clouds, extending over a region where the effective collision frequency upsilon sub e exceeds the electron cyclotron frequency omega sub ce, have low anode potentials, but would collect very little ambient electron current, much less than the emitted ion current. A new model is presented, for an anisotropic contactor cloud oriented along the magnetic field, with upsilon sub e less than omega sub ce. The electron motion along the magnetic field is nearly collisionless, forming double layers in that direction, while across the magnetic field the electrons diffuse collisionally and the potential profile is determined by quasineutrality. Using a simplified expression for upsilon sub e due to ion acoustic turbulence, an analytic solution has been found for this model, which should be applicable to current collection in space. The anode potential is low and the collected ambient electron current can be several times the emitted ion current
Strong and weak thermalization of infinite non-integrable quantum systems
When a non-integrable system evolves out of equilibrium for a long time,
local observables are expected to attain stationary expectation values,
independent of the details of the initial state. However, intriguing
experimental results with ultracold gases have shown no thermalization in
non-integrable settings, triggering an intense theoretical effort to decide the
question. Here we show that the phenomenology of thermalization in a quantum
system is much richer than its classical counterpart. Using a new numerical
technique, we identify two distinct thermalization regimes, strong and weak,
occurring for different initial states. Strong thermalization, intrinsically
quantum, happens when instantaneous local expectation values converge to the
thermal ones. Weak thermalization, well-known in classical systems, happens
when local expectation values converge to the thermal ones only after time
averaging. Remarkably, we find a third group of states showing no
thermalization, neither strong nor weak, to the time scales one can reliably
simulate.Comment: 12 pages, 21 figures, including additional materia
Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity
It has become widely accepted that the most dangerous cardiac arrhythmias are
due to re- entrant waves, i.e., electrical wave(s) that re-circulate repeatedly
throughout the tissue at a higher frequency than the waves produced by the
heart's natural pacemaker (sinoatrial node). However, the complicated structure
of cardiac tissue, as well as the complex ionic currents in the cell, has made
it extremely difficult to pinpoint the detailed mechanisms of these
life-threatening reentrant arrhythmias. A simplified ionic model of the cardiac
action potential (AP), which can be fitted to a wide variety of experimentally
and numerically obtained mesoscopic characteristics of cardiac tissue such as
AP shape and restitution of AP duration and conduction velocity, is used to
explain many different mechanisms of spiral wave breakup which in principle can
occur in cardiac tissue. Some, but not all, of these mechanisms have been
observed before using other models; therefore, the purpose of this paper is to
demonstrate them using just one framework model and to explain the different
parameter regimes or physiological properties necessary for each mechanism
(such as high or low excitability, corresponding to normal or ischemic tissue,
spiral tip trajectory types, and tissue structures such as rotational
anisotropy and periodic boundary conditions). Each mechanism is compared with
data from other ionic models or experiments to illustrate that they are not
model-specific phenomena. The fact that many different breakup mechanisms exist
has important implications for antiarrhythmic drug design and for comparisons
of fibrillation experiments using different species, electromechanical
uncoupling drugs, and initiation protocols.Comment: 128 pages, 42 figures (29 color, 13 b&w
Fractal to Nonfractal Phase Transition in the Dielectric Breakdown Model
A fast method is presented for simulating the dielectric-breakdown model
using iterated conformal mappings. Numerical results for the dimension and for
corrections to scaling are in good agreement with the recent RG prediction of
an upper critical , at which a transition occurs between branching
fractal clusters and one-dimensional nonfractal clusters.Comment: 5 pages, 7 figures; corrections to scaling include
Multiscaling at Point J: Jamming is a Critical Phenomenon
We analyze the jamming transition that occurs as a function of increasing
packing density in a disordered two-dimensional assembly of disks at zero
temperature for ``Point J'' of the recently proposed jamming phase diagram. We
measure the total number of moving disks and the transverse length of the
moving region, and find a power law divergence as the packing density increases
toward a critical jamming density. This provides evidence that the T = 0
jamming transition as a function of packing density is a {\it second order}
phase transition. Additionally we find evidence for multiscaling, indicating
the importance of long tails in the velocity fluctuations.Comment: 4 pages, 5 figures; extensive new numerical data; final version in
press at PR
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