2,194 research outputs found
Haldane Statistics in the Finite Size Entanglement Spectra of Laughlin States
We conjecture that the counting of the levels in the orbital entanglement
spectra (OES) of finite-sized Laughlin Fractional Quantum Hall (FQH) droplets
at filling is described by the Haldane statistics of particles in a
box of finite size. This principle explains the observed deviations of the OES
counting from the edge-mode conformal field theory counting and directly
provides us with a topological number of the FQH states inaccessible in the
thermodynamic limit- the boson compactification radius. It also suggests that
the entanglement gap in the Coulomb spectrum in the conformal limit protects a
universal quantity- the statistics of the state. We support our conjecture with
ample numerical checks.Comment: 4.1 pages, published versio
Bulk-Edge Correspondence in the Entanglement Spectra
Li and Haldane conjectured and numerically substantiated that the
entanglement spectrum of the reduced density matrix of ground-states of
time-reversal breaking topological phases (fractional quantum Hall states)
contains information about the counting of their edge modes when the
ground-state is cut in two spatially distinct regions and one of the regions is
traced out. We analytically substantiate this conjecture for a series of FQH
states defined as unique zero modes of pseudopotential Hamiltonians by finding
a one to one map between the thermodynamic limit counting of two different
entanglement spectra: the particle entanglement spectrum, whose counting of
eigenvalues for each good quantum number is identical (up to accidental
degeneracies) to the counting of bulk quasiholes, and the orbital entanglement
spectrum (the Li-Haldane spectrum). As the particle entanglement spectrum is
related to bulk quasihole physics and the orbital entanglement spectrum is
related to edge physics, our map can be thought of as a mathematically sound
microscopic description of bulk-edge correspondence in entanglement spectra. By
using a set of clustering operators which have their origin in conformal field
theory (CFT) operator expansions, we show that the counting of the orbital
entanglement spectrum eigenvalues in the thermodynamic limit must be identical
to the counting of quasiholes in the bulk. The latter equals the counting of
edge modes at a hard-wall boundary placed on the sample. Moreover, we show this
to be true even for CFT states which are likely bulk gapless, such as the
Gaffnian wavefunction.Comment: 20 pages, 6 figure
Boxicity and separation dimension
A family of permutations of the vertices of a hypergraph is
called 'pairwise suitable' for if, for every pair of disjoint edges in ,
there exists a permutation in in which all the vertices in one
edge precede those in the other. The cardinality of a smallest such family of
permutations for is called the 'separation dimension' of and is denoted
by . Equivalently, is the smallest natural number so that
the vertices of can be embedded in such that any two
disjoint edges of can be separated by a hyperplane normal to one of the
axes. We show that the separation dimension of a hypergraph is equal to the
'boxicity' of the line graph of . This connection helps us in borrowing
results and techniques from the extensive literature on boxicity to study the
concept of separation dimension.Comment: This is the full version of a paper by the same name submitted to
WG-2014. Some results proved in this paper are also present in
arXiv:1212.6756. arXiv admin note: substantial text overlap with
arXiv:1212.675
Real-Space Entanglement Spectrum of Quantum Hall States
We investigate the entanglement spectra arising from sharp real-space
partitions of the system for quantum Hall states. These partitions differ from
the previously utilized orbital and particle partitions and reveal
complementary aspects of the physics of these topologically ordered systems. We
show, by constructing one to one maps to the particle partition entanglement
spectra, that the counting of the real-space entanglement spectra levels for
different particle number sectors versus their angular momentum along the
spatial partition boundary is equal to the counting of states for the system
with a number of (unpinned) bulk quasiholes excitations corresponding to the
same particle and flux numbers. This proves that, for an ideal model state
described by a conformal field theory, the real-space entanglement spectra
level counting is bounded by the counting of the conformal field theory edge
modes. This bound is known to be saturated in the thermodynamic limit (and at
finite sizes for certain states). Numerically analyzing several ideal model
states, we find that the real-space entanglement spectra indeed display the
edge modes dispersion relations expected from their corresponding conformal
field theories. We also numerically find that the real-space entanglement
spectra of Coulomb interaction ground states exhibit a series of branches,
which we relate to the model state and (above an entanglement gap) to its
quasiparticle-quasihole excitations. We also numerically compute the
entanglement entropy for the nu=1 integer quantum Hall state with real-space
partitions and compare against the analytic prediction. We find that the
entanglement entropy indeed scales linearly with the boundary length for large
enough systems, but that the attainable system sizes are still too small to
provide a reliable extraction of the sub-leading topological entanglement
entropy term.Comment: 13 pages, 11 figures; v2: minor corrections and formatting change
Morphology of the copepodid stage of three marine lernaeopodids (Crustacea: Copepoda) from the South-West Coast of India
Full illustrated descriptions are presented of the copepodid stage of Pseudocharopinus narcinae (Pillai), Isobranchia appendiculata Heegaard and Brachiella trichiuri Gnanamuthu. The structure of the copepodid of P. narcinae is similar to that of P. dentatus (Wilson). The copepodids of both I. appendiculata and B. trichiuri are identical with regard to the structure of the second antenna, first maxilla and second maxilla. This structural similarity of the copepodids of I. appendiculata and B. trichiuri indicate the phylogenetic position of the Brachiella and Clavella groups within the family Lernaeopodidae
Perpendicular Ion Heating by Low-Frequency Alfven-Wave Turbulence in the Solar Wind
We consider ion heating by turbulent Alfven waves (AWs) and kinetic Alfven
waves (KAWs) with perpendicular wavelengths comparable to the ion gyroradius
and frequencies smaller than the ion cyclotron frequency. When the turbulence
amplitude exceeds a certain threshold, an ion's orbit becomes chaotic. The ion
then interacts stochastically with the time-varying electrostatic potential,
and the ion's energy undergoes a random walk. Using phenomenological arguments,
we derive an analytic expression for the rates at which different ion species
are heated, which we test by simulating test particles interacting with a
spectrum of randomly phased AWs and KAWs. We find that the stochastic heating
rate depends sensitively on the quantity epsilon = dv/vperp, where vperp is the
component of the ion velocity perpendicular to the background magnetic field
B0, and dv (dB) is the rms amplitude of the velocity (magnetic-field)
fluctuations at the gyroradius scale. In the case of thermal protons, when
epsilon << eps1, where eps1 is a constant, a proton's magnetic moment is nearly
conserved and stochastic heating is extremely weak. However, when epsilon >
eps1, the proton heating rate exceeds the cascade power that would be present
in strong balanced KAW turbulence with the same value of dv, and
magnetic-moment conservation is violated. For the random-phase waves in our
test-particle simulations, eps1 is approximately 0.2. For protons in low-beta
plasmas, epsilon is approximately dB/B0 divided by the square root of beta, and
epsilon can exceed eps1 even when dB/B0 << eps1. At comparable temperatures,
alpha particles and minor ions have larger values of epsilon than protons and
are heated more efficiently as a result. We discuss the implications of our
results for ion heating in coronal holes and the solar wind.Comment: 14 pages, 5 figures, submitted to Ap
The Kibble-Zurek Problem: Universality and the Scaling Limit
Near a critical point, the equilibrium relaxation time of a system diverges
and any change of control/thermodynamic parameters leads to non-equilibrium
behavior. The Kibble-Zurek problem is to determine the dynamical evolution of
the system parametrically close to its critical point when the change is
parametrically slow. The non-equilibrium behavior in this limit is controlled
entirely by the critical point and the details of the trajectory of the system
in parameter space (the protocol) close to the critical point. Together, they
define a universality class consisting of critical exponents-discussed in the
seminal work by Kibble and Zurek-and scaling functions for physical quantities,
which have not been discussed hitherto. In this article, we give an extended
and pedagogical discussion of the universal content in the Kibble-Zurek
problem. We formally define a scaling limit for physical quantities near
classical and quantum transitions for different sets of protocols. We report
computations of a few scaling functions in model Gaussian and large-N problems
and prove their universality with respect to protocol choice. We also introduce
a new protocol in which the critical point is approached asymptotically at late
times with the system marginally out of equilibrium, wherein logarithmic
violations to scaling and anomalous dimensions occur even in the simple
Gaussian problem.Comment: 19 pages,10 figure
Radio-wave propagation through a medium containing electron-density fluctuations described by an anisotropic Goldreich-Sridhar spectrum
We study the propagation of radio waves through a medium possessing density
fluctuations that are elongated along the ambient magnetic field and described
by an anisotropic Goldreich-Sridhar power spectrum. We derive general formulas
for the wave phase structure function, visibility, angular broadening,
diffraction-pattern length scales, and scintillation time scale for arbitrary
distributions of turbulence along the line of sight, and specialize these
formulas to idealized cases.Comment: 25 pages, 3 figures, submitted to Ap
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