1,010 research outputs found
Aspects of migration in Victorian Lincolnshire.
SIGLEAvailable from British Library Document Supply Centre- DSC:D67153/86 / BLDSC - British Library Document Supply CentreGBUnited Kingdo
Exponential Decay of Correlations Implies Area Law
We prove that a finite correlation length, i.e. exponential decay of
correlations, implies an area law for the entanglement entropy of quantum
states defined on a line. The entropy bound is exponential in the correlation
length of the state, thus reproducing as a particular case Hastings proof of an
area law for groundstates of 1D gapped Hamiltonians.
As a consequence, we show that 1D quantum states with exponential decay of
correlations have an efficient classical approximate description as a matrix
product state of polynomial bond dimension, thus giving an equivalence between
injective matrix product states and states with a finite correlation length.
The result can be seen as a rigorous justification, in one dimension, of the
intuition that states with exponential decay of correlations, usually
associated with non-critical phases of matter, are simple to describe. It also
has implications for quantum computing: It shows that unless a pure state
quantum computation involves states with long-range correlations, decaying at
most algebraically with the distance, it can be efficiently simulated
classically.
The proof relies on several previous tools from quantum information theory -
including entanglement distillation protocols achieving the hashing bound,
properties of single-shot smooth entropies, and the quantum substate theorem -
and also on some newly developed ones. In particular we derive a new bound on
correlations established by local random measurements, and we give a
generalization to the max-entropy of a result of Hastings concerning the
saturation of mutual information in multiparticle systems. The proof can also
be interpreted as providing a limitation on the phenomenon of data hiding in
quantum states.Comment: 35 pages, 6 figures; v2 minor corrections; v3 published versio
Tensor network states and geometry
Tensor network states are used to approximate ground states of local
Hamiltonians on a lattice in D spatial dimensions. Different types of tensor
network states can be seen to generate different geometries. Matrix product
states (MPS) in D=1 dimensions, as well as projected entangled pair states
(PEPS) in D>1 dimensions, reproduce the D-dimensional physical geometry of the
lattice model; in contrast, the multi-scale entanglement renormalization ansatz
(MERA) generates a (D+1)-dimensional holographic geometry. Here we focus on
homogeneous tensor networks, where all the tensors in the network are copies of
the same tensor, and argue that certain structural properties of the resulting
many-body states are preconditioned by the geometry of the tensor network and
are therefore largely independent of the choice of variational parameters.
Indeed, the asymptotic decay of correlations in homogeneous MPS and MERA for
D=1 systems is seen to be determined by the structure of geodesics in the
physical and holographic geometries, respectively; whereas the asymptotic
scaling of entanglement entropy is seen to always obey a simple boundary law --
that is, again in the relevant geometry. This geometrical interpretation offers
a simple and unifying framework to understand the structural properties of, and
helps clarify the relation between, different tensor network states. In
addition, it has recently motivated the branching MERA, a generalization of the
MERA capable of reproducing violations of the entropic boundary law in D>1
dimensions.Comment: 18 pages, 18 figure
Crackling Noise, Power Spectra and Disorder Induced Critical Scaling
Crackling noise is observed in many disordered non-equilibrium systems in
response to slowly changing external conditions. Examples range from Barkhausen
noise in magnets to acoustic emission in martensites to earthquakes. Using the
non-equilibrium random field Ising model, we derive universal scaling
predictions for the dependence of the associated power spectra on the disorder
and field sweep rate, near an underlying disorder-induced non-equilibrium
critical point. Our theory applies to certain systems in which the crackling
noise results from avalanche-like response to a (slowly) increasing external
driving force, and is characterized by a broad power law scaling regime of the
power spectra. We compute the critical exponents and discuss the relevance of
the results to experiments.Comment: 27 Latex Pages, 14 eps figure
Harnessing Technology to Enable the Flow of Professional Capital:Exploring Experiences of Professional Learning in Rural Scotland
Observations of Low Frequency Solar Radio Bursts from the Rosse Solar-Terrestrial Observatory
The Rosse Solar-Terrestrial Observatory (RSTO; www.rosseobservatory.ie) was
established at Birr Castle, Co. Offaly, Ireland (53 05'38.9", 7 55'12.7") in
2010 to study solar radio bursts and the response of the Earth's ionosphere and
geomagnetic field. To date, three Compound Astronomical Low-cost Low-frequency
Instrument for Spectroscopy and Transportable Observatory (CALLISTO)
spectrometers have been installed, with the capability of observing in the
frequency range 10-870 MHz. The receivers are fed simultaneously by biconical
and log-periodic antennas. Nominally, frequency spectra in the range 10-400 MHz
are obtained with 4 sweeps per second over 600 channels. Here, we describe the
RSTO solar radio spectrometer set-up, and present dynamic spectra of a sample
of Type II, III and IV radio bursts. In particular, we describe fine-scale
structure observed in Type II bursts, including band splitting and rapidly
varying herringbone features
Residual cognitive deficits 50 years after lead poisoning during childhood
The long term neurobehavioural consequences of childhood lead poisoning are not known. In this study adult subjects with a documented history of lead poisoning before age 4 and matched controls were examined with an abbreviated battery of neuropsychological tests including measures of attention, reasoning, memory, motor speed, and current mood. The subjects exposed to lead were inferior to controls on almost all of the cognitive tasks. This pattern of widespread deficits resembles that found in children evaluated at the time of acute exposure to lead rather than the more circumscribed pattern typically seen in adults exposed to lead. Despite having completed as many years of schooling as controls, the subjects exposed to lead were lower in lifetime occupational status. Within the exposed group, performance on the neuropsychological battery and occupational status were related, consistent with the presumed impact of limitations in neuropsychological functioning on everyday life. The results suggest that many subjects exposed to lead suffered acute encephalopathy in childhood which resolved into a chronic subclinical encephalopathy with associated cognitive dysfunction still evident in adulthood. These findings lend support to efforts to limit exposure to lead in childhood
Non-Fermi liquid regime of a doped Mott insulator
We study the doping of a Mott insulator in the presence of quenched
frustrating disorder in the magnetic exchange. A low doping regime
is found, in which the quasiparticle coherent scale is low : with (the ratio of typical exchange to
hopping). In the ``quantum critical regime'' , several
physical quantities display Marginal Fermi Liquid behaviour : NMR relaxation
time , resistivity , optical lifetime
\tau_{opt}^{-1}\propto \omega/\ln(\omega/\epstar) and response functions obey
scaling, e.g. .
In contrast, single-electron properties display stronger deviations from Fermi
liquid theory in this regime with a dependence of the inverse
single-particle lifetime and a decay of the photoemission
intensity. On the basis of this model and of various experimental evidence, it
is argued that the proximity of a quantum critical point separating a glassy
Mott-Anderson insulator from a metallic ground-state is an important ingredient
in the physics of the normal state of cuprate superconductors (particularly the
Zn-doped materials). In this picture the corresponding quantum critical regime
is a ``slushy'' state of spins and holes with slow spin and charge dynamics
responsible for the anomalous properties of the normal state.Comment: 40 pages, RevTeX, including 13 figures in EPS. v2 : minor changes,
some references adde
SU(N) Evolution of a Frustrated Spin Ladder
Recent studies indicate that the weakly coupled spin-1/2 Heisenberg
antiferromagnet with next nearest neighbor frustration supports massive spinons
when suitably tuned. The straightforward SU(N) generalization of the low energy
ladder Hamiltonian yields two independent SU(N) Thirring models with N-1
multiplets of massive ``spinon'' excitations. We study the evolution of the
complete set of low-energy dynamical structure factors using form factors.
Those corresponding to the smooth (staggered) magnetizations are qualitatively
different (the same) in the N=2 and N>2 cases. The absence of single-particle
peaks preserves the notion of spinons stabilized by frustration. In contrast to
the ladder, we note that the N=infinity limit of the four chain magnet is not a
trivial free theory.Comment: 10 pages, RevTex, 5 figures; SU(N) approach clarifie
Non-Equilibrium Electron Transport in Two-Dimensional Nano-Structures Modeled by Green's Functions and the Finite-Element Method
We use the effective-mass approximation and the density-functional theory
with the local-density approximation for modeling two-dimensional
nano-structures connected phase-coherently to two infinite leads. Using the
non-equilibrium Green's function method the electron density and the current
are calculated under a bias voltage. The problem of solving for the Green's
functions numerically is formulated using the finite-element method (FEM). The
Green's functions have non-reflecting open boundary conditions to take care of
the infinite size of the system. We show how these boundary conditions are
formulated in the FEM. The scheme is tested by calculating transmission
probabilities for simple model potentials. The potential of the scheme is
demonstrated by determining non-linear current-voltage behaviors of resonant
tunneling structures.Comment: 13 pages,15 figure
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