9,617 research outputs found
Entanglement entropy and quantum field theory: a non-technical introduction
In these proceedings we give a pedagogical and non-technical introduction to
the Quantum Field Theory approach to entanglement entropy. Particular attention
is devoted to the one space dimensional case, with a linear dispersion
relation, that, at a quantum critical point, can be effectively described by a
two-dimensional Conformal Field Theory.Comment: 10 Pages, 2 figures. Talk given at the conference "Entanglement in
Physical and information sciences", Centro Ennio de Giorgi, Pisa, December
200
E-ELT constraints on runaway dilaton scenarios
We use a combination of simulated cosmological probes and astrophysical tests
of the stability of the fine-structure constant , as expected from the
forthcoming European Extremely Large Telescope (E-ELT), to constrain the class
of string-inspired runaway dilaton models of Damour, Piazza and Veneziano. We
consider three different scenarios for the dark sector couplings in the model
and discuss the observational differences between them. We improve previously
existing analyses investigating in detail the degeneracies between the
parameters ruling the coupling of the dilaton field to the other components of
the universe, and studying how the constraints on these parameters change for
different fiducial cosmologies. We find that if the couplings are small (e.g.,
) these degeneracies strongly affect the constraining
power of future data, while if they are sufficiently large (e.g.,
, as in agreement with current
constraints) the degeneracies can be partially broken. We show that E-ELT will
be able to probe some of this additional parameter space.Comment: 16 pages, 8 figures. Updated version matching the one accepted by
JCA
The Ubiquitous 'c': from the Stefan-Boltzmann Law to Quantum Information
I discuss various aspects of the role of the conformal anomaly number c in 2-
and 1+1-dimensional critical behaviour: its appearance as the analogue of
Stefan's constant, its fundamental role in conformal field theory, in the
classification of 2d universality classes, and as a measure of quantum
entanglement, among other topics.Comment: 8 pages, 2 figures. Boltzmann Medal Lecture, Statphys24, Cairns 2010.
v3: minor revision
Dynamical phase coexistence: A simple solution to the "savanna problem"
We introduce the concept of 'dynamical phase coexistence' to provide a simple
solution for a long-standing problem in theoretical ecology, the so-called
"savanna problem". The challenge is to understand why in savanna ecosystems
trees and grasses coexist in a robust way with large spatio-temporal
variability. We propose a simple model, a variant of the Contact Process (CP),
which includes two key extra features: varying external
(environmental/rainfall) conditions and tree age. The system fluctuates locally
between a woodland and a grassland phase, corresponding to the active and
absorbing phases of the underlying pure contact process. This leads to a highly
variable stable phase characterized by patches of the woodland and grassland
phases coexisting dynamically. We show that the mean time to tree extinction
under this model increases as a power-law of system size and can be of the
order of 10,000,000 years in even moderately sized savannas. Finally, we
demonstrate that while local interactions among trees may influence tree
spatial distribution and the order of the transition between woodland and
grassland phases, they do not affect dynamical coexistence. We expect dynamical
coexistence to be relevant in other contexts in physics, biology or the social
sciences.Comment: 8 pages, 7 figures. Accepted for publication in Journal of
Theoretical Biolog
Exact boundary conditions in numerical relativity using multiple grids: scalar field tests
Cauchy-Characteristic Matching (CCM), the combination of a central 3+1 Cauchy
code with an exterior characteristic code connected across a time-like
interface, is a promising technique for the generation and extraction of
gravitational waves. While it provides a tool for the exact specification of
boundary conditions for the Cauchy evolution, it also allows to follow
gravitational radiation all the way to infinity, where it is unambiguously
defined.
We present a new fourth order accurate finite difference CCM scheme for a
first order reduction of the wave equation around a Schwarzschild black hole in
axisymmetry. The matching at the interface between the Cauchy and the
characteristic regions is done by transfering appropriate characteristic/null
variables. Numerical experiments indicate that the algorithm is fourth order
convergent. As an application we reproduce the expected late-time tail decay
for the scalar field.Comment: 14 pages, 5 figures. Included changes suggested by referee
Entanglement Entropy in Extended Quantum Systems
After a brief introduction to the concept of entanglement in quantum systems,
I apply these ideas to many-body systems and show that the von Neumann entropy
is an effective way of characterising the entanglement between the degrees of
freedom in different regions of space. Close to a quantum phase transition it
has universal features which serve as a diagnostic of such phenomena. In the
second part I consider the unitary time evolution of such systems following a
`quantum quench' in which a parameter in the hamiltonian is suddenly changed,
and argue that finite regions should effectively thermalise at late times,
after interesting transient effects.Comment: 6 pages. Plenary talk delivered at Statphys 23, Genoa, July 200
Quantum Quench from a Thermal Initial State
We consider a quantum quench in a system of free bosons, starting from a
thermal initial state. As in the case where the system is initially in the
ground state, any finite subsystem eventually reaches a stationary thermal
state with a momentum-dependent effective temperature. We find that this can,
in some cases, even be lower than the initial temperature. We also study
lattice effects and discuss more general types of quenches.Comment: 6 pages, 2 figures; short published version, added references, minor
change
Entanglement entropy of two disjoint intervals in c=1 theories
We study the scaling of the Renyi entanglement entropy of two disjoint blocks
of critical lattice models described by conformal field theories with central
charge c=1. We provide the analytic conformal field theory result for the
second order Renyi entropy for a free boson compactified on an orbifold
describing the scaling limit of the Ashkin-Teller (AT) model on the self-dual
line. We have checked this prediction in cluster Monte Carlo simulations of the
classical two dimensional AT model. We have also performed extensive numerical
simulations of the anisotropic Heisenberg quantum spin-chain with tree-tensor
network techniques that allowed to obtain the reduced density matrices of
disjoint blocks of the spin-chain and to check the correctness of the
predictions for Renyi and entanglement entropies from conformal field theory.
In order to match these predictions, we have extrapolated the numerical results
by properly taking into account the corrections induced by the finite length of
the blocks to the leading scaling behavior.Comment: 37 pages, 23 figure
Field-theory results for three-dimensional transitions with complex symmetries
We discuss several examples of three-dimensional critical phenomena that can
be described by Landau-Ginzburg-Wilson theories. We present an
overview of field-theoretical results obtained from the analysis of high-order
perturbative series in the frameworks of the and of the
fixed-dimension d=3 expansions. In particular, we discuss the stability of the
O(N)-symmetric fixed point in a generic N-component theory, the critical
behaviors of randomly dilute Ising-like systems and frustrated spin systems
with noncollinear order, the multicritical behavior arising from the
competition of two distinct types of ordering with symmetry O() and
O() respectively.Comment: 9 pages, Talk at the Conference TH2002, Paris, July 200
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