9,118 research outputs found
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 of random quantum critical points in one dimension
For quantum critical spin chains without disorder, it is known that the
entanglement of a segment of N>>1 spins with the remainder is logarithmic in N
with a prefactor fixed by the central charge of the associated conformal field
theory. We show that for a class of strongly random quantum spin chains, the
same logarithmic scaling holds for mean entanglement at criticality and defines
a critical entropy equivalent to central charge in the pure case. This
effective central charge is obtained for Heisenberg, XX, and quantum Ising
chains using an analytic real-space renormalization group approach believed to
be asymptotically exact. For these random chains, the effective universal
central charge is characteristic of a universality class and is consistent with
a c-theorem.Comment: 4 pages, 3 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
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
Toward autonomous spacecraft
Ways in which autonomous behavior of spacecraft can be extended to treat situations wherein a closed loop control by a human may not be appropriate or even possible are explored. Predictive models that minimize mean least squared error and arbitrary cost functions are discussed. A methodology for extracting cyclic components for an arbitrary environment with respect to usual and arbitrary criteria is developed. An approach to prediction and control based on evolutionary programming is outlined. A computer program capable of predicting time series is presented. A design of a control system for a robotic dense with partially unknown physical properties is presented
Entanglement properties of quantum spin chains
We investigate the entanglement properties of a finite size 1+1 dimensional
Ising spin chain, and show how these properties scale and can be utilized to
reconstruct the ground state wave function. Even at the critical point, few
terms in a Schmidt decomposition contribute to the exact ground state, and to
physical properties such as the entropy. Nevertheless the entanglement here is
prominent due to the lower-lying states in the Schmidt decomposition.Comment: 5 pages, 6 figure
Violation of area-law scaling for the entanglement entropy in spin 1/2 chains
Entanglement entropy obeys area law scaling for typical physical quantum
systems. This may naively be argued to follow from locality of interactions. We
show that this is not the case by constructing an explicit simple spin chain
Hamiltonian with nearest neighbor interactions that presents an entanglement
volume scaling law. This non-translational model is contrived to have couplings
that force the accumulation of singlet bonds across the half chain. Our result
is complementary to the known relation between non-translational invariant,
nearest neighbor interacting Hamiltonians and QMA complete problems.Comment: 9 pages, 4 figure
Scaling of the von Neumann entropy across a finite temperature phase transition
The spectrum of the reduced density matrix and the temperature dependence of
the von Neumann entropy (VNE) are analytically obtained for a system of hard
core bosons on a complete graph which exhibits a phase transition to a
Bose-Einstein condensate at . It is demonstrated that the VNE undergoes
a crossover from purely logarithmic at T=0 to purely linear in block size
behaviour for . For intermediate temperatures, VNE is a sum of two
contributions which are identified as the classical (Gibbs) and the quantum
(due to entanglement) parts of the von Neumann entropy.Comment: 4 pages, 2 figure
Ground Response, Baltimore Lexington Market Tunnels
Soil response data and the results of soil deformation analyses are presented for twin tube rapid transit tunnels constructed in soil. The data collection and analyses were performed during the construction of the Lexington Market Line Tunnels in Baltimore, MD between 1977 and 1980. Sources and volumes of ground loss around the tunnels and the resulting ground surface settlement patterns are discussed. Analyses are presented indicating that substantial volume expansion of the soil over the tunnel occurred during construction. Comparisons are made to similar analyses of data reported in the literature for other tunnels driven in similar geologic conditions
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