4,604 research outputs found
On relations between one-dimensional quantum and two-dimensional classical spin systems
We exploit mappings between quantum and classical systems in order to obtain
a class of two-dimensional classical systems with critical properties
equivalent to those of the class of one-dimensional quantum systems discussed
in a companion paper (J. Hutchinson, J. P. Keating, and F. Mezzadri,
arXiv:1503.05732). In particular, we use three approaches: the Trotter-Suzuki
mapping; the method of coherent states; and a calculation based on commuting
the quantum Hamiltonian with the transfer matrix of a classical system. This
enables us to establish universality of certain critical phenomena by extension
from the results in our previous article for the classical systems identified.Comment: 36 page
Comb entanglement in quantum spin chains
Bipartite entanglement in the ground state of a chain of quantum spins
can be quantified either by computing pairwise concurrence or by dividing the
chain into two complementary subsystems. In the latter case the smaller
subsystem is usually a single spin or a block of adjacent spins and the
entanglement differentiates between critical and non-critical regimes. Here we
extend this approach by considering a more general setting: our smaller
subsystem consists of a {\it comb} of spins, spaced sites apart.
Our results are thus not restricted to a simple `area law', but contain
non-local information, parameterized by the spacing . For the XX model we
calculate the von-Neumann entropy analytically when and
investigate its dependence on and . We find that an external magnetic
field induces an unexpected length scale for entanglement in this case.Comment: 6 pages, 4 figure
Nodal domain distributions for quantum maps
The statistics of the nodal lines and nodal domains of the eigenfunctions of
quantum billiards have recently been observed to be fingerprints of the
chaoticity of the underlying classical motion by Blum et al. (Phys. Rev. Lett.,
Vol. 88 (2002), 114101) and by Bogomolny and Schmit (Phys. Rev. Lett., Vol. 88
(2002), 114102). These statistics were shown to be computable from the random
wave model of the eigenfunctions. We here study the analogous problem for
chaotic maps whose phase space is the two-torus. We show that the distributions
of the numbers of nodal points and nodal domains of the eigenvectors of the
corresponding quantum maps can be computed straightforwardly and exactly using
random matrix theory. We compare the predictions with the results of numerical
computations involving quantum perturbed cat maps.Comment: 7 pages, 2 figures. Second version: minor correction
Localization and its consequences for quantum walk algorithms and quantum communication
The exponential speed-up of quantum walks on certain graphs, relative to
classical particles diffusing on the same graph, is a striking observation. It
has suggested the possibility of new fast quantum algorithms. We point out here
that quantum mechanics can also lead, through the phenomenon of localization,
to exponential suppression of motion on these graphs (even in the absence of
decoherence). In fact, for physical embodiments of graphs, this will be the
generic behaviour. It also has implications for proposals for using spin
networks, including spin chains, as quantum communication channels.Comment: 4 pages, 1 eps figure. Updated references and cosmetic changes for v
A new correlator in quantum spin chains
We propose a new correlator in one-dimensional quantum spin chains, the
Emptiness Formation Probability (EFP). This is a natural generalization
of the Emptiness Formation Probability (EFP), which is the probability that the
first spins of the chain are all aligned downwards. In the EFP we let
the spins in question be separated by sites. The usual EFP corresponds to
the special case when , and taking allows us to quantify non-local
correlations. We express the EFP for the anisotropic XY model in a
transverse magnetic field, a system with both critical and non-critical
regimes, in terms of a Toeplitz determinant. For the isotropic XY model we find
that the magnetic field induces an interesting length scale.Comment: 6 pages, 1 figur
Ozone reference models for the middle atmosphere (new CIRA)
Models of ozone vertical structure were generated that were based on multiple data sets from satellites. The very good absolute accuracy of the individual data sets allowed the data to be directly combined to generate these models. The data used for generation of these models are from some of the most recent satellite measurements over the period 1978 to 1983. A discussion is provided of validation and error analyses of these data sets. Also, inconsistencies in data sets brought about by temporal variations or other factors are indicated. The models cover the pressure range from from 20 to 0.003 mb (25 to 90 km). The models for pressures less than 0.5 mb represent only the day side and are only provisional since there was limited longitudinal coverage at these levels. The models start near 25 km in accord with previous COSPAR international reference atmosphere (CIRA) models. Models are also provided of ozone mixing ratio as a function of height. The monthly standard deviation and interannual variations relative to zonal means are also provided. In addition to the models of monthly latitudinal variations in vertical structure based on satellite measurements, monthly models of total column ozone and its characteristic variability as a function of latitude based on four years of Nimbus 7 measurements, models of the relationship between vertical structure and total column ozone, and a midlatitude annual mean model are incorporated in this set of ozone reference atmospheres. Various systematic variations are discussed including the annual, semiannual, and quasibiennial oscillations, and diurnal, longitudinal, and response to solar activity variations
Spectral Statistics of "Cellular" Billiards
For a bounded planar domain whose boundary contains a number of
flat pieces we consider a family of non-symmetric billiards
constructed by patching several copies of along 's. It is
demonstrated that the length spectrum of the periodic orbits in is
degenerate with the multiplicities determined by a matrix group . We study
the energy spectrum of the corresponding quantum billiard problem in
and show that it can be split in a number of uncorrelated subspectra
corresponding to a set of irreducible representations of . Assuming
that the classical dynamics in are chaotic, we derive a
semiclassical trace formula for each spectral component and show that their
energy level statistics are the same as in standard Random Matrix ensembles.
Depending on whether is real, pseudo-real or complex, the spectrum
has either Gaussian Orthogonal, Gaussian Symplectic or Gaussian Unitary types
of statistics, respectively.Comment: 18 pages, 4 figure
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