3,535 research outputs found
Time-dependent Darboux (supersymmetric) transformations for non-Hermitian quantum systems
We propose time-dependent Darboux (supersymmetric) transformations that provide a scheme for the calculation of explicitly time-dependent solvable non-Hermitian partner Hamiltonians. Together with two Hermitian Hamilitonians the latter form a quadruple of Hamiltonians that are related by two time-dependent Dyson equations and two intertwining relations in form of a commutative diagram. Our construction is extended to the entire hierarchy of Hamiltonians obtained from time-dependent Darboux-Crum transformations. As an alternative approach we also discuss the intertwining relations for Lewis-Riesenfeld invariants for Hermitian as well as non-Hermitian Hamiltonians that reduce the time-dependent equations to auxiliary eigenvalue equations. The working of our proposals is discussed for a hierarchy of explicitly time-dependent rational, hyperbolic, Airy function and nonlocal potentials
Tracing the Warm Hot Intergalactic Medium in the local Universe
We present a simple method for tracing the spatial distribution and
predicting the physical properties of the Warm-Hot Intergalactic Medium (WHIM),
from the map of galaxy light in the local universe. Under the assumption that
biasing is local and monotonic we map the ~ 2 Mpc/h smoothed density field of
galaxy light into the mass density field from which we infer the spatial
distribution of the WHIM in the local supercluster. Taking into account the
scatter in the WHIM density-temperature and density-metallicity relation,
extracted from the z=0 outputs of high-resolution and large box size
hydro-dynamical cosmological simulations, we are able to quantify the
probability of detecting WHIM signatures in the form of absorption features in
the X-ray spectra, along arbitrary directions in the sky. To illustrate the
usefulness of this semi-analytical method we focus on the WHIM properties in
the Virgo Cluster region.Comment: 16 pages 11 Figures. Discussion clarified, alternative methods
proposed. Results unchanged. MNRAS in pres
Galaxies Inside Stromgren Spheres of Luminous Quasars at z>6: Detection of The First Galaxies
The intrinsic Lyman-alpha emission lines of normal galaxies before
reionization are much absorbed by the damping wing of the Gunn-Peterson trough,
rendering their direct detection nearly impossible, if their intrinsic line
widths are less than ~100km/s. High redshift luminous quasars prior to the
completion of cosmological reionization at z~6, on the other hand, are capable
of producing large HII regions around them (Stromgren spheres) to allow their
intrinsic Lyman-alpha emission lines to be transmitted without overwhelming
absorption (Cen & Haiman 2000). We suggest that targeted observations at the
Stromgren spheres of known luminous quasars at z >= 6 would be able to detect
Lyman-alpha emission lines of galaxies inside the Stromgren spheres largely
unattenuated. A tunable, very narrowband filter of \Delta\lambda\over \lambda ~
0.1% or a narrowband filter of \Delta\lambda\over \lambda ~1% with follow-up
spectroscopic identifications will be required. Such observations could
directly observe the sources of cosmological reionization including possibly
the Pop III galaxies at z=6-20 by JWST. Possible applications include
determinations of the ionization state of the intergalactic medium, the sizes
of the Stromgren spheres, the ages of the quasars, the luminosity function of
high redshift galaxies and its evolution, the spatial distribution of galaxies
and its evolution, the biased distribution of galaxies around quasars and the
anisotropy of quasar emission. Observations using Keck-class telescopes may
already be made to enable a differentiation between a fully neutral and a 10%
neutral intergalactic medium at z>6.Comment: Submitted to ApJ Letters, 10 page
Topology of Large-Scale Structure by Galaxy Type: Hydrodynamic Simulations
The topology of large scale structure is studied as a function of galaxy type
using the genus statistic. In hydrodynamical cosmological CDM simulations,
galaxies form on caustic surfaces (Zeldovich pancakes) then slowly drain onto
filaments and clusters. The earliest forming galaxies in the simulations
(defined as ``ellipticals") are thus seen at the present epoch preferentially
in clusters (tending toward a meatball topology), while the latest forming
galaxies (defined as ``spirals") are seen currently in a spongelike topology.
The topology is measured by the genus (= number of ``donut" holes - number of
isolated regions) of the smoothed density-contour surfaces. The measured genus
curve for all galaxies as a function of density obeys approximately the
theoretical curve expected for random-phase initial conditions, but the early
forming elliptical galaxies show a shift toward a meatball topology relative to
the late forming spirals. Simulations using standard biasing schemes fail to
show such an effect. Large observational samples separated by galaxy type could
be used to test for this effect.Comment: Princeton University Observatory, submitted to The Astrophysical
Journal, figures can be ftp'ed from ftp://astro.princeton.edu/cen/TOP
Probing the Reionization History Using the Spectra of High-Redshift Sources
We quantify and discuss the footprints of neutral hydrogen in the
intergalactic medium (IGM) on the spectra of high-redshift (z ~ 6) sources,
using mock spectra generated from hydrodynamical simulations of the IGM. We
show that it should be possible to extract relevant parameters, including the
mean neutral fraction in the IGM, and the radius of the local cosmological
Stromgren region, from the flux distribution in the observed spectra of distant
sources. We focus on quasars, but a similar analysis is applicable to galaxies
and gamma ray burst (GRB) afterglows. We explicitly include uncertainties in
the spectral shape of the assumed source template near the Lyman alpha line.
Our results suggest that a mean neutral hydrogen fraction, x(HI) of unity can
be statistically distinguished from x(HI)<0.01, by combining the spectra of
tens of bright (M = -27) quasars. Alternatively, the same distinction can be
achieved using the spectra of several hundred sources that are ~100 times
fainter. Furthermore, if the radius of the Stromgren sphere can be
independently constrained to within ~10 percent, this distinction can be
achieved using a single source. The information derived from such spectra will
help in settling the current debate as to what extent the universe was
reionized at redshifts near z=6.Comment: modified version, accepted to appear in ApJ, vol. 613, 20 September
200
Cosmological Shock Waves in the Large Scale Structure of the Universe: Non-gravitational Effects
Cosmological shock waves result from supersonic flow motions induced by
hierarchical clustering of nonlinear structures in the universe. These shocks
govern the nature of cosmic plasma through thermalization of gas and
acceleration of nonthermal, cosmic-ray (CR) particles. We study the statistics
and energetics of shocks formed in cosmological simulations of a concordance
CDM universe, with a special emphasis on the effects of
non-gravitational processes such as radiative cooling, photoionization/heating,
and galactic superwind feedbacks. Adopting an improved model for gas
thermalization and CR acceleration efficiencies based on nonlinear diffusive
shock acceleration calculations, we then estimate the gas thermal energy and
the CR energy dissipated at shocks through the history of the universe. Since
shocks can serve as sites for generation of vorticity, we also examine the
vorticity that should have been generated mostly at curved shocks in
cosmological simulations. We find that the dynamics and energetics of shocks
are governed primarily by the gravity of matter, so other non-gravitational
processes do not affect significantly the global energy dissipation and
vorticity generation at cosmological shocks. Our results reinforce scenarios in
which the intracluster medium and warm-hot intergalactic medium contain
energetically significant populations of nonthermal particles and turbulent
flow motions.Comment: Submitted to ApJ. Pdf with full resolution figures can be downloaded
from http://canopus.cnu.ac.kr/ryu/krco.pd
Refocusing schemes for holonomic quantum computation in presence of dissipation
The effects of dissipation on a holonomic quantum computation scheme are
analyzed within the quantum-jump approach. We extend to the non-Abelian case
the refocusing strategies formerly introduced for (Abelian) geometric
computation. We show how double loop symmetrization schemes allow one to get
rid of the unwanted influence of dissipation in the no-jump trajectory.Comment: 4 pages, revtex
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Nonlinear classical and quantum integrable systems with PT -symmetries
A key feature of integrable systems is that they can be solved to obtain exact analytical solutions. In this thesis we show how new models can be found through generalisations of some well known nonlinear partial differential equations including the Korteweg-de Vries, modified Korteweg-de Vries, sine-Gordon, Hirota, Heisenberg and Landau-Lifschitz types with joint parity and time symmetries whilst preserving integrability properties.
The first joint parity and time symmetric generalizations we take are extensions to the complex and multicomplex fields, such as bicomplex, quaternionic, coquaternionic and octonionic types. Subsequently, we develop new methods from well-known ones, such as Hirotaâs direct method, BĂ€cklund transformations and Darboux-Crum transformations to solve for these newsystems to obtain exact analytical solutions of soliton and multi-soliton types. Moreover, in agreement with the reality property present in joint parity and time symmetric non-Hermitian quantum systems, we find joint parity and time symmetries also play a key role for reality of conserved charges for the new systems, even though the soliton solutions are complex or multicomplex.
Our complex extensions have proved to be successful in helping one to obtain regularized degenerate multi-soliton solutions for the Korteweg-de Vries equation, which has not been realised before. We extend our investigations to explore degenerate multi-soliton solutions for the sine-Gordon equation and Hirota equation. In particular, we find the usual time-delays from degenerate soliton solution scattering are time-dependent, unlike the non-degenerate multi-soliton solutions, and provide a universal formula to compute the exact time-delay values for scattering of N-soliton solutions.
Other joint parity and time symmetric extensions of integrable systems we take are of nonlocal nature, with nonlocalities in space and/or in time, of time crystal type. Whilst developing new methods for the construction of soliton solutions for these systems, we xiv find new types of solutions with different parameter dependence and qualitative behaviour even in the one-soliton solution cases. We exploit gauge equivalence between the Hirota system with continuous Heisenberg and Landau-Lifschitz systems to see how nonlocality is inherited from one system to another and vice versa. In the final part of the thesis, we extend some of our investigations to the quantum regime. In particularwe generalize the scheme of Darboux transformations for fully timedependent non-Hermitian quantum systems, which allows us to create an infinite tower of solvable models
Scalable solid-state quantum computation in decoherence-free subspaces with trapped ions
We propose a decoherence-free subspaces (DFS) scheme to realize scalable
quantum computation with trapped ions. The spin-dependent Coulomb interaction
is exploited, and the universal set of unconventional geometric quantum gates
is achieved in encoded subspaces that are immune from decoherence by collective
dephasing. The scalability of the scheme for the ion array system is
demonstrated, either by an adiabatic way of switching on and off the
interactions, or by a fast gate scheme with comprehensive DFS encoding and
noise decoupling techniques.Comment: 4 pages, 1 figur
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