34,745 research outputs found
Chaos in Time Dependent Variational Approximations to Quantum Dynamics
Dynamical chaos has recently been shown to exist in the Gaussian
approximation in quantum mechanics and in the self-consistent mean field
approach to studying the dynamics of quantum fields. In this study, we first
show that any variational approximation to the dynamics of a quantum system
based on the Dirac action principle leads to a classical Hamiltonian dynamics
for the variational parameters. Since this Hamiltonian is generically nonlinear
and nonintegrable, the dynamics thus generated can be chaotic, in distinction
to the exact quantum evolution. We then restrict attention to a system of two
biquadratically coupled quantum oscillators and study two variational schemes,
the leading order large N (four canonical variables) and Hartree (six canonical
variables) approximations. The chaos seen in the approximate dynamics is an
artifact of the approximations: this is demonstrated by the fact that its onset
occurs on the same characteristic time scale as the breakdown of the
approximations when compared to numerical solutions of the time-dependent
Schrodinger equation.Comment: 10 pages (12 figures), RevTeX (plus macro), uses epsf, minor typos
correcte
A trap-based pulsed positron beam optimised for positronium laser spectroscopy
We describe a pulsed positron beam that is optimised for positronium (Ps) laser-spectroscopy experiments. The system is based on a two-stage Surko-type buffer gas trap that produces 4 ns wide pulses containing up to 5 × 105 positrons at a rate of 0.5-10 Hz. By implanting positrons from the trap into a suitable target material, a dilute positronium gas with an initial density of the order of 107 cm−3 is created in vacuum. This is then probed with pulsed (ns) laser systems, where various Ps-laser interactions have been observed via changes in Ps annihilation rates using a fast gamma ray detector. We demonstrate the capabilities of the apparatus and detection methodology via the observation of Rydberg positronium atoms with principal quantum numbers ranging from 11 to 22 and the Stark broadening of the n = 2 → 11 transition in electric fields
(1,4,7,10,13,16-Hexaoxacyclooctadecane)dimethylindium(III) trifluoromethanesulfonate
In the title compound, [In(CH3)2(C12H24O6)](CF3O3S), two of the In—O distances within the cation are significantly shorter than the other four. The InIII atom is in a distorted hexagonal–bipyramidal coordination geometry in which the C—In—C angle is 175.44 (12)°. The crystal structure is stabilized by weak intermolecular C—H⋯O hydrogen bonds
Non-equilibrium dynamics in quantum field theory at high density: the tsunami
The dynamics of a dense relativistic quantum fluid out of thermodynamic
equilibrium is studied in the framework of the Phi^4 scalar field theory in the
large N limit. The time evolution of a particle distribution in momentum space
(the tsunami) is computed. The effective mass felt by the particles in such a
high density medium equals the tree level mass plus the expectation value of
the squared field. The case of negative tree level squared mass is particularly
interesting. In such case dynamical symmetry restoration as well as dynamical
symmetry breaking can happen. Furthermore, the symmetry may stay broken with
vanishing asymptotic squared mass showing the presence of out of equilibrium
Goldstone bosons. We study these phenomena and identify the set of initial
conditions that lead to each case. We compute the equation of state which turns
to depend on the initial state. Although the system does not thermalize, the
equation of state for asymptotically broken symmetry is of radiation type. We
compute the correlation functions at equal times. The two point correlator for
late times is the sum of different terms. One stems from the initial particle
distribution. Another term accounts for the out of equilibrium Goldstone bosons
created by spinodal unstabilities when the symmetry is asymptotically
broken.Both terms are of the order of the inverse of the coupling for distances
where causal signals can connect the two points. The contribution of the out of
equilibrium Goldstones exhibits scaling behaviour in a generalized sense.Comment: LaTex, 49 pages, 15 .ps figure
Supersymmetry, Shape Invariance and Solvability of and Calogero-Sutherland Model
Using the ideas of supersymmetry and shape invariance we re-derive the
spectrum of the and Calogero-Sutherland model. We briefly
discuss as to how to obtain the corresponding eigenfunctions. We also discuss
the difficulties involved in extending this approach to the trigonometric
models.Comment: 15 pages, REVTeX,No figure
Equilibrium and nonequilibrium properties associated with the chiral phase transition at finite density in the Gross-Neveu Model
We study the dynamics of the chiral phase transition at finite density in the
Gross-Neveu (GN) model in the leading order in large-N approximation. The phase
structure of the GN model in this approximation has the property that there is
a tricritical point at a fixed temperature and chemical potential separating
regions where the chiral transition is first order from that where it is second
order. We consider evolutions starting in local thermal and chemical
equilibrium in the massless unbroken phase for conditions pertaining to
traversing a first or second order phase transition. We assume boost invariant
kinematics and determine the evolution of the order parameter , the
energy density and pressure as well as the effective temperature, chemical
potential and interpolating number densities as a function of the proper time
. We find that before the phase transition, the system behaves as if it
were an ideal fluid in local thermal equilibrium with equation of state
. After the phase transition, the system quickly reaches its true
broken symmetry vacuum value for the fermion mass and for the energy density.
The single particle distribution functions for Fermions and anti-Fermions go
far out of equilibrium as soon as the plasma traverses the chiral phase
transition. We have also determined the spatial dependence of the "pion"
Green's function as a function of the proper time.Comment: 39 pages, 23 figure
Free expansion of lowest Landau level states of trapped atoms: a wavefunction microscope
We show that for any lowest-Landau-level state of a trapped, rotating,
interacting Bose gas, the particle distribution in coordinate space in a free
expansion (time of flight) experiment is related to that in the trap at the
time it is turned off by a simple rescaling and rotation. When the
lowest-Landau-level approximation is valid, interactions can be neglected
during the expansion, even when they play an essential role in the ground state
when the trap is present. The correlations in the density in a single snapshot
can be used to obtain information about the fluid, such as whether a transition
to a quantum Hall state has occurred.Comment: 5 pages, no figures. v2: discussion of neglect of interactions during
expansion improved, refs adde
Potential and current distribution in strongly anisotropic Bi(2)Sr(2) CaCu(2)O(8) single crystals at current breakdown
Experiments on potential differences in the low-temperature vortex solid
phase of monocrystalline platelets of superconducting Bi(2)Sr(2)CaCu(2)O(8)
(BSCCO) subjected to currents driven either through an "ab" surface or from one
such surface to another show evidence of a resistive/nonresistive front moving
progressively out from the current contacts as the current increases. The depth
of the resistive region has been measured by a novel in-depth voltage probe
contact. The position of the front associated with an injection point appears
to depend only on the current magnitude and not on its withdrawal point. It is
argued that enhanced nonresistive superconducting anisotropy limits current
penetration to less than the London length and results in a flat rectangular
resistive region with simultaneous "ab" and "c" current breakdown which moves
progressively out from the injection point with increasing current.
Measurements in "ab" or "c" configurations are seen to give the same
information, involving both ab-plane and c-axis conduction properties.Comment: 9 pages, 13 figures, typo error corrected, last section was refine
Optical investigations on : Electronic structure evolutions related to the metal-insulator transition
Optical conductivity spectra of cubic pyrochlore
(0.0{\it x}2.0) compounds are investigated. As a metal-insulator
transition (MIT) occurs around {\it x}0.8, large spectral changes are
observed. With increase of {\it x}, the correlation-induced peak between the
lower and the upper Hubbard bands seems to be suppressed, and a strong
mid-infrared feature is observed. In addition, the charge transfer peak
shifts to the lower energies. The spectral changes cannot be explained by
electronic structural evolutions in the simple bandwidth-controlled MIT
picture, but are consistent with those in the filling-controlled MIT picture.
In addition, they are also similar to the spectral changes of
YCaRuO compounds, which is a typical
filling-controlled system. This work suggests that, near the MIT, the Ru bands
could be doped with the easily polarizable Bi cations.Comment: 5 figure
Algebraic Approach to Shape Invariance
The integrability condition called shape invariance is shown to have an
underlying algebraic structure and the associated Lie algebras are identified.
These shape-invariance algebras transform the parameters of the potentials such
as strength and range. Shape-invariance algebras, in general, are shown to be
infinite-dimensional. The conditions under which they become finite-dimensional
are explored.Comment: Submitted to Physical Review A. Latex file, 9 pages. Manuscript is
also available at http://nucth.physics.wisc.edu/preprints
- …