40,393 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
Exact and approximate dynamics of the quantum mechanical O(N) model
We study a quantum dynamical system of N, O(N) symmetric, nonlinear
oscillators as a toy model to investigate the systematics of a 1/N expansion.
The closed time path (CTP) formalism melded with an expansion in 1/N is used to
derive time evolution equations valid to order 1/N (next-to-leading order). The
effective potential is also obtained to this order and its properties
areelucidated. In order to compare theoretical predictions against numerical
solutions of the time-dependent Schrodinger equation, we consider two initial
conditions consistent with O(N) symmetry, one of them a quantum roll, the other
a wave packet initially to one side of the potential minimum, whose center has
all coordinates equal. For the case of the quantum roll we map out the domain
of validity of the large-N expansion. We discuss unitarity violation in the 1/N
expansion; a well-known problem faced by moment truncation techniques. The 1/N
results, both static and dynamic, are also compared to those given by the
Hartree variational ansatz at given values of N. We conclude that late-time
behavior, where nonlinear effects are significant, is not well-described by
either approximation.Comment: 16 pages, 12 figrures, revte
Pauli equation and the method of supersymmetric factorization
We consider different variants of factorization of a 2x2 matrix
Schroedinger/Pauli operator in two spatial dimensions. They allow to relate its
spectrum to the sum of spectra of two scalar Schroedinger operators, in a
manner similar to one-dimensional Darboux transformations. We consider both the
case when such factorization is reduced to the ordinary 2-dimensional SUSY QM
quasifactorization and a more general case which involves covariant
derivatives. The admissible classes of electromagnetic fields are described and
some illustrative examples are given.Comment: 18 pages, Late
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
Factorization of non-linear supersymmetry in one-dimensional Quantum Mechanics. II: proofs of theorems on reducibility
In this paper, we continue to study factorization of supersymmetric (SUSY)
transformations in one-dimensional Quantum Mechanics into chains of elementary
Darboux transformations with nonsingular coefficients. We define the class of
potentials that are invariant under the Darboux - Crum transformations and
prove a number of lemmas and theorems substantiating the formulated formerly
conjectures on reducibility of differential operators for spectral equivalence
transformations. Analysis of the general case is performed with all the
necessary proofs.Comment: 13 page
Resumming the large-N approximation for time evolving quantum systems
In this paper we discuss two methods of resumming the leading and next to
leading order in 1/N diagrams for the quartic O(N) model. These two approaches
have the property that they preserve both boundedness and positivity for
expectation values of operators in our numerical simulations. These
approximations can be understood either in terms of a truncation to the
infinitely coupled Schwinger-Dyson hierarchy of equations, or by choosing a
particular two-particle irreducible vacuum energy graph in the effective action
of the Cornwall-Jackiw-Tomboulis formalism. We confine our discussion to the
case of quantum mechanics where the Lagrangian is . The
key to these approximations is to treat both the propagator and the
propagator on similar footing which leads to a theory whose graphs have the
same topology as QED with the propagator playing the role of the photon.
The bare vertex approximation is obtained by replacing the exact vertex
function by the bare one in the exact Schwinger-Dyson equations for the one and
two point functions. The second approximation, which we call the dynamic Debye
screening approximation, makes the further approximation of replacing the exact
propagator by its value at leading order in the 1/N expansion. These two
approximations are compared with exact numerical simulations for the quantum
roll problem. The bare vertex approximation captures the physics at large and
modest better than the dynamic Debye screening approximation.Comment: 30 pages, 12 figures. The color version of a few figures are
separately liste
2 and 3-dimensional Hamiltonians with Shape Invariance Symmetry
Via a special dimensional reduction, that is, Fourier transforming over one
of the coordinates of Casimir operator of su(2) Lie algebra and 4-oscillator
Hamiltonian, we have obtained 2 and 3 dimensional Hamiltonian with shape
invariance symmetry. Using this symmetry we have obtained their eigenspectrum.
In the mean time we show equivalence of shape invariance symmetry and Lie
algebraic symmetry of these Hamiltonians.Comment: 24 Page
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
Quantum Oscillations in the Underdoped Cuprate YBa2Cu4O8
We report the observation of quantum oscillations in the underdoped cuprate
superconductor YBa2Cu4O8 using a tunnel-diode oscillator technique in pulsed
magnetic fields up to 85T. There is a clear signal, periodic in inverse field,
with frequency 660+/-15T and possible evidence for the presence of two
components of slightly different frequency. The quasiparticle mass is
m*=3.0+/-0.3m_e. In conjunction with the results of Doiron-Leyraud et al. for
YBa2Cu3O6.5, the present measurements suggest that Fermi surface pockets are a
general feature of underdoped copper oxide planes and provide information about
the doping dependence of the Fermi surface.Comment: Contains revisions addressing referees' comments including a
different Fig 1b. 4 pages, 4 figure
Gauge Fields Out-Of-Equilibrium: A Gauge Invariant Formulation and the Coulomb Gauge
We study the abelian Higgs model out-of-equilibrium in two different
approaches, a gauge invariant formulation, proposed by Boyanovsky et al.
\cite{Boyanovsky:1996dc} and in the Coulomb gauge. We show that both approaches
become equivalent in a consistent one loop approximation. Furthermore, we carry
out a proper renormalization for the model in order to prepare the equations
for a numerical implementation. The additional degrees of freedom, which arise
in gauge theories, influence the behavior of the system dramatically. A
comparison with results in the 't Hooft-Feynman background gauge found by us
recently, shows very good agreement.Comment: 32 pages, 8 figure
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