64,611 research outputs found
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
Dynamic nuclear polarisation in biased quantum wires with spin-orbit interaction
We propose a new method for dynamic nuclear polarisation in a quasi
one-dimensional quantum wire utilising the spin-orbit interaction, the
hyperfine interaction, and a finite source-drain potential difference. In
contrast with current methods, our scheme does not rely on external magnetic or
optical sources which makes independent control of closely placed devices much
more feasible. Using this method, a significant polarisation of a few per cent
is possible in currently available InAs wires which may be detected by
conductance measurements. This may prove useful for nuclear-magnetic-resonance
studies in nanoscale systems as well as in spin-based devices where external
magnetic and optical sources will not be suitable.Comment: 6 pages, published versio
Solitary Waves and Compactons in a class of Generalized Korteweg-DeVries Equations
We study the class of generalized Korteweg-DeVries equations derivable from
the Lagrangian: L(l,p) = \int \left( \frac{1}{2} \vp_{x} \vp_{t} - {
{(\vp_{x})^{l}} \over {l(l-1)}} + \alpha(\vp_{x})^{p} (\vp_{xx})^{2} \right)
dx, where the usual fields of the generalized KdV equation are
defined by u(x,t) = \vp_{x}(x,t). This class contains compactons, which are
solitary waves with compact support, and when , these solutions have the
feature that their width is independent of the amplitude. We consider the
Hamiltonian structure and integrability properties of this class of KdV
equations. We show that many of the properties of the solitary waves and
compactons are easily obtained using a variational method based on the
principle of least action. Using a class of trial variational functions of the
form we
find soliton-like solutions for all , moving with fixed shape and constant
velocity, . We show that the velocity, mass, and energy of the variational
travelling wave solutions are related by , where , independent of .\newline \newline PACS numbers: 03.40.Kf,
47.20.Ky, Nb, 52.35.SbComment: 16 pages. LaTeX. Figures available upon request (Postscript or hard
copy
Edge excitations and Topological orders in rotating Bose gases
The edge excitations and related topological orders of correlated states of a
fast rotating Bose gas are studied. Using exact diagonalization of small
systems, we compute the energies and number of edge excitations, as well as the
boson occupancy near the edge for various states. The chiral Luttinger-liquid
theory of Wen is found to be a good description of the edges of the bosonic
Laughlin and other states identified as members of the principal Jain sequence
for bosons. However, we find that in a harmonic trap the edge of the state
identified as the Moore-Read (Pfaffian) state shows a number of anomalies. An
experimental way of detecting these correlated states is also discussed.Comment: Results extended to larger systems. Improved presentatio
Effects of Disorder and Momentum Relaxation on the Intertube Transport of Incommensurate Carbon Nanotube Ropes and Multiwall Nanotubes
We study theoretically the electrical transport between aligned carbon
nanotubes in nanotube ropes, and between shells in multiwall carbon nanotubes.
We focus on transport between two metallic nanotubes (or shells) of different
chiralities with mismatched Fermi momenta and incommensurate periodicities. We
perform numerical calculations of the transport properties of such systems
within a tight-binding formalism. For clean (disorder-free) nanotubes the
intertube transport is strongly suppressed as a result of momentum
conservation. For clean nanotubes, the intertube transport is typically
dominated by the loss of momentum conservation at the contacts. We discuss in
detail the effects of disorder, which also breaks momentum conservation, and
calculate the effects of localised scatterers of various types. We show that
physically relevant disorder potentials lead to very dramatic enhancements of
the intertube conductance. We show that recent experimental measurements of the
intershell transport in multiwall nanotubes are consistent with our theoretical
results for a model of short-ranged correlated disorder.Comment: References adde
Gamma-Ray Burst and Relativistic Shells: The Surface Filling Factor
The variability observed in many complex gamma-ray bursts (GRBs) is
inconsistent with causally connected variations in a single, symmetric,
relativistic shell interacting with the ambient material ("external shocks").
Rather, the symmetry of the shell must be broken on an angular scale much
smaller than Gamma^{-1} where Gamma is the bulk Lorentz factor for the shell.
The observed variability in the external shock models arises from the number of
causally connected regions that (randomly) become active. We define the
"surface filling factor" to be the ratio of the area of causally connected
regions that become active to the observable area of the shell. From the
observed variability in 52 BATSE bursts, we estimate the surface filling factor
to be typically 0.005 although some values are near unity. We find that the
surface filling factor is about 0.1 Delta T/T in both the constant Gamma phase
(which probably produces the GRB) and the deaccelerating phase (which probably
produces the x-ray afterglows). Here, \Delta T is a typical time scale of
variability and T is the time since the initial signal. We analyze the 2 hr
flare seen by ASCA 36 hr after the GRB and conclude that the surface filling
factor must be small (0.001) in the x-ray afterglow phase as well. Explanations
for low surface filling factor can either require more or less energy (by a
factor of about 1000) compared to that expected for a symmetric shell.Comment: 26 pages, 5 embedded figures, Latex, revised version as in press,
ApJ, added figure to show the possible expanding shell geometries that can
give low filling facto
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