1,205 research outputs found
Quantum harmonic oscillator with superoscillating initial datum
In this paper we study the evolution of superoscillating initial data for the
quantum driven harmonic oscillator. Our main result shows that
superoscillations are amplified by the harmonic potential and that the analytic
solution develops a singularity in finite time. We also show that for a large
class of solutions of the Schr\"odinger equation, superoscillating behavior at
any given time implies superoscillating behavior at any other time.Comment: 12 page
Thermal radiation in non-static curved spacetimes: quantum mechanical path integrals and configuration space topology
A quantum mechanical path integral derivation is given of a thermal
propagator in non-static Gui spacetime. The thermal nature of the propagator is
understood in terms of homotopically non-trivial paths in the configuration
space appropriate to tortoise coordinates. The connection to thermal emission
from collapsing black holes is discussed.Comment: 20 pages, major revised version, 9 figures, new titl
Quantum mechanical path integrals and thermal radiation in static curved spacetimes
The propagator of a spinless particle is calculated from the quantum
mechanical path integral formalism in static curved spacetimes endowed with
event-horizons. A toy model, the Gui spacetime, and the 2D and 4D Schwarzschild
black holes are considered. The role of the topology of the coordinates
configuration space is emphasised in this framework. To cover entirely the
above spacetimes with a single set of coordinates, tortoise coordinates are
extended to complex values. It is shown that the homotopic properties of the
complex tortoise configuration space imply the thermal behaviour of the
propagator in these spacetimes. The propagator is calculated when end points
are located in identical or distinct spacetime regions separated by one or
several event-horizons. Quantum evolution through the event-horizons is shown
to be unitary in the fifth variable.Comment: 22 pages, 10 figure
Rotational Symmetry of Classical Orbits, Arbitrary Quantization of Angular Momentum and the Role of Gauge Field in Two-Dimensional Space
We study the quantum-classical correspondence in terms of coherent wave
functions of a charged particle in two-dimensional central-scalar-potentials as
well as the gauge field of a magnetic flux in the sense that the probability
clouds of wave functions are well localized on classical orbits. For both
closed and open classical orbits, the non-integer angular-momentum quantization
with the level-space of angular momentum being greater or less than is
determined uniquely by the same rotational symmetry of classical orbits and
probability clouds of coherent wave functions, which is not necessarily
-periodic. The gauge potential of a magnetic flux impenetrable to the
particle cannot change the quantization rule but is able to shift the spectrum
of canonical angular momentum by a flux-dependent value, which results in a
common topological phase for all wave functions in the given model. The quantum
mechanical model of anyon proposed by Wilczek (Phys. Rev. Lette. 48, 1144)
becomes a special case of the arbitrary-quantization.Comment: 6 pages, 5 figure
Propagation of charged particle waves in a uniform magnetic field
This paper considers the probability density and current distributions
generated by a point-like, isotropic source of monoenergetic charges embedded
into a uniform magnetic field environment. Electron sources of this kind have
been realized in recent photodetachment microscopy experiments. Unlike the
total photocurrent cross section, which is largely understood, the spatial
profiles of charge and current emitted by the source display an unexpected
hierarchy of complex patterns, even though the distributions, apart from
scaling, depend only on a single physical parameter. We examine the electron
dynamics both by solving the quantum problem, i. e., finding the energy Green
function, and from a semiclassical perspective based on the simple cyclotron
orbits followed by the electron. Simulations suggest that the semiclassical
method, which involves here interference between an infinite set of paths,
faithfully reproduces the features observed in the quantum solution, even in
extreme circumstances, and lends itself to an interpretation of some (though
not all) of the rich structure exhibited in this simple problem.Comment: 39 pages, 16 figure
Proposal for an experiment to measure the Hausdorff dimension of quantum mechanical trajectories
We make a proposal for a Gedanken experiment, based on the Aharonov-Bohm
effect, how to measure in principle the zig-zagness of the trajectory of
propagation (abberation from its classical trajectory) of a massive particle in
quantum mechanics. Experiment I is conceived to show that contributions from
quantum paths abberating from the classical trajectory are directly observable.
Experiment II is conceived to measure average length, scaling behavior and
critical exponent (Hausdorff dimension) of quantum mechanical paths.Comment: 35 pages, LaTeX + 27 figures, ps and gi
Conformations of Randomly Linked Polymers
We consider polymers in which M randomly selected pairs of monomers are
restricted to be in contact. Analytical arguments and numerical simulations
show that an ideal (Gaussian) chain of N monomers remains expanded as long as
M<<N; its mean squared end to end distance growing as r^2 ~ M/N. A possible
collapse transition (to a region of order unity) is related to percolation in a
one dimensional model with long--ranged connections. A directed version of the
model is also solved exactly. Based on these results, we conjecture that the
typical size of a self-avoiding polymer is reduced by the links to R >
(N/M)^(nu). The number of links needed to collapse a polymer in three
dimensions thus scales as N^(phi), with (phi) > 0.43.Comment: 6 pages, 3 Postscript figures, LaTe
Phase Space Reduction and Vortex Statistics: An Anyon Quantization Ambiguity
We examine the quantization of the motion of two charged vortices in a
Ginzburg--Landau theory for the fractional quantum Hall effect recently
proposed by the first two authors. The system has two second-class constraints
which can be implemented either in the reduced phase space or
Dirac-Gupta-Bleuler formalism. Using the intrinsic formulation of statistics,
we show that these two ways of implementing the constraints are inequivalent
unless the vortices are quantized with conventional statistics; either
fermionic or bosonic.Comment: 14 pages, PHYZZ
A Fully Tunable Single-Walled Carbon Nanotube Diode
We demonstrate a fully tunable diode structure utilizing a fully suspended
single-walled carbon nanotube (SWNT). The diode's turn-on voltage under forward
bias can be continuously tuned up to 4.3 V by controlling gate voltages, which
is ~6 times the nanotube bandgap energy. Furthermore, the same device design
can be configured into a backward diode by tuning the band-to-band tunneling
current with gate voltages. A nanotube backward diode is demonstrated for the
first time with nonlinearity exceeding the ideal diode. These results suggest
that a tunable nanotube diode can be a unique building block for developing
next generation programmable nanoelectronic logic and integrated circuits.Comment: 14 pages, 4 figure
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