3,061 research outputs found
Gauge transformation through an accelerated frame of reference
The Schr\"{o}dinger equation of a charged particle in a uniform electric
field can be specified in either a time-independent or a time-dependent gauge.
The wave-function solutions in these two gauges are related by a phase-factor
reflecting the gauge symmetry of the problem. In this article we show that the
effect of such a gauge transformation connecting the two wave-functions can be
mimicked by the effect of two successive extended Galilean transformations
connecting the two wave-function. An extended Galilean transformation connects
two reference frames out of which one is accelerating with respect to the
other.Comment: 7 Pages, Latex fil
Remarks on transient photon production in heavy ion collisions
In this note, we discuss the derivation of a formula that has been used in
the literature in order to compute the number of photons emitted by a hot or
dense system during a finite time. Our derivation is based on a variation of
the standard operator-based -matrix approach. The shortcomings of this
formula are then emphasized, which leads to a negative conclusion concerning
the possibility of using it to predict transient effects for the photon rate.Comment: 13 page
Neural Network Model for Apparent Deterministic Chaos in Spontaneously Bursting Hippocampal Slices
A neural network model that exhibits stochastic population bursting is
studied by simulation. First return maps of inter-burst intervals exhibit
recurrent unstable periodic orbit (UPO)-like trajectories similar to those
found in experiments on hippocampal slices. Applications of various control
methods and surrogate analysis for UPO-detection also yield results similar to
those of experiments. Our results question the interpretation of the
experimental data as evidence for deterministic chaos and suggest caution in
the use of UPO-based methods for detecting determinism in time-series data.Comment: 4 pages, 5 .eps figures (included), requires psfrag.sty (included
The heavy fermion damping rate puzzle
: We examine again the problem of the damping rate of a moving heavy fermion
in a hot plasma within the resummed perturbative theory of Pisarski and
Braaten. The ansatz for its evaluation which relates it to the imaginary part
of the fermion propagator pole in the framework of a self-consistent approach
is critically analyzed. As already pointed out by various authors, the only way
to define the rate is through additional implementation of magnetic screening.
We show in detail how the ansatz works in this case and where we disagree with
other authors. We conclude that the self-consistent approach is not
satisfactory.Comment: 17 page
Sufficiency Criterion for the Validity of the Adiabatic Approximation
We examine the quantitative condition which has been widely used as a
criterion for the adiabatic approximation but was recently found insufficient.
Our results indicate that the usual quantitative condition is sufficient for a
special class of quantum mechanical systems. For general systems, it may not be
sufficient, but it along with additional conditions is sufficient. The usual
quantitative condition and the additional conditions constitute a general
criterion for the validity of the adiabatic approximation, which is applicable
to all dimensional quantum systems. Moreover, we illustrate the use of the
general quantitative criterion in some physical models.Comment: 9 pages, no figure,appearing in PRL98(2007)15040
The Universal Gaussian in Soliton Tails
We show that in a large class of equations, solitons formed from generic
initial conditions do not have infinitely long exponential tails, but are
truncated by a region of Gaussian decay. This phenomenon makes it possible to
treat solitons as localized, individual objects. For the case of the KdV
equation, we show how the Gaussian decay emerges in the inverse scattering
formalism.Comment: 4 pages, 2 figures, revtex with eps
Spin-dependent Bohm trajectories associated with an electronic transition in hydrogen
The Bohm causal theory of quantum mechanics with spin-dependence is used to
determine electron trajectories when a hydrogen atom is subjected to
(semi-classical) radiation. The transition between the 1s ground state and the
2p0 state is examined. It is found that transitions can be identified along
Bohm trajectories. The trajectories lie on invariant hyperboloid surfaces of
revolution in R^3. The energy along the trajectories is also discussed in
relation to the hydrogen energy eigenvalues.Comment: 18 pages, 8 figure
Electron Transport through Disordered Domain Walls: Coherent and Incoherent Regimes
We study electron transport through a domain wall in a ferromagnetic nanowire
subject to spin-dependent scattering. A scattering matrix formalism is
developed to address both coherent and incoherent transport properties. The
coherent case corresponds to elastic scattering by static defects, which is
dominant at low temperatures, while the incoherent case provides a
phenomenological description of the inelastic scattering present in real
physical systems at room temperature. It is found that disorder scattering
increases the amount of spin-mixing of transmitted electrons, reducing the
adiabaticity. This leads, in the incoherent case, to a reduction of conductance
through the domain wall as compared to a uniformly magnetized region which is
similar to the giant magnetoresistance effect. In the coherent case, a
reduction of weak localization, together with a suppression of spin-reversing
scattering amplitudes, leads to an enhancement of conductance due to the domain
wall in the regime of strong disorder. The total effect of a domain wall on the
conductance of a nanowire is studied by incorporating the disordered regions on
either side of the wall. It is found that spin-dependent scattering in these
regions increases the domain wall magnetoconductance as compared to the effect
found by considering only the scattering inside the wall. This increase is most
dramatic in the narrow wall limit, but remains significant for wide walls.Comment: 23 pages, 12 figure
Perturbative and non-perturbative studies with the delta function potential
We show that the delta function potential can be exploited along with
perturbation theory to yield the result of certain infinite series. The idea is
that any exactly soluble potential if coupled with a delta function potential
remains exactly soluble. We use the strength of the delta function as an
expansion parameter and express the second-order energy shift as an infinite
sum in perturbation theory. The analytical solution is used to determine the
second-order energy shift and hence the sum of an infinite series. By an
appropriate choice of the unperturbed system, we can show the importance of the
continuum in the energy shift of bound states.Comment: 19 pages, 2 table
Proposed direct test of a certain type of noncontextuality in quantum mechanics
The noncontextuality of quantum mechanics can be directly tested by measuring
two entangled particles with more than two outcomes per particle. The two
associated contexts are "interlinked" by common observables.Comment: 9 pages 2 figure
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