2,199 research outputs found
Renormalization and Essential Singularity
In usual dimensional counting, momentum has dimension one. But a function
f(x), when differentiated n times, does not always behave like one with its
power smaller by n. This inevitable uncertainty may be essential in general
theory of renormalization, including quantum gravity. As an example, we
classify possible singularities of a potential for the Schr\"{o}dinger
equation, assuming that the potential V has at least one class eigen
function. The result crucially depends on the analytic property of the eigen
function near its 0 point.Comment: 12 pages, no figures, PTPTeX with amsfonts. 2 pages added for detail
Towards reliable calculations of the correlation function
The correlation function of two identical pions interacting via Coulomb
potential is computed for a general case of anisotropic particle's source of
finite life time. The effect of halo is taken into account as an additional
particle's source of large spatial extension. Due to the Coulomb interaction,
the effect of halo is not limited to very small relative momenta but it
influences the correlation function in a relatively large domain. The
relativistic effects are discussed in detail and it is argued that the
calculations have to be performed in the center-of-mass frame of particle's
pair where the (nonrelativistic) wave function of particle's relative motion is
meaningful. The Bowler-Sinyukov procedure to remove the Coulomb interaction is
tested and it is shown to significantly underestimate the source's life time.Comment: 18 pages, presented at XIth International Workshop on Correlation and
Fluctuation in Multiparticle Production, Hangzhou, China, November 21-24,
200
Bosonization solution of the Falicov-Kimball model
We use a novel approach to analyze the one dimensional spinless
Falicov-Kimball model. We derive a simple effective model for the occupation of
the localized orbitals which clearly reveals the origin of the known ordering.
Our study is extended to a quantum model with hybridization between the
localized and itinerant states; we find a crossover between the well-known
weak- and strong-coupling behaviour. The existence of electronic polarons at
intermediate coupling is confirmed. A phase diagram is presented and discussed
in detail.Comment: RevTex, 10 pages, 1 figur
Adiabatic theorems for linear and nonlinear Hamiltonians
Conditions for the validity of the quantum adiabatic approximation are
analyzed. For the case of linear Hamiltonians, a simple and general sufficient
condition is derived, which is valid for arbitrary spectra and any kind of time
variation. It is shown that in some cases the found condition is necessary and
sufficient. The adiabatic theorem is generalized for the case of nonlinear
Hamiltonians
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
Gauge invariance and non-constant gauge couplings
It is shown that space-time dependent gauge couplings do not completely break
gauge invariance. We demonstrate this in various gauge theories.Comment: 18 page
The quantitative condition is necessary in guaranteeing the validity of the adiabatic approximation
The usual quantitative condition has been widely used in the practical
applications of the adiabatic theorem. However, it had never been proved to be
sufficient or necessary before. It was only recently found that the
quantitative condition is insufficient, but whether it is necessary remains
unresolved. In this letter, we prove that the quantitative condition is
necessary in guaranteeing the validity of the adiabatic approximation.Comment: 4 pages,1 figue
Normalization of Collisional Decoherence: Squaring the Delta Function, and an Independent Cross-Check
We show that when the Hornberger--Sipe calculation of collisional decoherence
is carried out with the squared delta function a delta of energy instead of a
delta of the absolute value of momentum, following a method introduced by
Di\'osi, the corrected formula for the decoherence rate is simply obtained. The
results of Hornberger and Sipe and of Di\'osi are shown to be in agreement. As
an independent cross-check, we calculate the mean squared coordinate diffusion
of a hard sphere implied by the corrected decoherence master equation, and show
that it agrees precisely with the same quantity as calculated by a classical
Brownian motion analysis.Comment: Tex: 14 pages 7/30/06: revisions to introduction, and references
added 9/29/06: further minor revisions and references adde
Consequences of Zeeman Degeneracy for van der Waals Blockade between Rydberg Atoms
We analyze the effects of Zeeman degeneracies on the long-range interactions
between like Rydberg atoms, with particular emphasis on applications to quantum
information processing using van der Waals blockade. We present a general
analysis of how degeneracies affect the primary error sources in blockade
experiments, emphasizing that blockade errors are sensitive primarily to the
weakest possible atom-atom interactions between the degenerate states, not the
mean interaction strength. We present explicit calculations of the van der
Waals potentials in the limit where the fine-structure interaction is large
compared to the atom-atom interactions. The results are presented for all
potential angular momentum channels invoving s, p, and d states. For most
channels there are one or more combinations of Zeeman levels that have
extremely small dipole-dipole interactions and are therefore poor candidates
for effective blockade experiments. Channels with promising properties are
identified and discussed. We also present numerical calculations of Rb and Cs
dipole matrix elements and relevant energy levels using quantum defect theory,
allowing for convenient quantitative estimates of the van der Waals
interactions to be made for principal quantum numbers up to 100. Finally, we
combine the blockade and van der Waals results to quantitatively analyze the
angular distribution of the blockade shift and its consequence for angular
momentum channels and geometries of particular interest for blockade
experiments with Rb.Comment: 16 figure
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