130 research outputs found
Solution of the one-dimensional Dirac equation with a linear scalar potential
We solve the Dirac equation in one space dimension for the case of a linear,
Lorentz-scalar potential. This extends earlier work of Bhalerao and Ram [Am. J.
Phys. 69 (7), 817-818 (2001)] by eliminating unnecessary constraints. The
spectrum is shown to match smoothly to the nonrelativistic spectrum in a
weak-coupling limit.Comment: 7 pages, 1 figure, RevTE
Two observers calculate the trace anomaly
We adapt a calculation due to Massacand and Schmid to the coordinate
independent definition of time and vacuum given by Capri and Roy in order to
compute the trace anomaly for a massless scalar field in a curved spacetime in
1+1 dimensions. The computation which requires only a simple regulator and
normal ordering yields the well-known result in a
straightforward manner.Comment: RevTeX, 13 pages, some typos corrected and an appendix added, this is
the version to appear in Class. and Quantum Gavit
Massive particle creation in a static 1+1 dimensional spacetime
We show explicitly that there is particle creation in a static spacetime.
This is done by studying the field in a coordinate system based on a physical
principle which has recently been proposed. There the field is quantized by
decomposing it into positive and negative frequency modes on a particular
spacelike surface. This decomposition depends explicitly on the surface where
the decomposition is performed, so that an observer who travels from one
surface to another will observe particle production due to the different vacuum
state.Comment: 17 pages, RevTeX, no figure
Charge Fluctuations in Soliton Anti-Soliton Systems Without Conjugation Symmetry
We construct the charge operator and discuss the limits of their eigenvalues
as the separation between background soliton and anti-solitons goes to infinity
and analyze the fluctuations of the charge. This is performed in a (1+1)D model
with charge conjugation breaking
The Second Virial Coefficient of Spin-1/2 Interacting Anyon System
Evaluating the propagator by the usual time-sliced manner, we use it to
compute the second virial coefficient of an anyon gas interacting through the
repulsive potential of the form . All the cusps for the
unpolarized spin-1/2 as well as spinless cases disappear in the
limit, where is a frequency of harmonic oscillator which is introduced
as a regularization method. As approaches to zero, the result reduces to
the noninteracting hard-core limit.Comment: 9 pages, 2 figs include
Topological mass mechanism and exact fields mapping
We present a class of mappings between models with topological mass mechanism
and purely topological models in arbitrary dimensions. These mappings are
established by directly mapping the fields of one model in terms of the fields
of the other model in closed expressions. These expressions provide the
mappings of their actions as well as the mappings of their propagators. For a
general class of models in which the topological model becomes the BF model the
mappings present arbitrary functions which otherwise are absent for
Chern-Simons like actions. This work generalizes the results of [1] for
arbitrary dimensions.Comment: 11 page
Energy and Efficiency of Adiabatic Quantum Search Algorithms
We present the results of a detailed analysis of a general, unstructured
adiabatic quantum search of a data base of items. In particular we examine
the effects on the computation time of adding energy to the system. We find
that by increasing the lowest eigenvalue of the time dependent Hamiltonian {\it
temporarily} to a maximum of , it is possible to do the
calculation in constant time. This leads us to derive the general theorem which
provides the adiabatic analogue of the bound of conventional quantum
searches. The result suggests that the action associated with the oracle term
in the time dependent Hamiltonian is a direct measure of the resources required
by the adiabatic quantum search.Comment: 6 pages, Revtex, 1 figure. Theorem modified, references and comments
added, sections introduced, typos corrected. Version to appear in J. Phys.
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