153 research outputs found
The Importance of Boundary Conditions in Quantum Mechanics
We discuss the role of boundary conditions in determining the physical
content of the solutions of the Schrodinger equation. We study the
standing-wave, the ``in,'' the ``out,'' and the purely outgoing boundary
conditions. As well, we rephrase Feynman's prescription as a
time-asymmetric, causal boundary condition, and discuss the connection of
Feynman's prescription with the arrow of time of Quantum
Electrodynamics. A parallel of this arrow of time with that of Classical
Electrodynamics is made. We conclude that in general, the time evolution of a
closed quantum system has indeed an arrow of time built into the propagators.Comment: Contribution to the proceedings of the ICTP conference "Irreversible
Quantum Dynamics," Trieste, Italy, July 200
Quantum metastability in a class of moving potentials
In this paper we consider quantum metastability in a class of moving
potentials introduced by Berry and Klein. Potential in this class has its
height and width scaled in a specific way so that it can be transformed into a
stationary one. In deriving the non-decay probability of the system, we argue
that the appropriate technique to use is the less known method of scattering
states. This method is illustrated through two examples, namely, a moving
delta-potential and a moving barrier potential. For expanding potentials, one
finds that a small but finite non-decay probability persists at large times.
Generalization to scaling potentials of arbitrary shape is briefly indicated.Comment: 10 pages, 1 figure
Boundary element method for resonances in dielectric microcavities
A boundary element method based on a Green's function technique is introduced
to compute resonances with intermediate lifetimes in quasi-two-dimensional
dielectric cavities. It can be applied to single or several optical resonators
of arbitrary shape, including corners, for both TM and TE polarization. For
cavities with symmetries a symmetry reduction is described. The existence of
spurious solutions is discussed. The efficiency of the method is demonstrated
by calculating resonances in two coupled hexagonal cavities.Comment: 9 pages, 7 figures (quality reduced
Gamow Shell Model Description of Weakly Bound Nuclei and Unbound Nuclear States
We present the study of weakly bound, neutron-rich nuclei using the nuclear
shell model employing the complex Berggren ensemble representing the bound
single-particle states, unbound Gamow states, and the non-resonant continuum.
In the proposed Gamow Shell Model, the Hamiltonian consists of a one-body
finite depth (Woods-Saxon) potential and a residual two-body interaction. We
discuss the basic ingredients of the Gamow Shell Model. The formalism is
illustrated by calculations involving {\it several} valence neutrons outside
the double-magic core: He and O.Comment: 19 pages, 20 encapsulated PostScript figure
Decoherence, Correlation, and Unstable Quantum States in Semiclassical Cosmology
It is demonstrated that almost any S-matrix of quantum field theory in curved
spaces posses an infinite set of complex poles (or branch cuts). These poles
can be transformed into complex eigenvalues, the corresponding eigenvectors
being Gamow vectors. All this formalism, which is heuristic in ordinary Hilbert
space, becomes a rigorous one within the framework of a properly chosen rigged
Hilbert space. Then complex eigenvalues produce damping or growing factors. It
is known that the growth of entropy, decoherence, and the appearance of
correlations, occur in the universe evolution, but only under a restricted set
of initial conditions. It is proved that the damping factors allow to enlarge
this set up to almost any initial conditions.Comment: 19 pgs. Latex fil
Non-Hermitian Rayleigh-Schroedinger Perturbation Theory
We devise a non-Hermitian Rayleigh-Schroedinger perturbation theory for the
single- and the multireference case to tackle both the many-body problem and
the decay problem encountered, for example, in the study of electronic
resonances in molecules. A complex absorbing potential (CAP) is employed to
facilitate a treatment of resonance states that is similar to the
well-established bound-state techniques. For the perturbative approach, the
full CAP-Schroedinger Hamiltonian, in suitable representation, is partitioned
according to the Epstein-Nesbet scheme. The equations we derive in the
framework of the single-reference perturbation theory turn out to be identical
to those obtained by a time-dependent treatment in Wigner-Weisskopf theory. The
multireference perturbation theory is studied for a model problem and is shown
to be an efficient and accurate method. Algorithmic aspects of the integration
of the perturbation theories into existing ab initio programs are discussed,
and the simplicity of their implementation is elucidated.Comment: 10 pages, 1 figure, RevTeX4, submitted to Physical Review
Correction Factors for Reactions involving Quark-Antiquark Annihilation or Production
In reactions with production or annihilation, initial-
and final-state interactions give rise to large corrections to the lowest-order
cross sections. We evaluate the correction factor first for low relative
kinetic energies by studying the distortion of the relative wave function. We
then follow the procedure of Schwinger to interpolate this result with the
well-known perturbative QCD vertex correction factors at high energies, to
obtain an explicit semi-empirical correction factor applicable to the whole
range of energies. The correction factor predicts an enhancement for
in color-singlet states and a suppression for color-octet states, the effect
increasing as the relative velocity decreases. Consequences on dilepton
production in the quark-gluon plasma, the Drell-Yan process, and heavy quark
production processes are discussed.Comment: 25 pages (REVTeX), includes 2 uuencoded compressed postscript figure
Quantum tunneling across spin domains in a Bose-Einstein condensate
Quantum tunneling was observed in the decay of metastable spin domains in
gaseous Bose-Einstein condensates. A mean-field description of the tunneling
was developed and compared with measurement. The tunneling rates are a
sensitive probe of the boundary between spin domains, and indicate a spin
structure in the boundary between spin domains which is prohibited in the bulk
fluid. These experiments were performed with optically trapped F=1 spinor
Bose-Einstein condensates of sodium.Comment: 5 pages, 4 figure
Relativistic Modification of the Gamow Factor
In processes involving Coulomb-type initial- and final-state interactions,
the Gamow factor has been traditionally used to take into account these
additional interactions. The Gamow factor needs to be modified when the
magnitude of the effective coupling constant increases or when the velocity
increases. For the production of a pair of particles under their mutual
Coulomb-type interaction, we obtain the modification of the Gamow factor in
terms of the overlap of the Feynman amplitude with the relativistic wave
function of the two particles. As a first example, we study the modification of
the Gamow factor for the production of two bosons. The modification is
substantial when the coupling constant is large.Comment: 13 pages, in LaTe
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