20,560 research outputs found
Finite-element quantum field theory
An alternative approach to lattice gauge theory has been under development
for the past decade. It is based on discretizing the operator Heisenberg
equations of motion in such a way as to preserve the canonical commutation
relations at each lattice site. It is now known how to formulate a non-Abelian
gauge theory within this framework. The formulation appears to be free of
fermion doubling. Since the theory is unitary, a time-development operator
(Hamiltonian) can be constructed.Comment: Talk presented at LATTICE96(theoretical developments), 3 pages,
LATEX, uses espcrc2.st
Green Functions for the Wrong-Sign Quartic
It has been shown that the Schwinger-Dyson equations for non-Hermitian
theories implicitly include the Hilbert-space metric. Approximate Green
functions for such theories may thus be obtained, without having to evaluate
the metric explicitly, by truncation of the equations. Such a calculation has
recently been carried out for various -symmetric theories, in both quantum
mechanics and quantum field theory, including the wrong-sign quartic
oscillator. For this particular theory the metric is known in closed form,
making possible an independent check of these approximate results. We do so by
numerically evaluating the ground-state wave-function for the equivalent
Hermitian Hamiltonian and using this wave-function, in conjunction with the
metric operator, to calculate the one- and two-point Green functions. We find
that the Green functions evaluated by lowest-order truncation of the
Schwinger-Dyson equations are already accurate at the (6-8)% level. This
provides a strong justification for the method and a motivation for its
extension to higher order and to higher dimensions, where the calculation of
the metric is extremely difficult
Quantum tunneling as a classical anomaly
Classical mechanics is a singular theory in that real-energy classical
particles can never enter classically forbidden regions. However, if one
regulates classical mechanics by allowing the energy E of a particle to be
complex, the particle exhibits quantum-like behavior: Complex-energy classical
particles can travel between classically allowed regions separated by potential
barriers. When Im(E) -> 0, the classical tunneling probabilities persist.
Hence, one can interpret quantum tunneling as an anomaly. A numerical
comparison of complex classical tunneling probabilities with quantum tunneling
probabilities leads to the conjecture that as ReE increases, complex classical
tunneling probabilities approach the corresponding quantum probabilities. Thus,
this work attempts to generalize the Bohr correspondence principle from
classically allowed to classically forbidden regions.Comment: 12 pages, 7 figure
Entanglement Efficiencies in PT-Symmetric Quantum Mechanics
The degree of entanglement is determined for an arbitrary state of a broad
class of PT-symmetric bipartite composite systems. Subsequently we quantify the
rate with which entangled states are generated and show that this rate can be
characterized by a small set of parameters. These relations allow one in
principle to improve the ability of these systems to entangle states. It is
also noticed that many relations resemble corresponding ones in conventional
quantum mechanics.Comment: Published version with improved figures, 5 pages, 2 figure
Multiple-Scale Analysis of the Quantum Anharmonic Oscillator
Conventional weak-coupling perturbation theory suffers from problems that
arise from resonant coupling of successive orders in the perturbation series.
Multiple-scale perturbation theory avoids such problems by implicitly
performing an infinite reordering and resummation of the conventional
perturbation series. Multiple-scale analysis provides a good description of the
classical anharmonic oscillator. Here, it is extended to study the Heisenberg
operator equations of motion for the quantum anharmonic oscillator. The
analysis yields a system of nonlinear operator differential equations, which is
solved exactly. The solution provides an operator mass renormalization of the
theory.Comment: 12 pages, Revtex, no figures, available through anonymous ftp from
ftp://euclid.tp.ph.ic.ac.uk/papers/ or on WWW at
http://euclid.tp.ph.ic.ac.uk/Papers/papers_95-6_.htm
How are pension integration and pension benefits related?
Copyright 2009 Elsevier B.V., All rights reserved.Peer reviewedPostprin
WKB Analysis of PT-Symmetric Sturm-Liouville problems
Most studies of PT-symmetric quantum-mechanical Hamiltonians have considered
the Schroedinger eigenvalue problem on an infinite domain. This paper examines
the consequences of imposing the boundary conditions on a finite domain. As is
the case with regular Hermitian Sturm-Liouville problems, the eigenvalues of
the PT-symmetric Sturm-Liouville problem grow like for large .
However, the novelty is that a PT eigenvalue problem on a finite domain
typically exhibits a sequence of critical points at which pairs of eigenvalues
cease to be real and become complex conjugates of one another. For the
potentials considered here this sequence of critical points is associated with
a turning point on the imaginary axis in the complex plane. WKB analysis is
used to calculate the asymptotic behaviors of the real eigenvalues and the
locations of the critical points. The method turns out to be surprisingly
accurate even at low energies.Comment: 11 pages, 8 figure
Noise impact on wildlife: An environmental impact assessment
Various biological effects of noise on animals are discussed and a systematic approach for an impact assessment is developed. Further research is suggested to fully quantify noise impact on the species and its ecosystem
Level Crossings in Complex Two-Dimensional Potentials
Two-dimensional PT-symmetric quantum-mechanical systems with the complex
cubic potential V_{12}=x^2+y^2+igxy^2 and the complex Henon-Heiles potential
V_{HH}=x^2+y^2+ig(xy^2-x^3/3) are investigated. Using numerical and
perturbative methods, energy spectra are obtained to high levels. Although both
potentials respect the PT symmetry, the complex energy eigenvalues appear when
level crossing happens between same parity eigenstates.Comment: 9 pages, 4 figures. Submitted as a conference proceeding of PHHQP
Extending PT symmetry from Heisenberg algebra to E2 algebra
The E2 algebra has three elements, J, u, and v, which satisfy the commutation
relations [u,J]=iv, [v,J]=-iu, [u,v]=0. We can construct the Hamiltonian
H=J^2+gu, where g is a real parameter, from these elements. This Hamiltonian is
Hermitian and consequently it has real eigenvalues. However, we can also
construct the PT-symmetric and non-Hermitian Hamiltonian H=J^2+igu, where again
g is real. As in the case of PT-symmetric Hamiltonians constructed from the
elements x and p of the Heisenberg algebra, there are two regions in parameter
space for this PT-symmetric Hamiltonian, a region of unbroken PT symmetry in
which all the eigenvalues are real and a region of broken PT symmetry in which
some of the eigenvalues are complex. The two regions are separated by a
critical value of g.Comment: 8 pages, 7 figure
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