6,696 research outputs found
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
PT-symmetry breaking in complex nonlinear wave equations and their deformations
We investigate complex versions of the Korteweg-deVries equations and an Ito
type nonlinear system with two coupled nonlinear fields. We systematically
construct rational, trigonometric/hyperbolic, elliptic and soliton solutions
for these models and focus in particular on physically feasible systems, that
is those with real energies. The reality of the energy is usually attributed to
different realisations of an antilinear symmetry, as for instance PT-symmetry.
It is shown that the symmetry can be spontaneously broken in two alternative
ways either by specific choices of the domain or by manipulating the parameters
in the solutions of the model, thus leading to complex energies. Surprisingly
the reality of the energies can be regained in some cases by a further breaking
of the symmetry on the level of the Hamiltonian. In many examples some of the
fixed points in the complex solution for the field undergo a Hopf bifurcation
in the PT-symmetry breaking process. By employing several different variants of
the symmetries we propose many classes of new invariant extensions of these
models and study their properties. The reduction of some of these models yields
complex quantum mechanical models previously studied.Comment: 50 pages, 39 figures (compressed in order to comply with arXiv
policy; higher resolutions maybe obtained from the authors upon request
Weak Measurements in Non-Hermitian Systems
"Weak measurements" -- involving a weak unitary interaction between a quantum
system and a meter followed by a projective measurement -- are investigated
when the system has a non-Hermitian Hamiltonian. We show in particular how the
standard definition of the "weak value" of an observable must be modified.
These studies are undertaken in the context of bound state scattering theory, a
non-Hermitian formalism for which the Hilbert spaces involved are unambiguously
defined and the metric operators can be explicitly computed. Numerical examples
are given for a model system
Chaotic systems in complex phase space
This paper examines numerically the complex classical trajectories of the
kicked rotor and the double pendulum. Both of these systems exhibit a
transition to chaos, and this feature is studied in complex phase space.
Additionally, it is shown that the short-time and long-time behaviors of these
two PT-symmetric dynamical models in complex phase space exhibit strong
qualitative similarities.Comment: 22 page, 16 figure
Asymptotics of Expansion of the Evolution Operator Kernel in Powers of Time Interval
The upper bound for asymptotic behavior of the coefficients of expansion of
the evolution operator kernel in powers of the time interval \Dt was
obtained. It is found that for the nonpolynomial potentials the coefficients
may increase as . But increasing may be more slow if the contributions with
opposite signs cancel each other. Particularly, it is not excluded that for
number of the potentials the expansion is convergent. For the polynomial
potentials \Dt-expansion is certainly asymptotic one. The coefficients
increase in this case as , where is the order of
the polynom. It means that the point \Dt=0 is singular point of the kernel.Comment: 12 pp., LaTe
Convergence of the Optimized Delta Expansion for the Connected Vacuum Amplitude: Zero Dimensions
Recent proofs of the convergence of the linear delta expansion in zero and in
one dimensions have been limited to the analogue of the vacuum generating
functional in field theory. In zero dimensions it was shown that with an
appropriate, -dependent, choice of an optimizing parameter \l, which is an
important feature of the method, the sequence of approximants tends to
with an error proportional to . In the present paper we
establish the convergence of the linear delta expansion for the connected
vacuum function . We show that with the same choice of \l the
corresponding sequence tends to with an error proportional to . The rate of convergence of the latter sequence is governed by
the positions of the zeros of .Comment: 20 pages, LaTeX, Imperial/TP/92-93/5
PT-symmetric interpretation of double-scaling
The conventional double-scaling limit of an O(N)-symmetric quartic quantum
field theory is inconsistent because the critical coupling constant is
negative. Thus, at the critical coupling the Lagrangian defines a quantum
theory with an upside-down potential whose energy appears to be unbounded
below. Worse yet, the integral representation of the partition function of the
theory does not exist. It is shown that one can avoid these difficulties if one
replaces the original theory by its PT-symmetric analog. For a zero-dimensional
O(N)-symmetric quartic vector model the partition function of the PT-symmetric
analog is calculated explicitly in the double-scaling limit.Comment: 11 pages, 2 figure
The GL 569 Multiple System
We report the results of high spectral and angular resolution infrared
observations of the multiple system GL 569 A and B that were intended to
measure the dynamical masses of the brown dwarf binary believed to comprise GL
569 B. Our analysis did not yield this result but, instead, revealed two
surprises. First, at age ~100 Myr, the system is younger than had been reported
earlier. Second, our spectroscopic and photometric results provide support for
earlier indications that GL 569 B is actually a hierarchical brown dwarf triple
rather than a binary. Our results suggest that the three components of GL 569 B
have roughly equal mass, ~0.04 Msun.Comment: 29 pages, 10 figures, accepted for publication in the Astrophysical
Journal; minor corrections to Section 5.1; changed typo in 6.
Front Propagation up a Reaction Rate Gradient
We expand on a previous study of fronts in finite particle number
reaction-diffusion systems in the presence of a reaction rate gradient in the
direction of the front motion. We study the system via reaction-diffusion
equations, using the expedient of a cutoff in the reaction rate below some
critical density to capture the essential role of fl uctuations in the system.
For large density, the velocity is large, which allows for an approximate
analytic treatment. We derive an analytic approximation for the front velocity
depe ndence on bulk particle density, showing that the velocity indeed diverge
s in the infinite density limit. The form in which diffusion is impleme nted,
namely nearest-neighbor hopping on a lattice, is seen to have an essential
impact on the nature of the divergence
Interactions of Hermitian and non-Hermitian Hamiltonians
The coupling of non-Hermitian PT-symmetric Hamiltonians to standard Hermitian
Hamiltonians, each of which individually has a real energy spectrum, is
explored by means of a number of soluble models. It is found that in all cases
the energy remains real for small values of the coupling constant, but becomes
complex if the coupling becomes stronger than some critical value. For a
quadratic non-Hermitian PT-symmetric Hamiltonian coupled to an arbitrary real
Hermitian PT-symmetric Hamiltonian, the reality of the ground-state energy for
small enough coupling constant is established up to second order in
perturbation theory.Comment: 9 pages, 0 figure
- …