18,518 research outputs found

### Fractals and Scars on a Compact Octagon

A finite universe naturally supports chaotic classical motion. An ordered
fractal emerges from the chaotic dynamics which we characterize in full for a
compact 2-dimensional octagon. In the classical to quantum transition, the
underlying fractal can persist in the form of scars, ridges of enhanced
amplitude in the semiclassical wave function. Although the scarring is weak on
the octagon, we suggest possible subtle implications of fractals and scars in a
finite universe.Comment: 6 pages, 3 figs, LaTeX fil

### A polyphonic acoustic vortex and its complementary chords

Using an annular phased array of eight loudspeakers, we generate sound beams that simultaneously contain phase singularities at a number of different frequencies. These frequencies correspond to different musical notes and the singularities can be set to overlap along the beam axis, creating a polyphonic acoustic vortex. Perturbing the drive amplitudes of the speakers means that the singularities no longer overlap, each note being nulled at a slightly different lateral position, where the volume of the other notes is now nonzero. The remaining notes form a tri-note chord. We contrast this acoustic phenomenon to the optical case where the perturbation of a white light vortex leads to a spectral spatial distribution

### Geometric phases and anholonomy for a class of chaotic classical systems

Berry's phase may be viewed as arising from the parallel transport of a
quantal state around a loop in parameter space. In this Letter, the classical
limit of this transport is obtained for a particular class of chaotic systems.
It is shown that this ``classical parallel transport'' is anholonomic ---
transport around a closed curve in parameter space does not bring a point in
phase space back to itself --- and is intimately related to the Robbins-Berry
classical two-form.Comment: Revtex, 11 pages, no figures

### Reflectionless Potentials and PT Symmetry

Large families of Hamiltonians that are non-Hermitian in the conventional
sense have been found to have all eigenvalues real, a fact attributed to an
unbroken PT symmetry. The corresponding quantum theories possess an
unconventional scalar product. The eigenvalues are determined by differential
equations with boundary conditions imposed in wedges in the complex plane. For
a special class of such systems, it is possible to impose the PT-symmetric
boundary conditions on the real axis, which lies on the edges of the wedges.
The PT-symmetric spectrum can then be obtained by imposing the more transparent
requirement that the potential be reflectionless.Comment: 4 Page

### Quantum Spectra of Triangular Billiards on the Sphere

We study the quantal energy spectrum of triangular billiards on a spherical
surface. Group theory yields analytical results for tiling billiards while the
generic case is treated numerically. We find that the statistical properties of
the spectra do not follow the standard random matrix results and their peculiar
behaviour can be related to the corresponding classical phase space structure.Comment: 18 pages, 5 eps figure

### Note on the helicity decomposition of spin and orbital optical currents

In the helicity representation, the Poynting vector (current) for a
monochromatic optical field, when calculated using either the electric or the
magnetic field, separates into right-handed and left-handed contributions, with
no cross-helicity contributions. Cross-helicity terms do appear in the orbital
and spin contributions to the current. But when the electric and magnetic
formulas are averaged ('electric-magnetic democracy'), these terms cancel,
restoring the separation into right-handed and left-handed currents for orbital
and spin separately.Comment: 10 pages, no figure

### Statistical Properties of Many Particle Eigenfunctions

Wavefunction correlations and density matrices for few or many particles are
derived from the properties of semiclassical energy Green functions. Universal
features of fixed energy (microcanonical) random wavefunction correlation
functions appear which reflect the emergence of the canonical ensemble as the
number of particles approaches infinity. This arises through a little known
asymptotic limit of Bessel functions. Constraints due to symmetries,
boundaries, and collisions between particles can be included.Comment: 13 pages, 4 figure

### Berry phase in a non-isolated system

We investigate the effect of the environment on a Berry phase measurement
involving a spin-half. We model the spin+environment using a biased spin-boson
Hamiltonian with a time-dependent magnetic field. We find that, contrary to
naive expectations, the Berry phase acquired by the spin can be observed, but
only on timescales which are neither too short nor very long. However this
Berry phase is not the same as for the isolated spin-half. It does not have a
simple geometric interpretation in terms of the adiabatic evolution of either
bare spin-states or the dressed spin-resonances that remain once we have traced
out the environment. This result is crucial for proposed Berry phase
measurements in superconducting nanocircuits as dissipation there is known to
be significant.Comment: 4 pages (revTeX4) 2 fig. This version has MAJOR changes to equation

### Vector Potential and Berry phase-induced Force

We present a general theoretical framework for the exact treatment of a
hybrid system that is composed of a quantum subsystem and a classical
subsystem. When the quantum subsystem is dynamically fast and the classical
subsystem is slow, a vector potential is generated with a simple canonical
transformation. This vector potential, on one hand, gives rise to the familiar
Berry phase in the fast quantum dynamics; on the other hand, it yields a
Lorentz-like force in the slow classical dynamics. In this way, the pure phase
(Berry phase) of a wavefunction is linked to a physical force.Comment: 4 pages, 1 figur

### Nonperiodic Orbit Sums in Weyl's Expansion for Billiards

Weyl's expansion for the asymptotic mode density of billiards consists of the
area, length, curvature and corner terms. The area term has been associated
with the so-called zero-length orbits. Here closed nonperiodic paths
corresponding to the length and corner terms are constructed.Comment: 8 pages, 2 figure

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