6,779 research outputs found
Exact Eigenfunctions of a Chaotic System
The interest in the properties of quantum systems, whose classical dynamics
are chaotic, derives from their abundance in nature. The spectrum of such
systems can be related, in the semiclassical approximation (SCA), to the
unstable classical periodic orbits, through Gutzwiller's trace formula. The
class of systems studied in this work, tiling billiards on the pseudo-sphere,
is special in this correspondence being exact, via Selberg's trace formula. In
this work, an exact expression for Green's function (GF) and the eigenfunctions
(EF) of tiling billiards on the pseudo-sphere, whose classical dynamics are
chaotic, is derived. GF is shown to be equal to the quotient of two infinite
sums over periodic orbits, where the denominator is the spectral determinant.
Such a result is known to be true for typical chaotic systems, in the leading
SCA. From the exact expression for GF, individual EF can be identified. In
order to obtain a SCA by finite series for the infinite sums encountered,
resummation by analytic continuation in was performed. The result is
similar to known results for EF of typical chaotic systems. The lowest EF of
the Hamiltonian were calculated with the help of the resulting formulae, and
compared with exact numerical results. A search for scars with the help of
analytical and numerical methods failed to find evidence for their existence.Comment: 53 pages LaTeX, 10 Postscript figure
Double Exchange in a Magnetically Frustrated System
This work examines the magnetic order and spin dynamics of a double-exchange
model with competing ferromagnetic and antiferromagnetic Heisenberg
interactions between the local moments. The Heisenberg interactions are
periodically arranged in a Villain configuration in two dimensions with
nearest-neighbor, ferromagnetic coupling and antiferromagnetic coupling
. This model is solved at zero temperature by performing a
expansion in the rotated reference frame of each local moment.
When exceeds a critical value, the ground state is a magnetically
frustrated, canted antiferromagnet. With increasing hopping energy or
magnetic field , the local moments become aligned and the ferromagnetic
phase is stabilized above critical values of or . In the canted phase, a
charge-density wave forms because the electrons prefer to sit on lines of sites
that are coupled ferromagnetically. Due to a change in the topology of the
Fermi surface from closed to open, phase separation occurs in a narrow range of
parameters in the canted phase. In zero field, the long-wavelength spin waves
are isotropic in the region of phase separation. Whereas the average spin-wave
stiffness in the canted phase increases with or , it exhibits a more
complicated dependence on field. This work strongly suggests that the jump in
the spin-wave stiffness observed in PrCaMnO with at a field of 3 T is caused by the delocalization of the electrons rather
than by the alignment of the antiferromagnetic regions.Comment: 28 pages, 12 figure
Multifractals Competing with Solitons on Fibonacci Optical Lattice
We study the stationary states for the nonlinear Schr\"odinger equation on
the Fibonacci lattice which is expected to be realized by Bose-Einstein
condensates loaded into an optical lattice. When the model does not have a
nonlinear term, the wavefunctions and the spectrum are known to show fractal
structures. Such wavefunctions are called critical. We present a phase diagram
of the energy spectrum for varying the nonlinearity. It consists of three
portions, a forbidden region, the spectrum of critical states, and the spectrum
of stationary solitons. We show that the energy spectrum of critical states
remains intact irrespective of the nonlinearity in the sea of a large number of
stationary solitons.Comment: 5 pages, 4 figures, major revision, references adde
On the Spectrum of the Resonant Quantum Kicked Rotor
It is proven that none of the bands in the quasi-energy spectrum of the
Quantum Kicked Rotor is flat at any primitive resonance of any order.
Perturbative estimates of bandwidths at small kick strength are established for
the case of primitive resonances of prime order. Different bands scale with
different powers of the kick strength, due to degeneracies in the spectrum of
the free rotor.Comment: Description of related published work has been expanded in the
Introductio
Dynamics of Impurity and Valence Bands in GaMnAs within the Dynamical Mean Field Approximation
We calculate the density-of-states and the spectral function of GaMnAs within
the dynamical mean-field approximation. Our model includes the competing
effects of the strong spin-orbit coupling on the J=3/2 GaAs hole bands and the
exchange interaction between the magnetic ions and the itinerant holes. We
study the quasi-particle and impurity bands in the paramagnetic and
ferromagnetic phases for different values of impurity-hole coupling at the Mn
doping of x=0.05. By analyzing the anisotropic angular distribution of the
impurity band carriers at T=0, we conclude that the carrier polarization is
optimal when the carriers move along the direction parallel to the average
magnetization.Comment: 6 pages, 4 figure
Stable Quantum Resonances in Atom Optics
A theory for stabilization of quantum resonances by a mechanism similar to
one leading to classical resonances in nonlinear systems is presented. It
explains recent surprising experimental results, obtained for cold Cesium atoms
when driven in the presence of gravity, and leads to further predictions. The
theory makes use of invariance properties of the system, that are similar to
those of solids, allowing for separation into independent kicked rotor
problems. The analysis relies on a fictitious classical limit where the small
parameter is {\em not} Planck's constant, but rather the detuning from the
frequency that is resonant in absence of gravity.Comment: 5 pages, 3 figure
Brownian Motion Model of Quantization Ambiguity and Universality in Chaotic Systems
We examine spectral equilibration of quantum chaotic spectra to universal
statistics, in the context of the Brownian motion model. Two competing time
scales, proportional and inversely proportional to the classical relaxation
time, jointly govern the equilibration process. Multiplicity of quantum systems
having the same semiclassical limit is not sufficient to obtain equilibration
of any spectral modes in two-dimensional systems, while in three-dimensional
systems equilibration for some spectral modes is possible if the classical
relaxation rate is slow. Connections are made with upper bounds on
semiclassical accuracy and with fidelity decay in the presence of a weak
perturbation.Comment: 13 pages, 6 figures, submitted to Phys Rev
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