9,783 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
Localization of eigenstates in a modified Tomonaga-Luttinger model
We study the localization in the Hilbert space of a modified
Tomonaga-Luttinger model. For the standard version of this model, the states
are found to be extended in the basis of Slater determinants, representing the
eigenstates of the non-interacting system. The linear dispersion which leads to
the fact that these eigenstates are extended in the modified model is replaced
by one with random level spacings modeling the complicated one-particle spectra
of realistic models. The localization properties of the eigenstates are
studied. The interactions are simplified and an effective one-dimensional Lloyd
model is obtained. The effects of many-body energy correlations are studied
numerically. The eigenstates of the system are found to be localized in Fock
space for any strength of the interactions, but the localization is not
exponential.Comment: 19 pages, 7 figure
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Tertiary Alcohols as Radical Precursors for the Introduction of Tertiary Substituents into Heteroarenes
Despite many recent advances in the radical alkylation of electron-deficient heteroarenes since the seminal reports by Minisci and co-workers, methods for the direct incorporation of tertiary alkyl substituents into nitrogen heteroarenes are limited. This report describes the use of tert-alkyl oxalate salts, derived from tertiary alcohols, to introduce tertiary substituents into a variety of heterocyclic substrates. This reaction has reasonably broad scope, proceeds rapidly under mild conditions, and is initiated by either photochemical or thermal activation. Insights into the underlying mechanism of the higher yielding visible-light initiated process were obtained by flash photolysis studies, whereas computational studies provided insight into the reaction scope
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
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
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