1,223 research outputs found
Stochastic geometry and topology of non-Gaussian fields
Gaussian random fields pervade all areas of science. However, it is often the
departures from Gaussianity that carry the crucial signature of the nonlinear
mechanisms at the heart of diverse phenomena, ranging from structure formation
in condensed matter and cosmology to biomedical imaging. The standard test of
non-Gaussianity is to measure higher order correlation functions. In the
present work, we take a different route. We show how geometric and topological
properties of Gaussian fields, such as the statistics of extrema, are modified
by the presence of a non-Gaussian perturbation. The resulting discrepancies
give an independent way to detect and quantify non-Gaussianities. In our
treatment, we consider both local and nonlocal mechanisms that generate
non-Gaussian fields, both statically and dynamically through nonlinear
diffusion.Comment: 8 pages, 4 figure
Geometrical phase driven predissociation: Lifetimes of 2^2 A' levels of H_3
We discuss the role of the geometrical phase in predissociation dynamics of
vibrational states near a conical intersection of two electronic potential
surfaces of a D_{3h} molecule. For quantitative description of the
predissociation driven by the coupling near a conical intersection, we
developed a method for calculating lifetimes and positions of vibrational
predissociated states (Feshbach resonances) for X_3 molecule. The method takes
into account the two coupled three-body potential energy surfaces, which are
degenerate at the intersection. As an example, we apply the method to obtain
lifetimes and positions of resonances of predissociated vibrational levels of
the 2^2 A' electronic state of the H_3 molecule. The three-body recombination
rate coefficient for the H+H+H -> H_2+H process is estimated.Comment: 4 pages, 4 figure
Empirically testing <i>Tonnetz</i>, voice-leading, and spectral models of perceived triadic distance
We compare three contrasting models of the perceived distance between root-position major and minor chords and test them against new empirical data. The models include a recent psychoacoustic model called spectral pitch class distance, and two well-established music theoretical models – Tonnetz distance and voice-leading distance. To allow a principled challenge, in the context of these data, of the assumptions behind each of the models, we compare them with a simple “benchmark” model that simply counts the number of common tones between chords. Spectral pitch class and Tonnetz have the highest correlations with the experimental data and each other, and perform significantly better than the benchmark. The voice-leading model performs worse than the benchmark. We suggest that spectral pitch class distance provides a psychoacoustic explanation for perceived harmonic distance and its music theory representation, the Tonnetz. Scores and MIDI files of the stimuli, the experimental data, and the computational models are available in the online supplement
Quasi-exact-solution of the Generalized Exe Jahn-Teller Hamiltonian
We consider the solution of a generalized Exe Jahn-Teller Hamiltonian in the
context of quasi-exactly solvable spectral problems. This Hamiltonian is
expressed in terms of the generators of the osp(2,2) Lie algebra. Analytical
expressions are obtained for eigenstates and eigenvalues. The solutions lead to
a number of earlier results discussed in the literature. However, our approach
renders a new understanding of ``exact isolated'' solutions
Theory of dissociative recombination of highly-symmetric polyatomic ions
A general first-principles theory of dissociative recombination is developed
for highly-symmetric molecular ions and applied to HO and CH,
which play an important role in astrophysical, combustion, and laboratory
plasma environments. The theoretical cross-sections obtained for the
dissociative recombination of the two ions are in good agreement with existing
experimental data from storage ring experiments
Optimal Topological Test for Degeneracies of Real Hamiltonians
We consider adiabatic transport of eigenstates of real Hamiltonians around
loops in parameter space. It is demonstrated that loops that map to nontrivial
loops in the space of eigenbases must encircle degeneracies. Examples from
Jahn-Teller theory are presented to illustrate the test. We show furthermore
that the proposed test is optimal.Comment: Minor corrections, accepted in Phys. Rev. Let
A simplified picture for Pi electrons in conjugated polymers : from PPP Hamiltonian to an effective molecular crystal approach
An excitonic method proper to study conjugated oligomers and polymers is
described and its applicability tested on the ground state and first excited
states of trans-polyacetylene, taken as a model. From the Pariser-Parr-Pople
Hamiltonian, we derive an effective Hamiltonian based on a local description of
the polymer in term of monomers; the relevant electronic configurations are
build on a small number of pertinent local excitations. The intuitive and
simple microscopic physical picture given by our model supplement recent
results, such as the Rice and Garstein ones. Depending of the parameters, the
linear absorption appears dominated by an intense excitonic peak.Comment: 41 Pages, 6 postscript figure
Peierls transition in the quantum spin-Peierls model
We use the density matrix renormalization group method to investigate the
role of longitudinal quantized phonons on the Peierls transition in the
spin-Peierls model. For both the XY and Heisenberg spin-Peierls model we show
that the staggered phonon order parameter scales as (and the
dimerized bond order scales as ) as (where
is the electron-phonon interaction). This result is true for both linear and
cyclic chains. Thus, we conclude that the Peierls transition occurs at
in these models. Moreover, for the XY spin-Peierls model we show
that the quantum predictions for the bond order follow the classical prediction
as a function of inverse chain size for small . We therefore conclude
that the zero phase transition is of the mean-field type
Signed zeros of Gaussian vector fields-density, correlation functions and curvature
We calculate correlation functions of the (signed) density of zeros of
Gaussian distributed vector fields. We are able to express correlation
functions of arbitrary order through the curvature tensor of a certain abstract
Riemann-Cartan or Riemannian manifold. As an application, we discuss one- and
two-point functions. The zeros of a two-dimensional Gaussian vector field model
the distribution of topological defects in the high-temperature phase of
two-dimensional systems with orientational degrees of freedom, such as
superfluid films, thin superconductors and liquid crystals.Comment: 14 pages, 1 figure, uses iopart.cls, improved presentation, to appear
in J. Phys.
Topological properties of Berry's phase
By using a second quantized formulation of level crossing, which does not
assume adiabatic approximation, a convenient formula for geometric terms
including off-diagonal terms is derived. The analysis of geometric phases is
reduced to a simple diagonalization of the Hamiltonian in the present
formulation. If one diagonalizes the geometric terms in the infinitesimal
neighborhood of level crossing, the geometric phases become trivial for any
finite time interval . The topological interpretation of Berry's phase such
as the topological proof of phase-change rule thus fails in the practical
Born-Oppenheimer approximation, where a large but finite ratio of two time
scales is involved.Comment: 9 pages. A new reference was added, and the abstract and the
presentation in the body of the paper have been expanded and made more
precis
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