8,922 research outputs found
Probabilistic Weyl laws for quantized tori
For the Toeplitz quantization of complex-valued functions on a
-dimensional torus we prove that the expected number of eigenvalues of
small random perturbations of a quantized observable satisfies a natural Weyl
law. In numerical experiments the same Weyl law also holds for ``false''
eigenvalues created by pseudospectral effects.Comment: 33 pages, 3 figures, v2 corrected listed titl
Linear response functions for a vibrational configuration interaction state
Linear response functions are implemented for a vibrational configuration interaction state allowing accurate analytical calculations of pure vibrational contributions to dynamical polarizabilities. Sample calculations are presented for the pure vibrational contributions to the polarizabilities of water and formaldehyde. We discuss the convergence of the results with respect to various details of the vibrational wave function description as well as the potential and property surfaces. We also analyze the frequency dependence of the linear response function and the effect of accounting phenomenologically for the finite lifetime of the excited vibrational states. Finally, we compare the analytical response approach to a sum-over-states approac
Evolution in a Changing Environment
We propose a simple model for genetic adaptation to a changing environment, describing a fitness landscape characterized by two maxima. One is associated with “specialist” individuals that are adapted to the environment; this maximum moves over time as the environment changes. The other maximum is static, and represents “generalist” individuals not affected by environmental changes. The rest of the landscape is occupied by “maladapted” individuals. Our analysis considers the evolution of these three subpopulations. Our main result is that, in presence of a sufficiently stable environmental feature, as in the case of an unchanging aspect of a physical habitat, specialists can dominate the population. By contrast, rapidly changing environmental features, such as language or cultural habits, are a moving target for the genes; here, generalists dominate, because the best evolutionary strategy is to adopt neutral alleles not specialized for any specific environment. The model we propose is based on simple assumptions about evolutionary dynamics and describes all possible scenarios in a non-trivial phase diagram. The approach provides a general framework to address such fundamental issues as the Baldwin effect, the biological basis for language, or the ecological consequences of a rapid climate change
Propagating Torsion in 3D-Gravity and Dynamical Mass Generation
In this paper, fermions are minimally coupled to 3D-gravity where a dynamical
torsion is introduced. A Kalb-Ramond field is non-minimally coupled to these
fermions in a gauge-invariant way. We show that a 1-loop mass generation
mechanism takes place for both the 2-form gauge field and the torsion. As for
the fermions, no mass is dynamically generated: at 1-loop, there is only a mass
shift proportional to the Yukawa coupling whenever the fermions have a
non-vanishing tree-level mass.Comment: 13 pages, latex file, no figures, some corrections adde
Experimental Study of Parametric Autoresonance in Faraday Waves
The excitation of large amplitude nonlinear waves is achieved via parametric
autoresonance of Faraday waves. We experimentally demonstrate that phase
locking to low amplitude driving can generate persistent high-amplitude growth
of nonlinear waves in a dissipative system. The experiments presented are in
excellent agreement with theory.Comment: 4 pages, 4 eps figures, to appear in Phys. Rev. Let
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