1,720,997 research outputs found
Quantum evolution and classical flow in complex phase space
No full textFor a class of holomorphic perturbations of the harmonic oscillator in n degrees of freedom a local solution of the time-dependent Schrödinger equation in the Bargmann representation is constructed which pointwise propagates, to leading order in h{combining short stroke overlay}, along the classical trajectories in complex phase space. © 1990 Springer-Verlag
Quality & Quantity: Introduction
No full textThis special issue of Quality and Quantity stems from the workshop “How can
mathematics contribute to social science” organized by Nicola Bellomo, Pierluigi
Contucci and Sandro Graffi at the Department of Mathematics of the University of
Bologna in March 2006. The purpose of the meeting was to bring together expertises
from the two fields aiming at each other from the methodological perspective within
the social science investigations.
This collection, which follows the invitation of the Editor Vittorio Capecchi, has
a similar intention: to allow the interested reader to have a series of papers in which
problems coming from Social Sciences are studied and developed using methods and
models originated in the mathematical-physics investigations. It is our belief that the
two communities have a lot to learn from each other and our hope is to stimulate
further studies by suggesting some bridge between them
Stochastic properties of the quantum Arnold cat in the classical limit, in: `Proceedings of the Euler Institute of S. Petersburg', Tom 8 (1996), n.2.
No full textWe discuss the stochastic properties of the quantum version of a classical hyperbolic dynamical system, the Arnold toral automorphism, with particular focus on the classical limit
Classical Limit of the Quantized Hyperbolic Toral Automorphism
No full textThe canonical quantization of any hyperbolic
symplectomorphism of the 2-torus (in particular, of the Arnold cat map)
yields a periodic unitary operator on a -dimensional Hilbert space,
. We prove that this quantum system
becomes ergodic and mixing at the classical limit (,
prime) which can be interchanged with the time-average limit. The
recovery of the stochastic behaviour out of a
periodic one is based on the same mechanism under which the
uniform distribution
of the classical periodic orbits reproduces the Lebesgue measure: the Wigner
functions of the eigenstates, supported on the classical periodic orbits,
are indeed proved to become uniformly spread in phase space
Convergence of a quantum nornal form and a generalization of Cherry's theorem
No full textWe consider on L-2(T-2) the Schrodinger operator family H-epsilon : epsilon is an element of R with the domain and action defined as follows:
D(H-epsilon) = H-1 (T-2); H(epsilon)u = -i (h) over bar omega . del u + Vu,
where epsilon is an element of R, omega = (omega(1), omega(2)) is a vector of complex frequencies, and V is a pseudodifferential operator of order zero. H-epsilon represents the Weyl quantization of the Hamiltonian family H-epsilon defined on the phase space R-2 x T-2: (xi, chi) (sic) R-2 x T-2 bar right arrow H-epsilon(xi, chi) = omega . xi + epsilon V(xi, chi), where V(xi, chi). C-2(R-2 x T-2; R). We prove the uniform convergence with respect to (h) over bar is an element of [0, 1] of the quantum normal form, which reduces to the classical one for (h) over bar = 0. As a consequence, we simultaneously obtain an exact quantization formula for the quantum spectrum as well as a convergence criterion for the classical Birkhoff normal form generalizing a well- known theorem of Cherry
A quantum Cherry theorem for perturbations of the plane rotator
No full text{We consider on L^2(\T^2) the \Sc\ operator family L_\ep: \ep\in\R with domain and action defined as \ds
D(L_\ep)=H^2(\T^2),\; L_\ep u=-\frac12\hbar^2(\alpha_1\partial_{\phi_1}^2+\alpha_2\partial_{\phi_2}^2)u-i\hbar(\gamma_1\partial_{\phi_1}+\gamma_2\partial_{\phi_2})u+\ep Vu.
Here \ep\in\R, ,
are vectors of complex non-real frequencies, and a pseudodifferential operator of order zero. L_\ep represents the Weyl quantization of the Hamiltonian family \L_\ep(\xi,x)=\frac12(\alpha_1\xi_1^2+\alpha_2\xi_2^2)+\gamma_1\xi_1+\gamma_2\xi_2+\ep \V(\xi,x) defined on the phase space \R^2\times\T^2, where \V(\xi,x)\in C^2(\R^2\times \T^2;\R). We prove the uniform convergence with respect to of the quantum normal form, which reduces to the classical one for . This result simultaneously entails an exact quantization formula for the quantum spectrum as well as a convergence criterion for the classical Birkhoff normal form generalizing a well known theorem of Cherry to a class of perturbations of a non self-adoint quantum plane rotator.
Spectral analysis of transfer operators associated to Farey fractions
Full text linkThe spectrum of a one-parameter family of signed transfer operators associated to the Farey map is studied in detail. We show that when acting on a suitable Hilbert space of analytic functions they are self-adjoint and exhibit absolutely continuous spectrum and no non-zero point spectrum. Polynomial eigenfunctions when the parameter is a negative half-integer are also discussed
ACCURACY OF THE SEMICLASSICAL APPROXIMATION - THE PULLEN-EDMONDS HAMILTONIAN
Full text linkA test on the numerical accuracy of the semi-classical approximation as a function of the principal quantum number has been performed for the Pullen-Edmonds model, a two-dimensional, non-integrable, scaling-invariant perturbation of the resonant harmonic oscillator. A perturbative interpretation is obtained of the recently observed phenomenon of the accuracy decrease on the approximation of individual energy levels at the increase of the principal quantum number. Moreover, the accuracy provided by the semi-classical approximation formula is on average the same as that provided by quantum perturbation theory
QUANTAL OVERLAPPING RESONANCE CRITERION - THE PULLEN-EDMONDS MODEL
No full textIn order to highlight the onset of chaos in the Pullen-Edmonds model a quantal analog of the resonance overlap criterion has been examined. A quite good agreement between analytical and numerical results is obtained
Failures induced on analog integrated circuits by conveyed electromagnetic interferences: A review
No full textFailures induced on analog integrated circuits by electromagnetic interference (EMI) will be analyzed with particular emphasis on integrated operational amplifiers built with different technologies. Additionally, the correlation found between EMI susceptibility and large-signal opamp behavior will be discussed. Some criteria for the design of low EMI susceptibility opamps will be derived. Finally, as an application example, the design of a BiCMOS opamp with an extremely low-probability EMI-induced failure will be presented. Copyright © 1996 Elsevier Science Ltd
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