7,482 research outputs found
Stochastic resonance in a suspension of magnetic dipoles under shear flow
We show that a magnetic dipole in a shear flow under the action of an
oscillating magnetic field displays stochastic resonance in the linear response
regime. To this end, we compute the classical quantifiers of stochastic
resonance, i.e. the signal to noise ratio, the escape time distribution, and
the mean first passage time. We also discuss limitations and role of the linear
response theory in its applications to the theory of stochastic resonance.Comment: 17 pages, 5 figures, approved for publication in PR
Reply to ``Comment on `On the inconsistency of the Bohm-Gadella theory with quantum mechanics'''
In this reply, we show that when we apply standard distribution theory to the
Lippmann-Schwinger equation, the resulting spaces of test functions would
comply with the Hardy axiom only if classic results of Paley and Wiener, of
Gelfand and Shilov, and of the theory of ultradistributions were wrong. As
well, we point out several differences between the ``standard method'' of
constructing rigged Hilbert spaces in quantum mechanics and the method used in
Time Asymmetric Quantum Theory.Comment: 13 page
Gibbs Entropy and Irreversibility
This contribution is dedicated to dilucidating the role of the Gibbs entropy
in the discussion of the emergence of irreversibility in the macroscopic world
from the microscopic level. By using an extension of the Onsager theory to the
phase space we obtain a generalization of the Liouville equation describing the
evolution of the distribution vector in the form of a master equation. This
formalism leads in a natural way to the breaking of the BBGKY hierarchy. As a
particular case we derive the Boltzmann equation
The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part I
We exemplify the way the rigged Hilbert space deals with the
Lippmann-Schwinger equation by way of the spherical shell potential. We
explicitly construct the Lippmann-Schwinger bras and kets along with their
energy representation, their time evolution and the rigged Hilbert spaces to
which they belong. It will be concluded that the natural setting for the
solutions of the Lippmann-Schwinger equation--and therefore for scattering
theory--is the rigged Hilbert space rather than just the Hilbert space.Comment: 34 pages, 1 figur
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