1,188 research outputs found
A general resonance theory based on Mourre's inequality
We study the perturbation of bound states embedded in the continuous spectrum
which are unstable by the Fermi Golden Rule. The approach to resonance theory
based on spectral deformation is extended to a more general class of quantum
systems characterized by Mourre's inequality and smoothness of the resolvent.
Within the framework of perturbation theory it is still possible to give a
definite meaning to the notion of complex resonance energies and of
corresponding metastable states. The main result is a quasi-exponential decay
estimate up to a controlled error of higher order in perturbation theory.Comment: 17 page
Assumptions that imply quantum dynamics is linear
A basic linearity of quantum dynamics, that density matrices are mapped
linearly to density matrices, is proved very simply for a system that does not
interact with anything else. It is assumed that at each time the physical
quantities and states are described by the usual linear structures of quantum
mechanics. Beyond that, the proof assumes only that the dynamics does not
depend on anything outside the system but must allow the system to be described
as part of a larger system. The basic linearity is linked with previously
established results to complete a simple derivation of the linear Schrodinger
equation. For this it is assumed that density matrices are mapped one-to-one
onto density matrices. An alternative is to assume that pure states are mapped
one-to-one onto pure states and that entropy does not decrease.Comment: 10 pages. Added references. Improved discussion of equations of
motion for mean values. Expanded Introductio
Limiting absorption principle and perfectly matched layer method for Dirichlet Laplacians in quasi-cylindrical domains
We establish a limiting absorption principle for Dirichlet Laplacians in
quasi-cylindrical domains. Outside a bounded set these domains can be
transformed onto a semi-cylinder by suitable diffeomorphisms. Dirichlet
Laplacians model quantum or acoustically-soft waveguides associated with
quasi-cylindrical domains. We construct a uniquely solvable problem with
perfectly matched layers of finite length. We prove that solutions of the
latter problem approximate outgoing or incoming solutions with an error that
exponentially tends to zero as the length of layers tends to infinity. Outgoing
and incoming solutions are characterized by means of the limiting absorption
principle.Comment: to appear in SIAM Journal on Mathematical Analysi
On the Born-Oppenheimer approximation of diatomic molecular resonances
We give a new reduction of a general diatomic molecular Hamiltonian, without
modifying it near the collision set of nuclei. The resulting effective
Hamiltonian is the sum of a smooth semiclassical pseudodifferential operator
(the semiclassical parameter being the inverse of the square-root of the
nuclear mass), and a semibounded operator localised in the elliptic region
corresponding to the nuclear collision set. We also study its behaviour on
exponential weights, and give several applications where molecular resonances
appear and can be well located.Comment: 22 page
Canonical Expansion of PT-Symmetric Operators and Perturbation Theory
Let be any \PT symmetric Schr\"odinger operator of the type on , where is
any odd homogeneous polynomial and . It is proved that is
self-adjoint and that its eigenvalues coincide (up to a sign) with the singular
values of , i.e. the eigenvalues of . Moreover we
explicitly construct the canonical expansion of and determine the singular
values of through the Borel summability of their divergent
perturbation theory. The singular values yield estimates of the location of the
eigenvalues \l_j of by Weyl's inequalities.Comment: 20 page
Oenothera bahia-blancae W. Dietr.
Pedro Luro, Estancia Santa María, costa del río ColoradoAriza Espinar. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales; Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Multidisciplinario de Biología Vegetal; Argentin
Heat kernel estimates and spectral properties of a pseudorelativistic operator with magnetic field
Based on the Mehler heat kernel of the Schroedinger operator for a free
electron in a constant magnetic field an estimate for the kernel of E_A is
derived, where E_A represents the kinetic energy of a Dirac electron within the
pseudorelativistic no-pair Brown-Ravenhall model. This estimate is used to
provide the bottom of the essential spectrum for the two-particle
Brown-Ravenhall operator, describing the motion of the electrons in a central
Coulomb field and a constant magnetic field, if the central charge is
restricted to Z below or equal 86
Perturbation of a lattice spectral band by a nearby resonance
A soluble model of weakly coupled "molecular" and "nuclear" Hamiltonians is
studied in order to exhibit explicitly the mechanism leading to the enhancement
of fusion probability in case of a narrow near-threshold nuclear resonance. We,
further, consider molecular cells of this type being arranged in lattice
structures. It is shown that if the real part of the narrow nuclear resonance
lies within the molecular band generated by the intercellular interaction, an
enhancement, proportional to the inverse width of the nuclear resonance, is to
be expected.Comment: RevTeX, 2 figures within the file. In May 2000 the title changed and
some minor corrections have been don
Ultrafast all-optical demultiplexer based on monolithic Mach-Zehnder interferometer with integrated semiconductor optical amplifiers
A monolithically integrated and fully packaged Mach-Zehnder interferometer with semiconductor optical amplifiers (MZI-SOA) is demonstrated as polarisation-independent high-speed demultiplexer for up to 160 Gbit/s optical time division multiplexed (OTDM) data stream
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