619 research outputs found
Generalized definition of time delay in scattering theory
We advocate for the systematic use of a symmetrized definition of time delay
in scattering theory. In two-body scattering processes, we show that the
symmetrized time delay exists for arbitrary dilated spatial regions symmetric
with respect to the origin. It is equal to the usual time delay plus a new
contribution, which vanishes in the case of spherical spatial regions. We also
prove that the symmetrized time delay is invariant under an appropriate mapping
of time reversal. These results are also discussed in the context of classical
scattering theory.Comment: 18 page
Time delay for one-dimensional quantum systems with steplike potentials
This paper concerns time-dependent scattering theory and in particular the
concept of time delay for a class of one-dimensional anisotropic quantum
systems. These systems are described by a Schr\"{o}dinger Hamiltonian with a potential converging to different limits
and as and respectively. Due to the
anisotropy they exhibit a two-channel structure. We first establish the
existence and properties of the channel wave and scattering operators by using
the modern Mourre approach. We then use scattering theory to show the identity
of two apparently different representations of time delay. The first one is
defined in terms of sojourn times while the second one is given by the
Eisenbud-Wigner operator. The identity of these representations is well known
for systems where vanishes as (). We show
that it remains true in the anisotropic case , i.e. we prove
the existence of the time-dependent representation of time delay and its
equality with the time-independent Eisenbud-Wigner representation. Finally we
use this identity to give a time-dependent interpretation of the
Eisenbud-Wigner expression which is commonly used for time delay in the
literature.Comment: 48 pages, 1 figur
On the Lax-Phillips scattering theory
We give a simple description of the wave operators appearing in the Lax-Phillips scattering theory. This is used to derive a relation between the scattering matrix and a kind of time delay operator and to characterize all scattering systems having the same scattering operato
Independent electrons model for open quantum systems: Landauer-Buettiker formula and strict positivity of the entropy production
A general argument leading from the formula for currents through an open
noninteracting mesoscopic system given by the theory of non-equilibrium steady
states (NESS) to the Landauer-Buettiker formula is pointed out. Time reversal
symmetry is not assumed. As a consequence it follows that, as far as the system
has a nontrivial scattering theory and the reservoirs have different
temperatures and/or chemical potentials, the entropy production is strictly
positive.Comment: 12 pages. Submitted for publication in J. Math. Phys. on 2006-06-05.
Revision and extension of: G. Nenciu, A general proof of Landauer-Buettiker
formula, [math-ph/0603030
Scattering into Cones and Flux across Surfaces in Quantum Mechanics: a Pathwise Probabilistic Approach
We show how the scattering-into-cones and flux-across-surfaces theorems in
Quantum Mechanics have very intuitive pathwise probabilistic versions based on
some results by Carlen about large time behaviour of paths of Nelson
diffusions. The quantum mechanical results can be then recovered by taking
expectations in our pathwise statements.Comment: To appear in Journal of Mathematical Physic
A comparative study of mechanisms of surfactant inhibition
AbstractPulmonary surfactant spreads to the hydrated air–lung interface and reduces the surface tension to a very small value. This function fails in acute respiratory distress syndrome (ARDS) and the surface tension stays high. Dysfunction has been attributed to competition for the air–lung interface between plasma proteins and surfactant or, alternatively, to ARDS-specific alterations of the molecular profile of surfactant. Here, we compared the two mechanisms in vitro, to assess their potential role in causing respiratory distress. Albumin and fibrinogen exposure at or above blood level concentrations served as the models for testing competitive adsorption. An elevated level of cholesterol was chosen as a known adverse change in the molecular profile of surfactant in ARDS. Bovine lipid extract surfactant (BLES) was spread from a small bolus of a concentrated suspension (27 mg/ml) to the air–water interface in a captive bubble surfactometer (CBS) and the bubble volume was cyclically reduced and increased to assess surface activity of the spread material. Concentrations of inhibitors and the concentration and spreading method of pulmonary surfactant were chosen in an attempt to reproduce the exposure of surfactant to inhibitors in the lung. Under these conditions, neither serum albumin nor fibrinogen was persistently inhibitory and normal near-zero minimum surface tension values were obtained after a small number of cycles. In contrast, inhibition by an increased level of cholesterol persisted even after extensive cycling. These results suggest that in ARDS, competitive adsorption may not sufficiently explain high surface tension, and that disruption of the surfactant film needs to be given causal consideration
Photon position measure
The positive operator valued measure (POVM) for a photon counting array
detector is derived and found to equal photon flux density integrated over
pixel area and measurement time. Since photon flux density equals number
density multiplied by the speed of light, this justifies theoretically the
observation that a photon counting array provides a coarse grained measurement
of photon position. The POVM obtained here can be written as a set of
projectors onto a basis of localized states, consistent with the description of
photon position in a recent quantum imaging proposal [M. Tsang, Phys. Rev.
Lett. \textbf{102}, 253601 (2009)]. The wave function that describes a photon
counting experiment is the projection of the photon state vector onto this
localized basis. Collapse is to the electromagnetic vacuum and not to a
localized state, thus violating the text book rules of quantum mechanics but
compatible with the theory of generalized observables and the nonlocalizability
of an incoming photon
Hardy-Carleman Type Inequalities for Dirac Operators
General Hardy-Carleman type inequalities for Dirac operators are proved. New
inequalities are derived involving particular traditionally used weight
functions. In particular, a version of the Agmon inequality and Treve type
inequalities are established. The case of a Dirac particle in a (potential)
magnetic field is also considered. The methods used are direct and based on
quadratic form techniques
Extreme Covariant Quantum Observables in the Case of an Abelian Symmetry Group and a Transitive Value Space
We represent quantum observables as POVMs (normalized positive operator
valued measures) and consider convex sets of observables which are covariant
with respect to a unitary representation of a locally compact Abelian symmetry
group . The value space of such observables is a transitive -space. We
characterize the extreme points of covariant observables and also determine the
covariant extreme points of the larger set of all quantum observables. The
results are applied to position, position difference and time observables.Comment: 23 page
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