707 research outputs found
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
Scanning Tunneling Microscopy of Biological Macromolecular Structures Coated with a Conducting Film
We have studied the capability of scanning tunneling microscopy (STM) to reveal the three-dimensional structure of biological macromolecular structures that have been rendered conductive by metal-coating. The sample preparation used has been derived from a well established method in transmission electron microscopy (TEM). It includes adsorption, freezing and dehydration by vacuum-sublimation, followed by metal-shadowing of the specimen. As an alternative to adsorption and coating, fluid biomaterials can be replaced by conductive freeze-fracture replica.
We give an introduction into the sample preparation of metal-coated specimens and discuss how each step can affect the structural preservation and thereby the quality of the data. Some aspects of the data acquisition and the quantitative evaluation of STM data are shown. Possible contributions of STM in the biological macromolecular research are pointed out
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
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
Rigorous Real-Time Feynman Path Integral for Vector Potentials
we will show the existence and uniqueness of a real-time, time-sliced Feynman
path integral for quantum systems with vector potential. Our formulation of the
path integral will be derived on the transition probability amplitude via
improper Riemann integrals. Our formulation will hold for vector potential
Hamiltonian for which its potential and vector potential each carries at most a
finite number of singularities and discontinuities
Magnetic transport in a straight parabolic channel
We study a charged two-dimensional particle confined to a straight
parabolic-potential channel and exposed to a homogeneous magnetic field under
influence of a potential perturbation . If is bounded and periodic along
the channel, a perturbative argument yields the absolute continuity of the
bottom of the spectrum. We show it can have any finite number of open gaps
provided the confining potential is sufficiently strong. However, if
depends on the periodic variable only, we prove by Thomas argument that the
whole spectrum is absolutely continuous, irrespectively of the size of the
perturbation. On the other hand, if is small and satisfies a weak
localization condition in the the longitudinal direction, we prove by Mourre
method that a part of the absolutely continuous spectrum persists
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