scholarly journals SPECTRAL AND SCATTERING THEORY FOR THE AHARONOV–BOHM OPERATORS

2011 ◽  
Vol 23 (01) ◽  
pp. 53-81 ◽  
Author(s):  
KONSTANTIN PANKRASHKIN ◽  
SERGE RICHARD

We review the spectral and the scattering theory for the Aharonov–Bohm model on ℝ2. New formulae for the wave operators and for the scattering operator are presented. The asymptotics at high energy and at low energy of the scattering operator are computed.

Author(s):  
W. O. Amrein ◽  
M. Wollenberg

SynopsisWe 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 operator.


1970 ◽  
Vol 25 (5) ◽  
pp. 752-760 ◽  
Author(s):  
Anthony R. Moon

A perturbation theory of thermal diffuse scattering of low-energy electrons is developed along the lines of von Laue's “reciprocity theorem” approach successfully used by Kainuma in the consideration of diffuse scattering in high-energy electron diffraction. This theory takes into account the multiple scattering of the electrons within the crystal, and is so formulated that it may be used in conjunction with present LEED calculations for the elastic scattering from a perfect crystal. It is shown that by a pseudokinematical approximation for the perfect crystal wave functions, the normal pseudokinematical result for the diffuse intensity is obtained. Under certain conditions differences between the multiple scattering theory and the pseudokinematical theory are expected to occur. These deviations have their origin in resonance processes. Some numerical results comparing the two theories are presented.


2019 ◽  
Vol 489 (2) ◽  
pp. 142-146
Author(s):  
B. A. Plamenevskii ◽  
A. S. Poretskii ◽  
O. V. Sarafanov

A waveguide occupies a domain G with several cylindrical ends. The waveguide is described by a nonstationary equation of the form it f = Af ,where A is a selfadjoint second order elliptic operator with variable coefficients (in particular, for A = -, where stands for the Laplace operator, the equation coincides with the Schrodinger equation). For the corresponding stationary problem with spectral parameter, we define continuous spectrum eigenfunctions and a scattering matrix. The limiting absorption principle provides expansion in the continuous spectrum eigenfunctions. We also calculate wave operators and prove their completeness. Then we define a scattering operator and describe its connections with the scattering matrix.


2019 ◽  
Vol 32 (01) ◽  
pp. 2050002
Author(s):  
Benjamin Louis Alvarez ◽  
Jérémy Faupin

We consider mathematical models of the weak decay of the vector bosons [Formula: see text] into leptons. The free quantum field Hamiltonian is perturbed by an interaction term from the standard model of particle physics. After the introduction of high energy and spatial cut-offs, the total quantum Hamiltonian defines a self-adjoint operator on a tensor product of Fock spaces. We study the scattering theory for such models. First, the masses of the neutrinos are supposed to be positive: for all values of the coupling constant, we prove asymptotic completeness of the wave operators. In a second model, neutrinos are treated as massless particles and we consider a simpler interaction Hamiltonian: for small enough values of the coupling constant, we prove again asymptotic completeness, using singular Mourre’s theory, suitable propagation estimates and the conservation of the difference of some number operators.


1992 ◽  
Vol 15 (1) ◽  
pp. 175-182
Author(s):  
Denis A. W. White

Spectral and scattering theory is discussed for the Stark effect HamiltoniansH0=−(1/2)Δ−x1andH=H0+VwhereVis a long range perturbation. Most significantly, in one dimension, and forVconsisting of a slowly decaying term and an almost periodic term, the two Hilbert space wave operators (of Isozaki and Kitada) are shown to exist and be complete by Enss's time dependent method.


2001 ◽  
Vol 28 (1) ◽  
pp. 37-40 ◽  
Author(s):  
Gabriele Carannante ◽  
A. Laviano ◽  
D. Ruberti ◽  
Lucia Simone ◽  
G. Sirna ◽  
...  

Author(s):  
Peter Rez

Transportation efficiency can be measured in terms of the energy needed to move a person or a tonne of freight over a given distance. For passengers, journey time is important, so an equally useful measure is the product of the energy used and the time taken for the journey. Transportation requires storage of energy. Rechargeable systems such as batteries have very low energy densities as compared to fossil fuels. The highest energy densities come from nuclear fuels, although, because of shielding requirements, these are not practical for most forms of transportation. Liquid hydrocarbons represent a nice compromise between high energy density and ease of use.


2021 ◽  
Vol 22 (15) ◽  
pp. 7879
Author(s):  
Yingxia Gao ◽  
Yi Zheng ◽  
Léon Sanche

The complex physical and chemical reactions between the large number of low-energy (0–30 eV) electrons (LEEs) released by high energy radiation interacting with genetic material can lead to the formation of various DNA lesions such as crosslinks, single strand breaks, base modifications, and cleavage, as well as double strand breaks and other cluster damages. When crosslinks and cluster damages cannot be repaired by the cell, they can cause genetic loss of information, mutations, apoptosis, and promote genomic instability. Through the efforts of many research groups in the past two decades, the study of the interaction between LEEs and DNA under different experimental conditions has unveiled some of the main mechanisms responsible for these damages. In the present review, we focus on experimental investigations in the condensed phase that range from fundamental DNA constituents to oligonucleotides, synthetic duplex DNA, and bacterial (i.e., plasmid) DNA. These targets were irradiated either with LEEs from a monoenergetic-electron or photoelectron source, as sub-monolayer, monolayer, or multilayer films and within clusters or water solutions. Each type of experiment is briefly described, and the observed DNA damages are reported, along with the proposed mechanisms. Defining the role of LEEs within the sequence of events leading to radiobiological lesions contributes to our understanding of the action of radiation on living organisms, over a wide range of initial radiation energies. Applications of the interaction of LEEs with DNA to radiotherapy are briefly summarized.


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