Related papers: Quantum Scattering and Classical Solutions
The problem of extending quantum-mechanical formal scattering theory to a more general class of models that also includes quantum field theories is discussed, with the aim of clarifying certain aspects of the definition of scattering…
This is the first in a series of papers presenting a new understanding of scattering amplitudes based on fundamentally combinatorial ideas in the kinematic space of the scattering data. We study the simplest theory of colored scalar…
We consider a model dissipative quantum-mechanical system realized by coupling a quantum oscillator to a semi-infinite classical string which serves as a means of energy transfer from the oscillator to the infinity and thus plays the role…
The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding…
The theory of elastic light scattering by semiconductor quantum dots is suggested. The semiclassical method, applying retarded potentials to avoid the problem of bounder conditions for electric and magnetic field, is used. The exact results…
The scattering problems of a scalar point particle from a finite assembly of n>1 non-overlapping and disconnected hard disks, fixed in the two-dimensional plane, belong to the simplest realizations of classically hyperbolic scattering…
We study the effects of an arbitrary external perturbation in the statistical properties of the S-matrix of quantum chaotic scattering systems in the limit of isolated resonances. We derive, using supersymmetry, an exact non-perturbative…
We apply quantum integration to elementary particle-physics processes. In particular, we look at scattering processes such as ${\rm e}^+{\rm e}^- \to q \bar q$ and ${\rm e}^+{\rm e}^- \to q \bar q' {\rm W}$. The corresponding probability…
An $S$--matrix approach is developed for the chaotic dynamics of a nonlinear oscillator with dissipation. The quantum--classical crossover is studied in the framework of the semiclassical expansion for the $S$--matrix. Analytical…
These lectures treat scattering theory from a non-perturbative point of view. The course begins with a review of formal aspects in scattering theory, discussing the in/out states and the $S$ matrix that connects them. Unitarity relations,…
We introduce the notion of multi-dimensional chaos that applies to processes described by erratic functions of several dynamical variables. We employ this concept in the interpretation of classical and quantum scattering off a pinball…
As a step toward satisfactory understanding of the quantum dynamics of Dirichlet \break (D-) particles, the amplitude for the basic process describing the scattering of two quantized D-particles is computed in bosonic string theory. The…
The numerical treatment of quantum mechanics in the semi-classical regime is known to be computationally demanding, due to the highly oscillatory behaviour of the wave function and its large spatial extension. A recently proposed…
In this thesis, we describe some recent results obtained in the analysis of two-dimensional quantum field theories by means of semiclassical techniques. These achievements represent a natural development of the non-perturbative studies…
We develop a statistical theory that describes quantum-mechanical scattering of a particle by a cavity when the geometry is such that the classical dynamics is chaotic. This picture is relevant to a variety of physical systems, ranging from…
We consider the nonlinear Schr{\"o}dinger equation with a short-range external potential, in a semi-classical scaling. We show that for fixed Planck constant, a com-plete scattering theory is available, showing that both the potential and…
This review is devoted to the different techniques that have been developed to compute the phase-coherent transport properties of quantum nanoelectronic systems connected to electrodes. Beside a review of the different algorithms proposed…
We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…
Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…
The functional integral method can be used in quantum mechanics to find the scattering amplitude for particles in the external field. We will obtain the potential scattering amplitude form the complete Green function in the corresponding…