Scattering Theory

A mobile communications system depends on the propagation loss due to the environment between the transmitter and the mobile receiver located at the street level. A theoretical model is proposed to include the effects of trees as well as buildingshouses on the propagation in residential environments. As in past models, the rows of buildinghouses are modeled as diffracting cylinders lying on the earth, but now the canopies of the trees adjacent to and above the buildinghouses are included in the model. The buildinghouses are represented as absorbing screens and the trees as phase screens. The phase screen properties are found by representing the trees as a timeinvariant ensemble of leaves (discs) and branches (cylinders) all having a prescribed location and orientation statistics. The mean field at the aperture of the absorbing screen depends on the mean field in the canopy, which is calculated using the discrete scattering theory of Foldy and Lax.

We consider a hydrogen atom in the background spacetimes generated by an infinitely thin cosmic string and by a point-like global monopole. In both cases, we find the solutions of the corresponding Dirac equations and we determine the energy levels of the atom. We investigate how the geometric and topological features of these spacetimes leads to shifts in the energy levels as compared with the flat Minkowski spacetime.

— Theoretical modeling plays a significant role as forward and inverse problem in active and passive microwave remote sensing. Understanding the validity and limitations of the models is essential for model refinements and, perhaps more importantly, model applications. Motivated by these, this paper presents a comprehensive analysis of the scattering, both backscattering and bistatic scattering, and emission of rough soil surface predicted by the advanced integral equation model (AIEM), a well-established theoretical model. Numerically simulated data, covering a wide range of surface parameters, and in situ measurement data set of well-characterized bare soil surfaces were used to evaluate the performance of AIEM in predicting the scattering coefficient and microwave emissivity over a wide range of geometric parameters and ground surface conditions. The results show that the AIEM predictions are generally in good consistency with both numerical simulations and experiment measurements in terms of angular, frequency, and polarization dependences, except for some deviations in a few cases (e.g., at large incident angles and dry soil conditions). Extensive comparison confirms the effectiveness and practicability of AIEM for both scattering and emission of rough soil surface. Possible explanations for the discrepancy between the model prediction and data are given, together with suggestions for model usage and refinements.

The present paper describes an algorithm for rapid solution of boundary value problems for the Helmholtz equation in two dimensions based on iteratively solving integral equations of scattering theory. CPU time requirements of previously published algorithms of this type are of the order FZ', where n is the number of nodes in the discretization of the boundary of the scatterer. The CPU time requirements of the algorithm of the present paper are #3, and can be further reduced, making it considerably more practical for large scale problems.

Ultrasonic spectrometry was applied to the particle size analysis of disperse systems. The investigations were made for acoustic conditions called the long-wavelength regime (LWR). In the LWR the acoustic behaviour is governed by dissipative effects rather than by scattering. Two principal theoretical approaches to ultrasonic spectrometryscattering theory and coupled phase models -are introduced. A model based on a newly developed coupled phase model and the scattering theory (ECAH theory) is implemented in the ultrasonic spectrometer AcoustoPhor.

Οι σημειώσεις αφορούν μάθημα προχωρημένης Κβαντικής Μηχανικής. Η ανάπτυξη της θεωρίας ακολουθεί μια ομαδο-θεωρητική κατεύθυνση. Αφού αναλυθούν οι αναπαραστάσεις της ομάδας Poincare, διατυπώνεται η εξίσωση του Dirac και φανερώνονται οι αιτίες που καθιστούν αναγκαία τη δεύτερη κβάντωση. Τα μεθοδολογικά εργαλεία που αναπτύχθηκαν στο πρώτο μισό του μαθήματος, εφαρμόζονται μεθοδικά στην επίλυση προβλημάτων μεταβάσεων και σκέδασης. Τέλος γίνεται μια εισαγωγή στην Κβαντική Θεωρία Πεδίων καθώς και στα Ολοκληρώματα Διαδρομής.

The term 'laser cooling' is applied to the use of optical means to cool the motional energies of either atoms and molecules, or micromirrors. In the literature, these two strands are kept largely separate; both, however suffer from severe limitations. Laser cooling of atoms and molecules largely relies on the internal level structure of the species being cooled. As a result, only a small number of elements and a tiny number of molecules can be cooled this way. In the case of micromirrors, the problem lies in the engineering of micromirrors that need to satisfy a large number of constraints-these include a high mechanical Q-factor, high reflectivity and very good optical quality, weak coupling to the substrate, etc.-in order to enable efficient cooling.

The history of discovery of bosonic string theory is well documented. This theory evolved as an attempt to find a multidimensional analogue of Euler's beta function. Such an analogue had in fact been known in mathematics literature at least in 1922 and was studied subsequently by mathematicians such as Selberg, Weil and Deligne among others. The mathematical interpretation of this multidimensional beta function is markedly different from that described in physics literature. This paper aims to bridge the gap between the existing treatments. Preserving all results of conformal field theories intact, developed formalism employing topological, algebro-geometric, number-theoretic and combinatorial metods is aimed to provide better understanding of the Veneziano amplitudes and, thus, of string theories.

This paper treats in detail the life and work of Otto Blumenthal, one of the most tragic figures of the 188 emigré mathematicians from Germany and the Nazi-occupied continent. Blumenthal, the first doctoral student of David Hilbert, was crucial in the publication and communication system of German mathematics between the two World Wars. There has been an unusual revival of interest in his mathematical work in the last three decades. Thus his work on orthogonal polynomials whose zeros are dense in intervals, called the Blumenthal theorem by T.S. Chihara (1972), lead to over two dozen recent papers in the field. The Blumenthal-Nevai theorem, with applications to scattering theory in physics, is one example. In modern work on Hilbert modular forms, increasingly being called Hilbert-Blumenthal modular forms, many recent papers even contain the word Blumenthal in their titles. This paper contains 212 references.

We expose the Schrödinger quantum mechanics with traditional applications to Hydrogen atom: the calculation of the Hydrogen atom spectrum via Schrödinger, Pauli and Dirac equations, the Heisenberg representation, the selection rules, the calculation of quantum and classical scattering of light (Thomson cross section), photoeffect (Sommerfeld cross section), quantum and classical scattering of electrons (Rutherford cross section), normal and anomalous Zeemann effect (Landé factor), polarization and dispersion (Kramers-Kronig formula), diamagnetic susceptibility (Langevin formula). We discuss carefully the experimental and theoretical background for the introduction of the Schrödinger, Pauli and Dirac equations, as well as for the Maxwell equations. We explain in detail all basic theoretical concepts: the introduction of the quantum stationary states, charge density and electric current density, quantum magnetic moment, electron spin and spin-orbital coupling in "vector model" and in the Russel-Saunders approximation, differential cross section of scattering, the Lorentz theory of polarization and magnetization, the Einstein special relativity and covariance of the Maxwell Electrodynamics. We explain all details of the calculations and mathematical tools: Lagrangian and Hamiltonian formalism for the systems with finite degree of freedom and for fields, Geometric Optics, the Hamilton-Jacobi equation and WKB approximation, Noether theory of invariants including the theorem on currents, four conservation laws (energy, momentum, angular momentum and charge), Lie algebra of angular momentum and spherical functions, scattering theory (limiting amplitude principle and limiting absorption principle), the Lienard-Wiechert formulas, Lorentz group and Lorentz formulas, Pauli theorem and relativistic covariance of the Dirac equation, etc. We give a detailed oveview of the conceptual development of the quantum mechanics, and expose main achievements of the "old quantum mechanics" in the form of exercises. One of our basic aim in writing this book, is an open and concrete discussion of the problem of a mathematical description of the following two fundamental quantum phenomena: i) Bohr's quantum transitions and ii) de Broglie's wave-particle duality. Both phenomena cannot be described by autonomous linear dynamical equations, and we give them a new mathematical treatment related with recent progress in the theory of global attractors of nonlinear hyperbolic PDEs. Namely, we suggest that i) the quantum stationary states form a global attractor of the coupled Maxwell-Schrödinger or Maxwell-Dirac equations, in the presence of an external confining potential, and ii) the wave-particle duality corresponds to the soliton-like asymptotics for the solutions of the translation-invariant coupled equations without an external potential. We emphasize, in the whole of our exposition, that the coupled equations are nonlinear, and just this nonlinearity lies behind all traditional perturbative calculations that is known as the Born approximation. We suggest that both fundamental quantum phenomena could be described by this nonlinear coupling. The suggestion is confirmed by recent results on the global attractors and soliton asymptotics for model nonlinear hyperbolic PDEs.

Backscattered signal of coherent anti-Stokes Raman spectroscopy can be an extremely useful tool for remote identification of airborne particles, provided the signal is sufficiently large. We formulate a semiclassical theory of nonlinear scattering to estimate the number of detectable photons from a bacterial spore at a distance. For the first time, the theory incorporates enhanced quantum coherence via femtosecond pulses and a nonlinear process into the classical scattering problem. Our result shows a large backscattered signal in the far field, using typical parameters of an anthrax spore with maximally prepared vibrational coherence. Using train pulses of 1 kHz of repetition rate each with energy of 10 mJ, we estimate that about 10(7) photons can be detected by a 1 m diameter detector placed 1 km away from the spore in the backward scattering direction. The result shows the feasibility of developing a real time remote detection of hazardous microparticles in the atmosphere, particularly biopathogenic spores.

Ultrasonic measurements of acoustic wavefields scattered by single spheres placed in a homogenous background medium ͑water͒ are presented. The dimensions of the spheres are comparable to the wavelength and the wavelength and represent both positive ͑rubber͒ and negative ͑teflon͒ velocity anomalies with respect to the background medium. The sensitivity of the recorded wavefield to scattering in terms of traveltime delay and amplitude variation is investigated. The results validate a linear ͑first-order͒ diffraction theory for wavefields propagating in heterogeneous media with anomaly contrasts on the order of ±15%. The diffraction theory is compared further with the exact results known from literature for scattering from an elastic sphere, formulated in terms of Legendre polynomials. To investigate the 2D case, the firstorder scattering theory is tested against 2D elastic finite-difference calculations. As the presented theory involves a volume integral, it is applicable to any geometric shape, and the scattering object does not need to be spherical or any other specific symmetrical shape. Furthermore, it can be implemented easily in seismic data inversion schemes, which is illustrated with examples from seismic crosswell tomography and a reflection experiment.

This paper investigates the reconstruction of elastic Green's function from the cross-correlation of waves excited by random noise in the context of scattering theory. Using a general operator equation,-the resolvent formula-, Green's function reconstruction is established when the noise sources satisfy an equipartition condition. In an inhomogeneous medium, the operator formalism leads to generalized forms of optical theorem involving the off-shell T-matrix of elastic waves, which describes scattering in the near-field. The role of temporal absorption in the formulation of the theorem is discussed. Previously established symmetry and reciprocity relations involving the on-shell T-matrix are recovered in the usual far-field and infinitesimal absorption limits. The theory is applied to a point scattering model for elastic waves. The T-matrix of the point scatterer incorporating all recurrent scattering loops is obtained by a regularization procedure. The physical significance of the point scatterer is discussed. In particular this model satisfies the off-shell version of the generalized optical theorem. The link between equipartition and Green's function reconstruction in a scattering medium is discussed.

Conservation laws, heirarchies, scattering theory and Bäcklund transformations are known to be the building blocks of integrable partial differential equations. We identify these as facets of a theory of Poisson group actions, and apply the theory to the ZS-AKNS nxn heirarchy (which includes the non-linear Schrödinger equation, modified KdV, and the n-wave equation). We first find a simple model Poisson group action that contains flows for systems with a Lax pair whose terms all decay on R. Bäcklund transformations and flows arise from subgroups of this single Poisson group. For the ZS-AKNS nxn heirarchy defined by a constant a ∈ u(n), the simple model is no longer correct. The a determines two separate Poisson structures. The flows come from the Poisson action of the centralizer H a of a in the dual Poisson group (due to the behavior of e aλx at infinity). When a has distinct eigenvalues, H a is abelian and it acts symplectically. The phase space of these flows is the space S a of left cosets of the centralizer of a in D − , where D − is a certain loop group. The group D − contains both a Poisson subgroup corresponding to the continuous scattering data, and a rational loop group corresponding to the discrete scattering data. The H a -action is the right dressing action on S a . Bäcklund transformations arise from the action of the simple rational loops on S a by right multiplication. Various geometric equations arise from appropriate choice of a and restrictions of the phase space and flows. In particuar, we discuss applications to the sine-Gordon equation, harmonic maps, Schrödinger flows on symmetric spaces, Darboux orthogonal coordinates, and isometric immersions of one space-form in another.

We present a model for spectral theory of families of selfadjoint operators, and their corresponding unitary one-parameter groups (acting in Hilbert space.) The models allow for a scale of complexity, indexed by the natural numbers N. For each n ∈ N, we get families of selfadjoint operators indexed by: (i) the unitary matrix group U (n), and by (ii) a prescribed set of n nonoverlapping intervals. Take Ω to be the complement in R of n fixed closed finite and disjoint intervals, and let L 2 (Ω) be the corresponding Hilbert space. Moreover, given B ∈ U (n), then both the lengths of the respective intervals, and the gaps between them, show up as spectral parameters in our corresponding spectral resolutions within L 2 (Ω). Our models have two advantages: One, they encompass realistic features from quantum theory, from acoustic wave equations and their obstacle scattering; as well as from harmonic analysis.

Photo: width 7.5cm height 11cm 4 Dmitrii L. Maslov 7.3. Conductance of a wire attached to reservoirs 7.3.1. Inhomogeneous Luttinger-liquid model 7.3.2. Elastic-string analogy 7.3.3. Kubo formula for a wire attached to reservoirs 7.3.4. Experiment 7.4. Spin component of the conductance 7.5. Thermal conductance: Fabry-Perrot resonances of plasmons 8. Acknowledgments Appendix A. Polarization bubble for small q in arbitrary dimensionality Appendix B. Polarization bubble in 1D Appendix B.1. Small q Appendix B.2. q near 2k F Appendix C. Some details of bosonization procedure Appendix C.1. Anomalous commutators Appendix C.2. Bosonic operators Appendix C.2.1. Commutation relations for bosonic fields ϕ and ϑ Appendix C.3. Problem with backscattering References

Accurately modeling the behavior of a beam of positrons incident upon a solid is of crucial importance for depth-profiling and data analysis in slow positron experiments. We describe a suite of Fortran programs to perform a Monte Carlo calculation of positron implantation in amorphous metals and small bandgap semiconductors. This provides statistical information about penetration (stopping profiles, thermalization time, etc.), energy loss and reemission (backscattering, thin film transrr.ission, etc.). The calculation is implemented using a user-friendly Monte Carlo transport "engine", which is capable of treating particle transport in infinite, semi-infinite, and multilayer systems. A contingent of elastic (up m 10 keV) and inelastic (down to 30 eV) scattering mechanisms is included, but different mechanisms can be added via external data files or code modification. As a consequence of the scattering theory involved, this calculation is amenable to electron implantation and scattering.

It has been usually assumed that under very general and common conditions the outcome of a collision experiment does not depend on the properties of the projectiles' beam [1]. However, recent evidence in ionization experiments [2] points to a breakdown of these conditions and a dependence of the collision outcome on the incident beam's coherence properties. These facts open the question of how is the result of a collision affected by the preparation of the projectiles' beam.
This thesis presents a study of this problem analyzing inconsistencies of the standard stationary formulation of the scattering theory [1], and how these can affect the interpretation of projectile's coherence effects in ion impact collision experiments. To get this done, the framework of the De Broglie-Bohm formulation [3, 4] was used, which has recently recovered its lost mommentum due to its ability to deal with novel weak measurement results [5, 6]. In addition, this formulation is an advantageous option to describe a number of physical problems of current interest, such as the method of quantum trajectories developed by Robert E. Wyatt [7], or the study of effects such as the appearance of vortices in multichannel processes [8].

Volume 240, number 1,2 PHYSICS LETTERS B 19 April 1990 SCATTERING LENGTHS FROM FLUCTUATIONS Marco GUAGNELLI, Enzo MARINARI and Giorgio PARISI Dipartimento di Fisica, Universita di Roma "Tor Vergata", Via E. Carnevale, I00173 Rorne, ...

The underlying aim of presented article is to determine the optimal location and sizes of the air gaps inside a multi-slot coaxial antenna with 50-ohm feed based on the S11-parameter characteristics of microwave applicator to get the best antenna impedance matching to the treated tissue. The next step is the selection of the limit levels of the antenna input power, for which temperature of the tissue do not exceed known therapeutic elevations for microwave therapies at hyperthermic and ablation temperatures. The proposed approach provides a relatively simple method for optimization of the location and size of slots in the antenna structure. The proper choice of limit values of total antenna input power enables appropriate adjustment of temperature of the target tissue to preserve optimal cancer treatment.

We study the wave equation for the gravitational fluctuations in the Randall-Sundrum brane cosmology model. We solve the global Cauchy problem and we establish that the solutions are the sum of a slowly decaying massless wave localized near the brane, and a superposition of massive dispersive waves. We compute the kernel of the truncated resolvent. We prove some L 1 − L ∞ , L 2 − L ∞ decay estimates and global L p Strichartz type inequalities. We develop the complete scattering theory : existence and asymptotic completness of the wave operators, computation of the scattering matrix, determination of the resonances on the logarithmic Riemann surface.

We discuss a basic thermodynamic properties of systems with multifractal structure. This is possible by extending the notion of Gibbs-Shannon's entropy into more general framework -Rényi's information entropy. We show a connection of Rényi's parameter q with the multifractal singularity spectrum f (α) and clarify a relationship with the Tsallis-Havrda-Charvat entropy. Finally, we generalize Hagedorn's statistical theory and apply it to high-energy particle collisions.

The theory of a complex scalar Higgs field which provides a mechanism for electroweak symmetry breaking (EWSB) is outlined to provide motivation for the study of the electroweak sector through vector boson scattering (VBS). Many of the exact mechanisms of EWSB have yet to be confirmed in the TeV scale, where the existence of new physics is sought after as a source of unitarity preservation. The use of an effective field theory as a way of incorporating anomalous couplings of new physics is presented as a modern way to study EWSB beyond the standard model.

Abstract. In these lectures 4 quantum physics in noncommutative spacetime is developed. It is based on the work of Doplicher et al. which allows for time-space noncommutativity. In the context of noncommutative quantum mechanics, some important points are explored, such as the ...

Blackledge, Jonathan Electromagnetic Scattering Solutions for Digital Signal Processing Jyväskylä: University of Jyväskylä, 2009, 297 p. (nid.), 2010 (PDF) (Jyväskylä Studies in Computing ISSN 1456-5390; 108) ISBN 978-951-39-3944-1 (PDF), 978-951-39-3741-6 (nid.) Electromagnetic scattering theory is fundamental to understanding the interaction between electromagnetic waves and inhomogeneous dielectric materials. The theory unpins the engineering of electromagnetic imaging systems over a broad range of frequencies, from optics to radio and microwave imaging, for example. Developing accurate scattering models is particularly important in the field of image understanding and the interpretation of electromagnetic signals generated by scattering events. To this end there are a number of approaches that can be taken. For relatively simple geometric configurations, approximation methods are used to develop a transformation from the object plane (where scattering events take place) to the i...

We analyze the spectral properties and discuss the scattering theory of operators of the form H = H 0 +V> H 0 =-A+Ex. Among our results are the existence of wave operators, Ω ± (H,H 0), the nonexistence of bound states, and a (speculative) description of resonances for certain classes of potentials.

] has presented a straightforward technique employing the Dirac formalism to calculate single- and double-slit interference patterns. He claims that no reference is made to classical optics or scattering theory and that his method therefore provides a purely quantum mechanical description of these experiments. He also presents his calculation as if no approximations are employed. We show that he implicitly makes the same approximations found in classical treatments of interference and that no new physics has been introduced. At the same time, some of the quantum mechanical arguments Marcella gives are, at best, misleading.

We study the classical limit of the stationary scattering theory for a Schro dinger operator in a compactly supported gauge field. We show that, under suitable hypotheses on the associated classical flow, the scattering amplitude has a complete asymptotic expansion in the semi-classical parameter, and we determine the main term of this expansion.

The surface photoelectron and inner shell electron spectroscopy (SURPRISES) program suite performs ab initio calculations of photoionization and non-radiative decay spectra in nanoclusters and solid state systems by using a space-energy similarity procedure to reproduce the band-like part of the spectra. This approach provides an extension of Fano resonant multichannel scattering theory dealing with the complexity arising from condensed matter calculations at a computational cost comparable to that of molecules. The bottleneck of electron spectroscopy ab initio calculations in condensed matter is the size of the Hilbert space where the wavefunctions are expanded and the increase in number of final decay states in comparison to that of atoms and molecules. In particular, the diagonalization of the interchannel interaction to take into account the correlation between the double ion and the escaping electron is impracticable when hole delocalization on valence bands and electronic excitations are included in the model. To overcome this problem SURPRISES uses a 'space-energy similarity' approach, which allows the spreading of the Auger probability over the bands without tuning semi-empirical parameters. Furthermore, a completely new feature in the landscape of ab initio resonant decay processes calculations is represented by including energy loss through a statistical approach. Using the calculated lineshape as electron source, a Monte Carlo routine simulates the effect of inelastic losses on the original lineshape. In this process, the computed spectrum can be directly compared with acquired experimental spectra, thus avoiding background subtraction, a procedure not free from uncertainty. The program can exploit the symmetry of the system under investigation to reduce the calculation scaling and may compute photoemission and Auger decay angular distribution patterns including energy loss for the electrons emitted in resonance-affected photoionization processes. In this paper, we present general methods, computational techniques and a number of numerical tests applied to the calculation of Si K-LL and O K-LL Auger spectra from different SiO2 nanoclusters.

We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, nonzero temperatures, and spatial arrangements in which one object is enclosed in another. Our method combines each object's classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. The method is illustrated by re-deriving the Lifshitz formula for infinite half spaces, by demonstrating the Casimir-Polder to van der Waals cross-over, and by computing the Casimir interaction energy of two infinite, parallel, perfect metal cylinders either inside or outside one another. Furthermore, it is used to obtain new results, namely the Casimir energies of a sphere or a cylinder opposite a plate, all with finite permittivity and permeability, to leading order at large separation.

Backscattered signal of coherent anti-Stokes Raman spectroscopy can be an extremely useful tool for remote identification of airborne particles, provided the signal is sufficiently large. We formulate a semiclassical theory of nonlinear scattering to estimate the number of detectable photons from a bacterial spore at a distance. For the first time, the theory incorporates enhanced quantum coherence via femtosecond pulses and a nonlinear process into the classical scattering problem. Our result shows a large backscattered signal in the far field, using typical parameters of an anthrax spore with maximally prepared vibrational coherence. Using train pulses of 1 kHz of repetition rate each with energy of 10 mJ, we estimate that about 10 7 photons can be detected by a 1 m diameter detector placed 1 km away from the spore in the backward scattering direction. The result shows the feasibility of developing a real time remote detection of hazardous microparticles in the atmosphere, particularly biopathogenic spores.

As one of major tankers routes in Indonesia, Malacca Strait is potentially prone to oil spill pollution. SAR image data is used to detect oil slick on sea surface, because of its capability for large scale of sea monitoring, and to solve clouds covering problem in Indonesia. Oil slick is visible on SAR images as dark patches, because it decreases the radar backscatter on sea surface, which is explained by Bragg scattering theory. This project proposes the procedure for auto segmentation of oil slick in SAR image data. To reduce speckle in SAR image, we used the Bayesian approach with maximum a posteori filter with assumption that radar reflectivity and speckle noise follow Gamma distribution. This technique is compared with another adaptive filter such as Lee and Frost filter, which shows the best result on reducing speckle on whole area with the lowest ratio of mean and standard deviation, reducing the bright fleck on oil area, and showing the continuity on oil slick and sea area, which is make easier in feature extraction of oil slick. Maximum entropy technique is used for feature extraction on oil slick segmentation with assumption that only two moments are to be determined i.e. oil slick and sea area. It shows the best performance on oil slick segmentation among the others co-occurrence techniques. The area classification between oil slick and look-alike area on low wind area is done based on these result.

The aim of this book is to introduce the basic elements of the scattering matrix approach to transport phenomena in dynamical quantum systems of non-interacting electrons. This approach admits a physically clear and transparent description of transport processes in dynamical mesoscopic systems promising basic elements of solid-state devices for quantum information processing. One of the key effects, the quantum pump effect, is considered in detail. In addition, the theory for a recently implemented new dynamical source — injecting electrons with time delay much larger than the electron coherence time — is offered. This theory provides a simple description of quantum circuits with such a single-particle source and shows in an unambiguous way that the tunability inherent to the dynamical systems leads to a number of unexpected but fundamental effects.

A crucial element of scattering theory and the LSZ reduction formula is the assumption that the coupling vanishes at large times. This is known not to hold for the theories of the Standard Model and in general such asymptotic dynamics is not well understood. We give a description of asymptotic dynamics in field theories which incorporates the important features of weak convergence and physical boundary conditions. Applications to theories with three and four point interactions are presented and the results are shown to be completely consistent with the results of perturbation theory.