Alan R. Bishop – författare

There is no doubt that we have, during the last decade, moved into a "golden age" of condensed matter science. The sequence of discoveries of novel new states of matter and their rapid assimilation into experimental and theoretical research, as well as devices, has been remarkable. To name but a few: spin glasses; incommensurate, fractal, quasicrystal structures; synthetic metals; quantum well fabrication; fractional quantum Hall effect: solid state chaos; heavy fermions; and most spectacularly high-temperature superconductivity. This rapid evolution has been marked by the need to address the reality of materials in "extreme" conditions - - disordered, nonlinear systems in reduced dimensions, restricted geometries and at mesoscopic scales, often with striking competitions between several length and frequency scales, and between strong electron-phonon and electron-electron interactions. In such new territory it is not surprising that very interdisciplinary approaches are being explored and traditional boundaries between subjects and disciplines re-defined. In theory, this is evident, for instance, in attempts: (1) to advance the state of the art for elec­ tronic structure calculations so as to handle strongly interacting many-body systems and delicate competitions for collective ground states (spin models or many-electron Hamiltoni­ ans, field theory, band structure, quantum chemistry and numerical approaches); or (2) to understand pattern formation and complex (including chaotic) dynamics in extended sys­ tems. This demands close involvement with applied mathematics, numerical simulations and statistical mechanics techniques.

There is no doubt that we have, during the last decade, moved into a "golden age" of condensed matter science. The sequence of discoveries of novel new states of matter and their rapid assimilation into experimental and theoretical research, as well as devices, has been remarkable. To name but a few: spin glasses; incommensurate, fractal, quasicrystal structures; synthetic metals; quantum well fabrication; fractional quantum Hall effect: solid state chaos; heavy fermions; and most spectacularly high-temperature superconductivity. This rapid evolution has been marked by the need to address the reality of materials in "extreme" conditions - - disordered, nonlinear systems in reduced dimensions, restricted geometries and at mesoscopic scales, often with striking competitions between several length and frequency scales, and between strong electron-phonon and electron-electron interactions. In such new territory it is not surprising that very interdisciplinary approaches are being explored and traditional boundaries between subjects and disciplines re-defined. In theory, this is evident, for instance, in attempts: (1) to advance the state of the art for elec­ tronic structure calculations so as to handle strongly interacting many-body systems and delicate competitions for collective ground states (spin models or many-electron Hamiltoni­ ans, field theory, band structure, quantum chemistry and numerical approaches); or (2) to understand pattern formation and complex (including chaotic) dynamics in extended sys­ tems. This demands close involvement with applied mathematics, numerical simulations and statistical mechanics techniques.

The collection of articles in this volume represents the proceedings of the inau- gural Conference of the Institute of Theoretical Matter Physics at the University of Florence, Italy, June 7-13, 1990. The aim of this Institute (sponsored by the Con- sorzio Interuniversitario di Fisica della Materia, INFM) is to foster interdisciplinary approaches to theoretical problems in Solid State, Electronics and Optics. Corre- spondingly, the Conference surveyed a broad scope of modern analytic techniques in nonlinear science and their application to novel liquids, solids and optical environ- ments. The Conference was held at Centro Studi CISL, a magnificent Villa up to Florence.The major topics addressed through survey and specialized lectures, discussions and posters were: Complexity and Coherence in spin glasses, associative distribu- tive memory, low dimensional electronic materials, magnets, Josephson junction ar- rays, optics, semiconductors, convection cells, material science, high-temperature superconductivity; Physics of Quantum Devices such as nonlinear feedback oscilla- tors, macroscopic quantum tunneling, hetero structures, quantum ballistic devices, tunneling in atomic devices; Field Theory and Statistical Mechanics, especially for soliton-bearing and quantum chaotic systems. Many exciting ideas and results were presented and debated in lively fashion. Perhaps two major themes were evident throughout the workshop.

ill the past three decades there has been enonnous progress in identifying the es­ sential role that "nonlinearity" plays in physical systems. Classical nonlinear wave equations can support localized, stable "soliton" solutions, and nonlinearities in quantum systems can lead to self-trapped excitations, such as polarons. Since these nonlinear excitations often dominate the transport and response properties of the systems in which they exist, accurate modeling of their effects is essential to interpreting a wide range of physical phenomena. Further, the dramatic de­ velopments in "deterministic chaos", including the recognition that even simple nonlinear dynamical systems can produce seemingly random temporal evolution, have similarly demonstrated that an understanding of chaotic dynamics is vital to an accurate interpretation of the behavior of many physical systems. As a conse­ quence of these two developments, the study of nonlinear phenomena has emerged as a subject in its own right. During these same three decades, similar progress has occurred in understand­ ing the effects of "disorder". Stimulated by Anderson''s pioneering work on "dis­ ordered" quantum solid state materials, this effort has also grown into a field that now includes a variety of classical and quantum systems and treats "disorder" arising from many sources, including impurities, random spatial structures, and stochastic applied fields. Significantly, these two developments have occurred rather independently, with relatively little overlapping research.

ill the past three decades there has been enonnous progress in identifying the es­ sential role that "nonlinearity" plays in physical systems. Classical nonlinear wave equations can support localized, stable "soliton" solutions, and nonlinearities in quantum systems can lead to self-trapped excitations, such as polarons. Since these nonlinear excitations often dominate the transport and response properties of the systems in which they exist, accurate modeling of their effects is essential to interpreting a wide range of physical phenomena. Further, the dramatic de­ velopments in "deterministic chaos", including the recognition that even simple nonlinear dynamical systems can produce seemingly random temporal evolution, have similarly demonstrated that an understanding of chaotic dynamics is vital to an accurate interpretation of the behavior of many physical systems. As a conse­ quence of these two developments, the study of nonlinear phenomena has emerged as a subject in its own right. During these same three decades, similar progress has occurred in understand­ ing the effects of "disorder". Stimulated by Anderson's pioneering work on "dis­ ordered" quantum solid state materials, this effort has also grown into a field that now includes a variety of classical and quantum systems and treats "disorder" arising from many sources, including impurities, random spatial structures, and stochastic applied fields. Significantly, these two developments have occurred rather independently, with relatively little overlapping research.

The Sixth Annual Conference of the Center for Nonlinear Studies at the Los Alamos National Laboratory was held May 5-9, 1986, on the topic "Nonlinearity in Condensed Matter: Lessons from the Past and Prospects for the Future. " As conference organizers, we felt that the study of non­ linear phenomena in condensed matter had matured to the point where it made sense to take stock of the numerous lessons to be learned from a variety of contexts where nonlinearity plays a fundamental role and to evaluate the prospects for the growth of this general discipline. The successful 1978 Oxford Symposium on nonlinear (soliton) struc­ ture and dynamics in condensed matter (Springer Ser. Solid-State Sci. , Vol. 8) was held at a time when the ubiquity of solitons was just begin­ ning to be appreciated by the condensed matter community; in subsequent years the soliton paradigm has provided a rather useful framework for in­ vestigating a large number of phenomena, particularly in low-dimensional systems. Nevertheless, we felt that the importance of nonlinearity in wider arenas than "solitonics" merited a significant expansion in the scope of the conference over that of the 1978 symposium. Indeed, many of the lessons are quite general and their potential for cross-fertilization of otherwise poorly connected disciplines was certainly one of the prime motivations for this conference. Thus, while these proceedings contain many contribu­ tions pertaining to soliton behavior in different contexts, the reader will find much more as well, particularly in the later chapters.

The Sixth Annual Conference of the Center for Nonlinear Studies at the Los Alamos National Laboratory was held May 5-9, 1986, on the topic "Nonlinearity in Condensed Matter: Lessons from the Past and Prospects for the Future. " As conference organizers, we felt that the study of non­ linear phenomena in condensed matter had matured to the point where it made sense to take stock of the numerous lessons to be learned from a variety of contexts where nonlinearity plays a fundamental role and to evaluate the prospects for the growth of this general discipline. The successful 1978 Oxford Symposium on nonlinear (soliton) struc­ ture and dynamics in condensed matter (Springer Ser. Solid-State Sci. , Vol. 8) was held at a time when the ubiquity of solitons was just begin­ ning to be appreciated by the condensed matter community; in subsequent years the soliton paradigm has provided a rather useful framework for in­ vestigating a large number of phenomena, particularly in low-dimensional systems. Nevertheless, we felt that the importance of nonlinearity in wider arenas than "solitonics" merited a significant expansion in the scope of the conference over that of the 1978 symposium. Indeed, many of the lessons are quite general and their potential for cross-fertilization of otherwise poorly connected disciplines was certainly one of the prime motivations for this conference. Thus, while these proceedings contain many contribu­ tions pertaining to soliton behavior in different contexts, the reader will find much more as well, particularly in the later chapters.

In the past three decades there has been enormous progressin identifying the essential role that nonlinearity playsin physical systems, including supporting soliton-likesolutions and self-trapped sxcitations such as polarons.during the same period, similarly impressive progress hasoccurred in understanding the effects of disorder in linearquantum problems, especially regarding Anderson localizationarising from impurities, random spatial structures,stochastic applied fields, and so forth.These striking consequences of disorder, noise andnonlinearity frequently occur together in physical systems.Yet there have been only limited attempts to developsystematic techniques which can include all of theseingredients, which may reinforce, complement or frustrateeach other. This book contains a range of articles whichprovide important steps toward the goal of systematicunderstanding and classification of phenomenology.Experts from Australia, Europe, Japan, USA, and the USSRdescribe both mathematical and numerical techniques -especially from soliton and statistical physics disciplines- and applicaations to a number of important physicalsystems and devices, including optical and electronictransmission lines, liquid crystals, biophysics andmagnetism.

In the past three decades there has been enormous progressin identifying the essential role that nonlinearity playsin physical systems, including supporting soliton-likesolutions and self-trapped sxcitations such as polarons.during the same period, similarly impressive progress hasoccurred in understanding the effects of disorder in linearquantum problems, especially regarding Anderson localizationarising from impurities, random spatial structures,stochastic applied fields, and so forth.These striking consequences of disorder, noise andnonlinearity frequently occur together in physical systems.Yet there have been only limited attempts to developsystematic techniques which can include all of theseingredients, which may reinforce, complement or frustrateeach other. This book contains a range of articles whichprovide important steps toward the goal of systematicunderstanding and classification of phenomenology.Experts from Australia, Europe, Japan, USA, and the USSRdescribe both mathematical and numerical techniques -especially from soliton and statistical physics disciplines- and applicaations to a number of important physicalsystems and devices, including optical and electronictransmission lines, liquid crystals, biophysics andmagnetism.