THE PROPAGATION OF GAMMA QUANTA IN MATTER

By DONALD CLARK

PART I NONLINEAR SYSTEMS GENERAL TOPICS TOWARDS ALGEBRO-GEOMETRIC INTEGRATION OF THE GROSS–PITAEVSKII EQUATION INTRODUCTION UTILIZATION OF THE SCHR¨ODINGER EQUATION SOLUTIONS IN TERMS OF HYPERELLIPTIC FUNCTIONS TWO COMPONENT GROSS-PITAEVSKII EQUATION AND THE MANAKOV SYSTEM ON MODELING ADIABATIC N-SOLITON INTERACTIONS N-SOLITON TRAINS OF THE NLS AND HNLS EQUATIONS N-SOLITON TRAINS OF THE MNLS EQUATION THE IMPORTANCE OF THE CTC MODEL DYNAMICAL REGIMES OF THE HNLS SOLITON TRAINS THE PERTURBED NLS AND PERTURBED CTC SECOND ORDER DISPERSION AND NONLINEAR GAIN QUADRATIC AND PERIODIC POTENTIALS ANALYSIS OF THE PERTURBED CTC DISCUSSION DYNAMICAL STABILIZATION OF NONLINEAR WAVES DYNAMICS OF SOLITONS IN BEC WITH RAPIDLY OSCILLATING TRAP STABLE TWO DIMENSIONAL BRIGHT SOLITON UNDER FESCHBACH RESO- NANCE MANAGEMENT STABLE TWO DIMENSIONAL DISPERSION-MANAGED SOLITON CONCLUSIONS CONTENT SOLITONS AS STRANGE ATTRACTORS MASTER EQUATION STATIONARY SOLUTION AND ITS STABILITY DYNAMICS BEYOND THE LINEAR REGIME DYNAMICS OVER A WIDE RANGE OF PARAMETER ? VARIATIONS UNIVERSALITY OF THE PHENOMENON MULTIDIMENSIONAL SOLITONS AND VORTICES IN PERIODIC POTENTIALS BASIC EQUATIONS AND THE VARIATIONAL APPROACH SOLITONS IN MULTI-MODE OPTICAL LATTICES VORTEX SOLITONS IN THE REPULSIVE MODEL SOLITONS IN LOW-DIMENSIONAL POTENTIALS THE MODEL THE VARIATIONAL APPROXIMATION NUMERICAL RESULTS COLLISIONS BETWEEN SOLITONS, AND FORMATION OF BOUND STATES CONCLUSION GLOBALLY-LINKED VORTEX CLUSTERS MODEL AND EQUATIONS VORTEX CLUSTERS IN THE NONINTERACTING CASE CLUSTERS OF PRODUCT VORTICES FLIPPING VORTEX CLUSTERS IN SYMMETRIC TRAPING POTENTIALS GLOBALLY LINKED VORTEX-CLUSTERS IN SYMMETRIC TRAPS VORTEX CLUSTERS IN ASYMMETRIC TRAPS VORTEX CLUSTERS IN THE INTERACTING CASE SOLUTIONS OF THE LOGARITHMIC SCHR¨ODINGER EQUATION IN A ROTATING HARMONIC TRAP FORMULATION OF THE PROBLEM SOLUTIONS AND THEIR STABILITY LINEAR AND NONLINEAR BOUND STATES IN CURVED WAVEGUIDES SETUP AND EQUATIONS OF MOTION LINEAR CASE: A = NUMERICAL RESULTS SUMMARY NUMERICAL STUDY OF A NONLOCAL SINE-GORDON EQUATION THE CONSTRUCTION OF THE BREATHERS KINK-ANTIKINK INTERACTIONS A FRUITFUL INTERPLAY: FROM NONLOCALITY TO FRACTIONAL CALCULUS NONLOCAL EQUATIONS FRACTIONAL CALCULUS FRAMEWORK OF APPLICATIONS INTERNAL DEGREES OF FREEDOM ON 3 + 1 DIMENSIONAL FRIEDMAN-ROBERTSON-WALKER UNIVERSES WITH MATTER STOCHASTIC E?ECTS ON THE ECKHAUS EQUATION SOLUTION STATISTICAL PROPERTIES MODULATIONAL INSTABILITY OF SOME NONLINEAR CONTINUUM AND DISCRETE MODELS SAMI FOR NLS EQUATION SAMI FOR DST EQUATION SAMI FOR MANAKOV SYSTEM SCATTERING OF NLS SOLITONS WITH BOUND QUANTUM STATES QUANTIZED SOLITARY WAVES INELASTIC SOLITON-RESONANT STATE COLLISION “OSCILLATOR-WAVE” MODEL: MULTIPLE ATTRACTORS AND STRONG STABILITY MODEL OF THE INTERACTION OF AN OSCILLATOR WITH AN ELECTROMAG- NETIC WAVE: APPROACH APPLICABLE FOR SMALL AMPLITUDES OF THE SYSTEM OSCILLATIONS GENERAL CONDITIONS FOR TRANSITION TO IRREGULAR BEHAVIOR IN AN OSCILLATOR UNDER WAVE ACTION PART II BOSE-EINSTEIN CONDENSATES AND MATTER WAVES BOSE-EINSTEIN CONDENSATION: THE ODD NONLINEAR QUANTUM MECHANICS OPTICAL LATTICE BOSE-EINSTEIN CONDENSATE IN A PERIODIC LATTICE GROUND STATE QUASI-MOMENTUM AND CURRENT SUPER?UID DENSITY SOLITONS AND SUPER?UIDITY IN A ONE-DIMENSIONAL BOSE-GAS GREY SOLITONS ONE-DIMENSIONAL BOSE GAS STATISTICAL MECHANICS OF QUANTUM INTEGRABLE SYSTEMS HARD-CORE BOSE GAS CLASSICAL LIMIT LOW-TEMPERATURE EXPANSIONS BETHE ANSATZ CLUSTER EXPANSION METHOD ?-FUNCTION BOSE GAS XXX HEISENBERG MODEL SOLUTIONS OF THE LIEB-LINIGER INTEGRAL EQUATION LARGE ? (LARGE ?) SMALL ? (SMALL ?) BOSE-EINSTEIN CONDENSATES IN AN OPTICAL LATTICE DYNAMICS OF A BEC IN A 1D OPTICAL LATTICE DRIVEN BY A HARMONIC POTENTIAL SUPER?UID REGIME DYNAMICAL SUPER?UID-INSULATOR TRANSITION EXPANSION OF A BEC IN A MOVING OPTICAL LATTICE BOSE-EINSTEIN CONDENSATES IN OPTICAL LATTICES IN THE NONLINEAR REGIME MATTER WAVES IN PERIODIC POTENTIALS - BASIC CONCEPTS EXPERIMENTAL REALIZATION OF BECS IN PERIODIC POTENTIALS NONLINEAR E?ECTS OF BECS IN OPTICAL LATTICES FREE EXPANSION AND VARIATION OF THE CHEMICAL POTENTIAL NONLINEAR AND ASYMMETRIC LANDAU-ZENER TUNNELING INSTABILITIES CONCLUSIONS AND OUTLOOK QUANTUM BOUND STATES AND MATTER WAVES DELOCALIZATIONS MATTER WAVES AS MACROSCOPIC QUANTUM BOUND STATES DELOCALIZING TRANSITIONS OF MATTER WAVES CONTROL OF MATTER WAVES IN OPTICAL LATTICES BY FESHBACH RESONANCE MEAN-?ELD APPROXIMATION AND PARAMETERS OF THE PROBLEM E?ECTIVE 1D EQUATIONS LONG TRAP AND RAPIDLY VARYING OL SHORT TRAP AND RAPIDLY VARYING OL LONG TRAP AND SMOOTH OL SHORT TRAP AND SMOOTH OL STATIONARY SOLUTION BACKGROUND PERIODIC SOLUTIONS BEC IN OL CONTROLLED BY FR DEFORMATION OF A CN-WAVE EVOLUTION PROBLEM CALCULATION OF THE NUMBER OF BRIGHT SOLITONS DEFORMATION OF A DN-WAVE DEFORMATION OF A SN-WAVE DISCUSSION AND CONCLUSION TWO-COMPONENT BOSE-EINSTEIN CONDENSATES IN OPTICAL LATTICES BASIC EQUATIONS STATIONARY SOLUTIONS WITH NON-TRIVIAL PHASES TRIVIAL PHASE SOLUTIONS MODULATIONAL INSTABILITY OF TRIVIAL PHASE SOLUTIONS AND GENERA- TION OF LOCALIZED MATTER WAVES DISCUSSIONS SHOCK WAVES IN BOSE-EINSTEIN CONDENSATES PART III NONLINEAR OPTICS AND PHOTONICS STOPPING AND BENDING LIGHT IN 2D PHOTONIC STRUCTURES UNIFORM GRATING STRUCTURES 1D STRUCTURES - ?BER GRATINGS 2D STRUCTURES - PLANAR WAVEGUIDE GRATINGS PHOTONIC STRUCTURES PERIODIC STRUCTURES WITH DEFECTS LINEAR DEFECT MODES FOR THE 2D CME FUTURE WORK MODEL OF THE TWO LEVEL QUANTUM DOTS ENSEMBLE INTERACTING WITH ULTRA-SHORT PULSE OF COHERENT RADIATION MODEL OF ISOLATED QUANTUM DOTS THE E?ECT OF ELECTRON TRANSPORT THE T-J MODEL THE GENERALIZED SYSTEM OF REDUCED MAXWELL-BLOCH EQUA- TIONS A PARTICULAR SOLUTION: A CIRCULARLY POLARIZED POLARITON ENHANCED OPTICAL TRANSMISSION VIA TUNNEL COUPLING IN SURFACE POLARITONIC CRYSTALS SPP MODES ON A PERIODICALLY STRUCTURED SURFACE SPP ?LM MODES OF A PERIODIC STRUCTURE TRANSMISSION AND RE?ECTION COE?CIENTS TRANSMISSION SPECTRA NEAR-?ELD AND FAR-?ELD TRANSMISSION LIQUID LIGHT IN CUBIC-QUINTIC NONLINEAR OPTICAL MATERIALS PHYSICAL MODEL STATIONARY NODELESS STATES DYNAMICS OF COLLECTIVE OSCILLATIONS COLLISIONAL DYNAMICS PULSED BEAMS LIGHT WHIRLPOOLS AZIMUTHAL EIGENSTATES STABILITY ANALYSIS OF THE AZIMUTHAL EIGENSTATES VORTICES IN PULSED BEAMS OPTICAL PULSE EVOLUTION TOWARD LIGHT BULLET AND VORTEX SOLUTION VARIATIONAL APPROACH FILAMENTATION BEAMS CARRYING PHASE SINGULARITY THE DESCRIPTION OF EXTREMELY SHORT PULSES IN NON-RESONANT MEDIA IN FRAME OF MAXWELL-DU?NG-TYPE MODELS CONSTITUTIVE MODEL STEADY STATE SOLUTIONS BILINEAR FORM OF THE TOTAL MAXWELL-DU?NG EQUATIONS TWO-COMPONENT (VECTOR) DU?NG MODEL QUINTIC DU?NG MODEL STEADY STATE SOLUTION ELECTROMAGNETIC DOMAIN STATISTICS OF THREE INTERACTING OPTICAL SOLITONS BASIC MODEL THREE-SOLITON SYSTEM FOKKER-PLANCK EQUATION STATISTICAL STUDY OF RAMAN SCATTERING IN OPTICAL ?BERS A?ECTED BY RANDOM CONDITIONS THE PHYSICAL FOUNDATIONS STATISTICAL PROPERTIES OF THE POWER GAUSSIAN APPROXIMATION ELECTROMAGNETICS OF UNHARMONIC WAVES – EXACTLY SOLVABLE MODELS PART IV NONLINEAR WAVES IN DISCRETE SYSTEMS QUANTUM BREATHERS IN AN ATTRACTIVE FERMIONIC HUBBARD MODEL QUANTUM BREATHERS IN A TRANSLATIONAL INVARIANT LATTICE TRAPPING IN A LATTICE WITH BROKEN TRANSLATIONAL SYMMETRY LOCALIZATION IN A CHAIN WITH IMPURITIES LOCALIZATION IN A TWISTED CHAIN LOCALIZATION IN A BENT CHAIN HIGHER NUMBER OF QUANTA ENERGY LOCALIZATION AND ?RST ORDER PHASE TRANSITION IN SOLIDS AND MOLECULES NONLINEAR MOLECULAR VIBRATIONS AND CHEMICAL DISSOCIATION EQUATIONS OF MOTION APPLICATIONS: 3-ATOM MOLECULE GENERAL THEORY AN ILLUSTRATIVE EXAMPLE, A LINEAR 3-ATOM MOLECULE AN IDEALIZED 3-ATOM MOLECULE IMPLICATION OF THE OBTAINED RESULT TO MELTING OF SOLIDS MARTENSITIC TRANSFORMATION OF A SMALL PURE CRYSTAL SOLITON DYNAMICS IN RANDOMLY PERTURBED DISCRETE LATTICES THE TODA CHAIN THE HOMOGENEOUS TODA CHAIN THE INVERSE SCATTERING TRANSFORM CONSERVED QUANTITIES SOLITON PROPAGATION WITH AN IMPURE SEGMENT PERTURBATION MODEL ASYMPTOTIC BEHAVIOR SMALL-AMPLITUDE SOLITON REGIME - WHITE NOISE LARGE-AMPLITUDE SOLITON REGIME - WHITE NOISE ROLE OF THE CORRELATION LENGTH THE ABLOWITZ-LADIK CHAIN THE HOMOGENEOUS ABLOWITZ-LADIK CHAIN A RANDOMLY PERTURBED ABLOWITZ-LADIK CHAIN THE MODEL: A RANDOM ON-SITE POTENTIAL ASYMPTOTIC BEHAVIOR OF THE SOLITON PARAMETERS EXISTENCE OF A CRITICAL NONLINEARITY ULTRAFAST ELECTRON TRANSFER: THE STANDARD THEORY REVISITED STANDARD THEORY OF ET: A THERMALLY ACTIVATED PROCESS BASIC HYPOTHESIS FOR AN IMPROVED THEORY DYNAMICAL EQUATION FOR ELECTRON TRANSFER AND DISSIPATION HAMILTON EQUATIONS PROPERTY OF THE RANDOM FORCE ENERGY DISSIPATION RECOVERING THE STANDARD MARCUS THEORY ELECTRON TRANSFER FROM DONOR TO ACCEPTOR: A DIMER MODEL MAIN PHYSICAL CONTRIBUTIONS TO ENERGY HT THE DIMER MODEL ADIABATIC ELECTRON TRANSFER AT NONZERO TEMPERATURE ENERGY BARRIER DURING ELECTRON TRANSFER NON ADIABATIC ELECTRON TRANSFER AT ZERO TEMPERATURE CLOSE TO THE INVERSION POINT TARGETED ELECTRON TRANSFER, COHERENT TRANSFER AND CATAL- YSIS CONCLUDING REMARKS NONLINEAR SPECTROSCOPY STUDY OF VIBRATIONAL SELF-TRAPPING IN HYDROGEN BONDED CRYSTALS RESULTS AND DISCUSSION THE AMIDE I MODE THE NH MODE N-METHYLACETAMIDE QUANTUM ANHARMONIC PHONONS IN THE FERMI-PASTA-ULAM CHAIN WORKING OUT THE SCHR¨ODINGER EQUATION RESULTS OBTAINED FOR A FPU CHAIN DYNAMICS OF THE PERTURBED ABLOWITZ-LADIK SOLITON BEYOND THE ADIABATIC APPROXIMATION THE MATRIX RIEMANN-HILBERT PROBLEM AND AL SOLITON SOLUTION PERTURBATION-INDUCED EVOLUTION OF RH DATA THE ?RST-ORDER APPROXIMATION TRAVELLING WAVES IN A PERTURBED DISCRETE SINE-GORDON EQUATION PERIODIC TRAVELLING WAVES-BIFURCATION ANALYSIS DYNAMICS OF MULTICOMPONENT SOLITONS IN PERTURBED LADDER LATTICES O O VAKHNENKO GENERAL MODEL OF PERTURBED LADDER LATTICES THREE- AND TWO-DIMENSIONAL SOLITONIC OSCILLATIONS IN UNIFORM LONGITUDINAL ?ELD SLALOM SOLITON DYNAMICS BETWEEN ZIGZAG-DISTRIBUTED IMPURITIES MIWA’S REPRESENTATION OF THE VOLTERRA HIERARCHY VOLTERRA HIERARCHY VH IN MIWA’S REPRESENTATION MIWA’S REPRESENTATION AND IST CONSERVATION LAWS BACKLUND TRANSFORMATIONS VOLTERRA AND OTHER HIERARCHIES MOVING TOPOLOGICAL SOLITONS IN THE DISCRETE KLEIN-GORDON EQUATION STATIC PROPERTIES OF DISCRETE KINKS DYNAMICS OF DISCRETE KINKS DYNAMICS OF DISCRETE SOLITONS IN MEDIA WITH VARYING NONLINEARITY SLOW MODULATIONS RAPID MODULATIONS ON CONTINUOUS LIMITS OF SOME GENERALIZED COMPRESSIBLE HEISENBERG SPIN CHAINS A LIST OF SOME SPIN SYSTEMS IN 1+1 DIMENSIONS L-EQUIVALENT COUNTERPARTS OF SPIN SYSTEMS ON THE GEOMETRY OF STATIONARY HEISENBERG FERROMAGNETS SOME FORMULAS ON THE THEORY OF SURFACES HEISENBERG FERROMAGNETS ASSOCIATED WITH THE SURFACES GENERALIZED SURFACES I NONLINEAR SYSTEMS: GENERAL TOPICS