Quantum Statistics in Optics and Solid-state Physics - Graham, Haake

Quantum Statistics in Optics and Solid-state Physics - Graham, Haake

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"N TWNGER MODERN TRACTS PHYSICS Ergebnisse der exakten Natur- wissenschaften Volume 66 Editor: G. Hohler Associate Editor: E.A. Niekisch Editorial Board: S. Flugge J. Hamilton F. Hund H. Lehmann Leibfried W. Paul Springer - Verlag Berlin Heidelberg New York 1973
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B .I 3 ", ." .9 - ZSE 'S 0 m Z OEO 2 -2.2 .aG2V12 .2 .'1 "a .z ZZQQ GGbOd'
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Statistical Theory of Instabilities in Stationary Non- equilibrium Systems with Applications to Lasers and Nonlinear Optics Contents A . General Part .............................. 2 1 . Introduction and General Survey ..................... 2 2 . Continuous Markoff Systems ...................... 10 2.1. Basic Assumptions and Equations of Motion .............. 10 .... 2.2. Nonequilibrium Theory as a Generalization of Equilibrium Theory 15 ............ 2.3. Generalization of the Onsager-Machlmp Theory 17 ....................... 3 . The Stationary Distribution 21 3.1. Stability and Uniqueness 22 3.2. Consequences of Symmetry 25 3.3. Dissipation-Fluctuation Theorem for Stationary Nonequilibrium States . . 29 4 . Systems with Detailed Balance 30 4.1. Microscopic Reversibility and Detailed Balance ............. 31 4.2. The Potential Conditions 33 4.3. Consequences of the Potential Conditions ............... 36 B . Application to Optics .......................... 38 5 . Applicability of the Theory to Optical Instabilities 38 5.1. Validity of the Assumptions; the Observables 39 5.2. Outline of the Microscopic Theory .................. 42 5.3. Threshold Phenomena in Nonlinear Optics and Phase Transitions ..... 45 6 . Application to the Laser ......................... 47 6.1. Single Mode Laser 48 6.2. Multimode Laser with Random Phases ................ 52 6.3. Multimode Laser with Mode-Locking ................. 58 6.4. Light Propagation in an Infinite Laser Medium 64 7 . Parametric Oscillation 68 .......... 7.1. The Joint Stationary Distribution for Signal and Idler 69 7.2. Subharmonic Oscillation 73 8 . Simultaneous Application of the Microscopic and the Phenomenological Theory ................................ 74 8.1. A Class of Scattering Processes in Nonlinear Optics and Detailed Balance . . 75 8.2. Fokker-Planck Equations for the P-representation and the Wigner Distribution ............................ 79 8.3. Stationary Distribution for the General Process 81 8.4. Examples ............................. 82 References 95
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R. Graham: Statistical Theory of Instabilities in Stationary Nonequilibrium Systems A. General Part 1. Introduction and General Survey The transition of a macroscopic system from a disordered, chaotic state to an ordered more regular state is a very general phenomenon as is testified by the abundance of highly ordered macroscopic systems in nature. These transitions are of special interest, if the change in order is structural, i.e. connected with a change in the symmetry of the system's state. The existence of such symmetry changing transitions raises two general theoretical questions. In the first place one wants to know the conditions under which the transitions occur. Secondly, the mechanisms which characterize them are of interest. Since the entropy of a system decreases, when its order is increased, it is clear from the second law of thermodynamics that transitions to states with higher ordering can only take place in open systems inter- acting with their environment.
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Quantum Statistics in Optics and Solid-state Physics - Graham, Haake

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