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

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

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
"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 G. Leibfried W. Paul Springer - Verlag Berlin Heidelberg New York 1973
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
B .I 3 ", ." .9 - Z S E 'S 0 m Z O E O 2 3 - 2 . 2 . a G 2 V 1 2 .2 .'1 "a .z 0 Z Z Q Q G G b O d '
Image of page 2
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
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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.
Image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern