COHERENT WAVE TRANSPORT IN LOW DIMENSIONAL RANDOM MEDIA

The following sections are included:

• Introduction

  • Three Phases of the Physics of Anderson Localization

  • Random Interference and Diffusion

  • Coherent Back-Scattering (CBS)

  • Conditions for Phase Coherent Transport: Mesoscopic Conductors and Conductance Fluctuations

• SCATTERING MATRIX APPROACH TO SAMPLE SPECIFIC QUANTUM RESISTANCE

  • The S-matrix: 1-Channel

  • The Transfer Matrix: l-Channel

  • Four-Probe Conductance: 1-Channel

  • Two-Probe Conductance: 1-Channel

  • Generalization to an N-Channel Conductor: Thick Wire

  • Symmetry and reciprocity Relations for Conductances

  • Reservoirs, Leads, Incoherence, Dissipation, etc.

• INVARIANT IMBEDDING APPROACH TO MESOSCOPIC FLUCTUATIONS: DISORDERED WIRES

  • Invariant Imbedding: 1-Channel Case

  • Phase distribution: 1-Channel case

  • Resistance Fluctuation: 1-Channel Case

  • Multi-Channel Generalization

• STATISTICS OF CONDUCTANCE FLUCTUATIONS: AN INFORMATION THEORETIC APPROACH

  • The Maximum Entropy Method

  • Weighing the Random Matrices: The Measure

  • Probability Measure dμ(M) for the Transfer Matrices: 1-Channel case

  • Global Statistics from Local MEM: l-Channel Case

  • Generalization of MEM to the N-Channel Case (Thick Disordered Conductor): The DMPK Equation

• LIGHT PROPAGATION THROUGH A RANDOM AMPLIFYING MEDIUM: A NOVEL OPTICAL MATTER

  • Coherent Light and Coherent Amplification

  • Feedback: Non-resonant Distributed

  • Electromagnetic Wave Propagation in a Random Amplifying Medium

• References