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Intro -- Preface -- Contents -- 1 The Classical Smoluchowski Equation -- 1.1 History -- 1.2 The Methods -- 1.3 The Fokker-Planck Equation -- 1.4 Discretization of the Fokker-Planck Equation -- 1.4.1 Forward Time Central Space (FTCS) Method -- 1.4.2 Crank-Nicholson Method -- 1.4.3 Stability Analysis -- 1.4.4 Example -- 1.5 Program 1.1, Matlab Code -- References -- 2 The Quantum Smoluchowski Equation -- 2.1 The Effective Dimensionless Diffusion Coefficient -- 2.2 Discretization of the Quantum Smoluchowski Equation -- 2.2.1 Forward Time Central Space (FTCS) Method -- 2.2.2 Crank-Nicholson Method -- 2.2.3 Numerical Stability -- References -- 3 Dynamics of Protons in DNA -- 3.1 The Hydrogen Bond -- 3.2 Molecular Orbital Description -- 3.3 Empirical Potential Functions -- 3.4 Semi Empirical Methods in Quantum Chemistry -- 3.5 The Dynamics of Protons in a Base Pair -- 3.6 The Tunneling Quantum Dynamics -- 3.6.1 Escape from a Metastable Well -- 3.6.2 The Crossover Temperature -- 3.7 Programa 3.1, Matlab Code -- References -- 4 The Interaction with the Environment -- 4.1 The Magalinskiǐ's Equation -- 4.2 Introduction -- 4.2.1 The Quantum Correlation Function -- References -- 5 Classical and Quantum Mechanochemical Coupling -- 5.1 Diffusion -- 5.2 Chemical Kinetics -- 5.3 Absolute Reaction Rate Theory -- 5.4 Classical Mechanochemical Coupling -- 5.4.1 Numerical Computation of Mechanochemical Coupling -- 5.5 Quantum Mechanochemical Coupling -- 5.6 Program 5.1, Matlab Code -- References -- 6 Photosynthesis and the Quantum Mechanochemical Model -- 6.1 Overview of the Light-Dependent Reactions -- 6.1.1 Photosystem II -- 6.1.2 Electron Transport Chains and Photosystem I -- 6.2 Adiabatic Approximation -- 6.3 Conical Intersections -- 6.4 The Born-Oppenheimer Approximation -- 6.4.1 Hamiltonian for Molecules -- 6.4.2 Nonadiabatic Processes.
6.4.3 The Noncrossing Rule -- 6.4.4 Landau-Zener Model -- 6.4.5 Berry's Phase or Geometric Phase -- 6.5 Photosynthetic Electron Transfer Controlledby Protein Relaxation -- 6.6 Model Hamiltonian -- 6.7 Dependence of the Rate Constant on Electron Position -- 6.8 Program 61, Matlab Code -- 6.9 Program 62, Matlab Code -- References -- 7 Entanglement, Coherence and Decoherence -- 7.1 Entanglement -- 7.2 Coherence and Decoherence -- 7.2.1 Experiment on Coherence -- 7.3 Example of Decoherence -- 7.3.1 The Quantum Langevin Equation -- 7.4 The Spin-Boson Model in Photosynthesis -- 7.4.1 Independent Boson Model -- 7.4.2 The Spectral Density Function -- 7.4.3 Time Evolution of the Density Matrix -- 7.5 The Liouville Equation for the Two-State Density Matrix -- 7.5.1 Obtention of the Parameters -- 7.5.2 Rabi Cycle -- 7.6 The Caldeira-Leggett Master Equation -- 7.6.1 Decoherence Time -- References -- 8 Excitons -- 8.1 Chlorophyll Excitations in the Fenna-Matthews-Olson Complex -- 8.2 Förster Theory of Fluorescent Resonance Energy in Pigment-Protein Complexes -- 8.3 Program 8.1, Matlab Code -- 8.4 Program 8.2, Matlab Code -- References -- 9 Long Wavelength Quantum Energy Exchange and Its Possible Role in Cellular Recognition and Communication -- 9.1 Introduction -- 9.2 Basic Ideas of Rytov's Theory -- 9.3 The Poynting Vector in Medium 3 -- 9.4 The Electric Field in Medium 3 -- 9.5 Integrations of the Electric Field Fourier's Squared Component -- 9.5.1 Preliminary Definitions -- 9.5.2 Another Computing Version -- 9.6 Program 9.1, Fortran Code -- 9.7 Program 9.2, Fortran Code -- 9.8 Program 9.3, Fortran Code -- References -- A Appendix -- A.1 Forced Oscillations -- A.2 Damped Oscillations -- A.2.1 Classification -- A.2.2 Summary -- A.2.2.1 (a) Overdamped Oscillations, γ2 ω0 -- A.2.2.2 (b) Underdamped Oscillations, γ2 < -- ω0.
A.2.2.3 (c) Critical Damping Oscillations, γ2 = ω0 -- B Appendix -- B.1 Electrical and Mechanical Systems Analogies -- C Appendix -- C.1 The Fluctuation-Dissipation Theorem -- D Appendix -- D.1 Integral Algorithm for Colored Noise Simulation -- E Appendix -- E.1 Basic Concepts of Quantum Mechanics -- E.2 Analogy of with Vectors -- E.3 Dirac's Notation -- E.4 Identity Operator -- E.5 Adjoint and Auto-Adjoint Operators -- E.6 Eigenvalues and Eigenstates -- E.7 Discrete Set of Orthogonal Base -- E.8 Closure Relation -- E.9 Uncertainty Principle: General Relation -- E.10 Representation r (Space) -- E.11 The Postulates of Quantum Mechanics -- E.12 Operators and Observable Quantities -- E.13 The Schrödinger Equation -- E.14 The Ehrenfest Theorem -- E.15 Linear Harmonic Oscillator -- F Appendix -- F.1 Introducing Quantum Optics -- F.2 Squeeze State -- F.3 Quantum Superposition-The Coherent State -- F.4 Coherent State Wave Function -- F.4.1 Time Evolution of the Coherent States -- F.5 Mixed States and the Density Matrix -- F.5.1 Pure States -- F.5.2 Mixed States -- F.6 The Wigner's Function -- F.6.1 Quantum Phase Spaces -- F.6.2 Some Properties -- F.6.3 Marginals -- F.7 The von Neumann Entropy -- F.8 Entropy of Entanglement -- F.8.1 Properties -- G Appendix -- G.1 Excitons -- G.1.1 Hamiltonian of Hydrogenic Model -- G.1.2 Band Structure -- References.
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Electrical Fluctuations in Polyelectrolytes / / by José Antonio Fornés
