Molecular Excitation Dynamics and Relaxation -- Contents -- Preface -- Part One Dynamics and Relaxation -- 1 Introduction -- 2 Overview of Classical Physics -- 2.1 Classical Mechanics -- 2.1.1 Concepts of Theoretical Mechanics: Action, Lagrangian, and Lagrange Equations -- 2.1.2 Hamilton Equations -- 2.1.3 Classical Harmonic Oscillator -- 2.2 Classical Electrodynamics -- 2.2.1 Electromagnetic Potentials and the Coulomb Gauge -- 2.2.2 Transverse and Longitudinal Fields -- 2.3 Radiation in Free Space -- 2.3.1 Lagrangian and Hamiltonian of the Free Radiation -- 2.3.2 Modes of the Electromagnetic Field -- 2.4 Light-Matter Interaction -- 2.4.1 Interaction Lagrangian and Correct Canonical Momentum -- 2.4.2 Hamiltonian of the Interacting Particle-Field System -- 2.4.3 Dipole Approximation -- 3 Stochastic Dynamics -- 3.1 Probability and Random Processes -- 3.2 Markov Processes -- 3.3 Master Equation for Stochastic Processes -- 3.3.1 Two-Level System -- 3.4 Fokker-Planck Equation and Diffusion Processes -- 3.5 Deterministic Processes -- 3.6 Diffusive Flow on a Parabolic Potential (a Harmonic Oscillator) -- 3.7 Partially Deterministic Process and the Monte Carlo Simulation of a Stochastic Process -- 3.8 Langevin Equation and Its Relation to the Fokker-Planck Equation -- 4 Quantum Mechanics -- 4.1 Quantum versus Classical -- 4.2 The Schrödinger Equation -- 4.3 Bra-ket Notation -- 4.4 Representations -- 4.4.1 Schrödinger Representation -- 4.4.2 Heisenberg Representation -- 4.4.3 Interaction Representation -- 4.5 Density Matrix -- 4.5.1 Definition -- 4.5.2 Pure versus Mixed States -- 4.5.3 Dynamics in the Liouville Space -- 4.6 Model Systems -- 4.6.1 Harmonic Oscillator -- 4.6.2 Quantum Well -- 4.6.3 Tunneling -- 4.6.4 Two-Level System -- 4.6.5 Periodic Structures and the Kronig-Penney Model -- 4.7 Perturbation Theory.

4.7.1 Time-Independent Perturbation Theory -- 4.7.2 Time-Dependent Perturbation Theory -- 4.8 Einstein Coefficients -- 4.9 Second Quantization -- 4.9.1 Bosons and Fermions -- 4.9.2 Photons -- 4.9.3 Coherent States -- 5 Quantum States of Molecules and Aggregates -- 5.1 Potential Energy Surfaces, Adiabatic Approximation -- 5.2 Interaction between Molecules -- 5.3 Excitonically Coupled Dimer -- 5.4 Frenkel Excitons of Molecular Aggregates -- 5.5 Wannier-Mott Excitons -- 5.6 Charge-Transfer Excitons -- 5.7 Vibronic Interaction and Exciton Self-Trapping -- 5.8 Trapped Excitons -- 6 The Concept of Decoherence -- 6.1 Determinism in Quantum Evolution -- 6.2 Entanglement -- 6.3 Creating Entanglement by Interaction -- 6.4 Decoherence -- 6.5 Preferred States -- 6.6 Decoherence in Quantum Random Walk -- 6.7 Quantum Mechanical Measurement -- 6.8 Born Rule -- 6.9 Everett or Relative State Interpretation of Quantum Mechanics -- 6.10 Consequences of Decoherence for Transfer and Relaxation Phenomena -- 7 Statistical Physics -- 7.1 Concepts of Classical Thermodynamics -- 7.2 Microstates, Statistics, and Entropy -- 7.3 Ensembles -- 7.3.1 Microcanonical Ensemble -- 7.3.2 Canonical Ensemble -- 7.3.3 Grand Canonical Ensemble -- 7.4 Canonical Ensemble of Classical Harmonic Oscillators -- 7.5 Quantum Statistics -- 7.6 Canonical Ensemble of Quantum Harmonic Oscillators -- 7.7 Symmetry Properties of Many-Particle Wavefunctions -- 7.7.1 Bose-Einstein Statistics -- 7.7.2 Pauli-Dirac Statistics -- 7.8 Dynamic Properties of an Oscillator at Equilibrium Temperature -- 7.9 Simulation of Stochastic Noise from a Known Correlation Function -- 8 An Oscillator Coupled to a Harmonic Bath -- 8.1 Dissipative Oscillator -- 8.2 Motion of the Classical Oscillator -- 8.3 Quantum Bath -- 8.4 Quantum Harmonic Oscillator and the Bath: Density Matrix Description -- 8.5 Diagonal Fluctuations.

8.6 Fluctuations of a Displaced Oscillator -- 9 Projection Operator Approach to Open Quantum Systems -- 9.1 Liouville Formalism -- 9.2 Reduced Density Matrix of Open Systems -- 9.3 Projection (Super)operators -- 9.4 Nakajima-Zwanzig Identity -- 9.5 Convolutionless Identity -- 9.6 Relation between the Projector Equations in Low-Order Perturbation Theory -- 9.7 Projection Operator Technique with State Vectors -- 10 Path Integral Technique in Dissipative Dynamics -- 10.1 General Path Integral -- 10.1.1 Free Particle -- 10.1.2 Classical Brownian Motion -- 10.2 Imaginary-Time Path Integrals -- 10.3 Real-Time Path Integrals and the Feynman-Vernon Action -- 10.4 Quantum Stochastic Process: The Stochastic Schrödinger Equation -- 10.5 Coherent-State Path Integral -- 10.6 Stochastic Liouville Equation -- 11 Perturbative Approach to Exciton Relaxation in Molecular Aggregates -- 11.1 Quantum Master Equation -- 11.2 Second-Order Quantum Master Equation -- 11.3 Relaxation Equations from the Projection Operator Technique -- 11.4 Relaxation of Excitons -- 11.5 Modified Redfield Theory -- 11.6 Förster Energy Transfer Rates -- 11.7 Lindblad Equation Approach to Coherent Exciton Transport -- 11.8 Hierarchical Equations of Motion for Excitons -- 11.9 Weak Interchromophore Coupling Limit -- 11.10 Modeling of Exciton Dynamics in an Excitonic Dimer -- 11.11 Coherent versus Dissipative Dynamics: Relevance for Primary Processes in Photosynthesis -- Part Two Spectroscopy -- 12 Introduction -- 13 Semiclassical Response Theory -- 13.1 Perturbation Expansion of Polarization: Response Functions -- 13.2 First Order Polarization -- 13.2.1 Response Function and Susceptibility -- 13.2.2 Macroscopic Refraction Index and Absorption Coefficient -- 13.3 Nonlinear Polarization and Spectroscopic Signals -- 13.3.1 N-wave Mixing -- 13.3.2 Pump Probe -- 13.3.3 Heterodyne Detection.

14 Microscopic Theory of Linear Absorption and Fluorescence -- 14.1 A Model of a Two-State System -- 14.2 Energy Gap Operator -- 14.3 Cumulant Expansion of the First Order Response -- 14.4 Equation of Motion for Optical Coherence -- 14.5 Lifetime Broadening -- 14.6 Inhomogeneous Broadening in Linear Response -- 14.7 Spontaneous Emission -- 14.8 Fluorescence Line-Narrowing -- 14.9 Fluorescence Excitation Spectrum -- 15 Four-Wave Mixing Spectroscopy -- 15.1 Nonlinear Response of Multilevel Systems -- 15.1.1 Two- and Three-Band Molecules -- 15.1.2 Liouville Space Pathways -- 15.1.3 Third Order Polarization in the Rotating Wave Approximation -- 15.1.4 Third Order Polarization in Impulsive Limit -- 15.2 Multilevel System in Contact with the Bath -- 15.2.1 Energy Fluctuations of the General Multilevel System -- 15.2.2 Off-Diagonal Fluctuations and Energy Relaxation -- 15.2.3 Fluctuations in a Coupled Multichromophore System -- 15.2.4 Inter-Band Fluctuations: Relaxation to the Electronic Ground State -- 15.2.5 Energetic Disorder in Four-Wave Mixing -- 15.2.6 Random Orientations of Molecules -- 15.3 Application of the Response Functions to Simple FWM Experiments -- 15.3.1 Photon Echo Peakshift: Learning About System-Bath Interactions -- 15.3.2 Revisiting Pump-Probe -- 15.3.3 Time-Resolved Fluorescence -- 16 Coherent Two-Dimensional Spectroscopy -- 16.1 Two-Dimensional Representation of the Response Functions -- 16.2 Molecular System with Few Excited States -- 16.2.1 Two-State System -- 16.2.2 Damped Vibronic System - Two-Level Molecule -- 16.3 Electronic Dimer -- 16.4 Dimer of Three-Level Chromophores - Vibrational Dimer -- 16.5 Interferences of the 2D Signals: General Discussion Based on an Electronic Dimer -- 16.6 Vibrational vs. Electronic Coherences in 2D Spectrum of Molecular Systems.

17 Two Dimensional Spectroscopy Applications for Photosynthetic Excitons -- 17.1 Photosynthetic Molecular Aggregates -- 17.1.1 Fenna-Matthews-Olson Complex -- 17.1.2 LH2 Aggregate of Bacterial Complexes -- 17.1.3 Photosystem I (PS-I) -- 17.1.4 Photosystem II (PS-II) -- 17.2 Simulations of 2D Spectroscopy of Photosynthetic Aggregates -- 17.2.1 Energy Relaxation in FMO Aggregate -- 17.2.2 Energy Relaxation Pathways in PS-I -- 17.2.3 Quantum Transport in PS-II Reaction Center -- 18 Single Molecule Spectroscopy -- 18.1 Historical Overview -- 18.2 How Photosynthetic Proteins Switch -- 18.3 Dichotomous Exciton Model -- Appendix -- A.1 Elements of the Field Theory -- A.2 Characteristic Function and Cumulants -- A.3 Weyl Formula -- A.4 Thermodynamic Potentials and the Partition Function -- A.5 Fourier Transformation -- A.6 Born Rule -- A.7 Green's Function of a Harmonic Oscillator -- A.8 Cumulant Expansion in Quantum Mechanics -- A.8.1 Application to the Double Slit Experiment -- A.8.2 Application to Linear Optical Response -- A.8.3 Application to Third Order Nonlinear Response -- A.9 Matching the Heterodyned FWM Signal with the Pump-Probe -- A.10 Response Functions of an Excitonic System with Diagonal and Off-Diagonal Fluctuations in the Secular Limit -- References -- Index.