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447

Index

Aabsorption coefficient, 286action functional, 8, 228adiabatic approximation, 102Anderson localization, 130antisymmetric wavefunction, 177

BBloch theorem, 77, 119Bloch wavefunction, 77Boltzmann statistics, 170Born approximation, 247Born rule, 55, 149Born–Oppenheimer approximation, 102Bose–Einstein statistics, 93, 179boson, 177bra vector, 56Brownian motion, 27

CCaldeira–Leggett model, 190canonical equations, 10canonically conjugated momentum, 10Chapman–Kolmogorov equation, 33charge-transfer exciton, 121classical harmonic oscillator, 11closed system, 162coherences, 63coherent states, 98conditional probability, 30continuity equation, 15correspondence principle, 52Coulomb gauge, 14

Ddamped mode, 206Davydov ansatz, 127Davydov splitting, 109, 118Davydov subbands, 117

de Broglie wavelength, 52decoherence, 139, 144density matrix, 61density matrix tomography, 371density of modes, 19density operator, 62dephasing, 300detailed balance condition, 35dipole–dipole interaction, 107disorder, 305displaced oscillator, 203displacement operator, 99, 360displacement vector, 25doorway-window representation, 352double excited state, 112double quantum coherence, 326double sided Feynman diagrams, 322

Eeffective mass, 81Einstein coefficient, 90electromagnetic field modes, 94energy gap operator, 297energy relaxation, 295entanglement, 136entropy, 163Euclidean action, 231excitation self-trapping, 126excited state absorption, 291, 352excited state emission, 291, 352excitons, 107, 116expectation value, 55

FFermi golden rule, 88–90Fermi–Dirac statistics, 93, 181fermion, 177Feynman–Vernon functional, 234filter, 150

Molecular Excitation Dynamics and Relaxation, First Edition. L. Valkunas, D. Abramavicius, and T. Mancal.© 2013 WILEY-VCH Verlag GmbH & Co. KGaA. Published 2013 by WILEY-VCH Verlag GmbH & Co. KGaA.

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448 Index

fluctuation–dissipation theorem, 193, 196fluorescence blinking, 404fluorescence excitation spectrum, 312fluorescence intermittency, 404fluorescence line narrowing, 309Fokker–Planck equation, 39four wave mixing, 288Franck–Condon energy, 106Franck–Condon factor, 360Franck–Condon transition, 203Frenkel exciton, 112

Ggauge function, 14gauge invariance, 14generalized coordinates, 8generalized master equation, 247Green’s function, 66ground state bleach, 291, 352

HHamilton equations, 10Hamilton principle, 8Hamiltonian density, 18harmonic oscillator, 11, 41heat, 163Heaviside step function, 285Heisenberg representation, 59Heisenberg uncertainty principle, 52Heitler–London approximation, 108, 112Helmholtz theorem, 15heterodyne detection, 293hierarchical equations of motion, 244, 263highest occupied molecular orbital, 122high-temperature limit, 175Hilbert space, 53homogeneous broadening, 305Huang–Rhys factor, 203, 362

Iindependent events, 30induced absorption, 291, 352induced polarization, 282influence functional, 232inhomogeneous broadening, 305interaction representation, 60irreversible process, 163isolated system, 162

JJ aggregates, 115

Kket vector, 56

kinetic energy, 8Kolmogorov axioms, 29

LLagrange equation, 9Lagrangian, 8, 227Lagrangian density, 17Lambert–Beers law, 286Langevin equation, 47lifetime induced dephasing, 301Lindblad equation, 260line shape function, 298linear susceptibility, 285Liouville equation, 40Liouville space, 66Liouville space pathways, 319Liouville superoperator, 210Liouville theorem, 169Liouvillian, 210local oscillator, 293lowest unoccupied molecular orbital, 122low-temperature limit, 184

MMarkov process, 32master equation, 35Maxwell–Liouville equations, 279microcanonical ensemble, 167minimal coupling Hamiltonian, 23mixed states, 64mixing angle, 111modes of electromagnetic fields, 18modified Redfield theory, 256molecular exciton, 101

NNakajima–Zwanzig identity, 215nonadiabaticity operator, 103nonlocality, 136nonphotochemical quenching, 405nonrephasing pathway, 326

Oopen system, 162overdamped mode, 206, 207

Pp A Hamiltonian, 23partially deterministic process, 44partition function, 170path integral, 227Pauli commutation relations, 114Pauli exclusion principle, 93, 177permanent, 177

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Index 449

phase space, 6, 172photon echo effect, 338photon echo peakshift, 342physical delta function, 327Poisson brackets, 41, 168potential energy, 8preferred states, 145probability, 29probability amplitude, 55probability space, 28probability theory, 27pump probe experiment, 291pure dephasing, 295

Qquantum entropy, 168quantum harmonic oscillator, 67, 174, 183,

196quantum Langevin equation, 195

RRaman scattering, 222random process, 31random variables, 31Rashba effect, 130Redfield equation, 250reorganization energy, 106, 206rephasing pathway, 326resonance interaction, 109response function, 282rotating-wave approximation, 198, 251, 323

Sscalar potential, 14Schrödinger representation, 57secular approximation, 250secular Redfield equation, 252single-exciton state, 113Slater determinant, 177spectral density, 185, 194spectral diffusion, 404

spontaneous emission, 90state vector, 53stationary Schrödinger equation, 54statistical mixture, 64stimulated emission, 291, 352stochastic Liouville equation, 244stochastic Schrödinger equation, 239, 240stochasticity, 27Stokes shift, 122superoperator, 66superselection, 145supramolecule, 23system state, 162system–bath coupling, 190

Ttheorem of large numbers, 29thermal contact, 162thermal equilibrium, 162tight-binding approach, 122time-ordered exponential, 58, 143total density matrix, 295transition probability, 31Trapped exciton, 130two dimensional pump probe, 347two-photon absorption, 222

Uundamped mode, 206

Vvacuum fluctuations, 183vector potential, 14

Wwaiting time distribution, 45Wannier–Mott excitons, 119, 121Wiener–Khinchin theorem, 187

Zzero phonon line, 311