Starting from first principles, this book introduces the fundamental concepts and methods of dissipative quantum mechanics and explores related phenomena in condensed matter systems. Major experimental achievements in cooperation with theoretical advances have brightened the field and brought it to the attention of the general community in natural sciences. Nowadays, working knowledge of dissipative quantum mechanics is an essential tool for many physicists. This book - originally published in 1990 and republished in 1999 and and 2008 as enlarged second and third editions - delves significantly deeper than ever before into the fundamental concepts, methods and applications of quantum dissipative systems. This fourth edition provides a self-contained and updated account of the quantum mechanics of open systems and offers important new material including the most recent developments. The subject matter has been expanded by about fifteen percent. Many chapters have been completely rewritten to better cater to both the needs of newcomers to the field and the requests of the advanced readership. Two chapters have been added that account for recent progress in the field. This book should be accessible to all graduate students in physics. Researchers will find this a rich and stimulating source.

Description-Table Of Contents

1. Introduction -- 2. Diverse limited approaches: a brief survey. 2.1. Langevin equation for a damped classical system. 2.2. New schemes of quantization. 2.3. Traditional system-plus-reservoir methods. 2.4. Stochastic dynamics in Hilbert space -- 3. System-plus-reservoir models. 3.1. Harmonic oscillator bath with linear coupling. 3.2. Ergodicity. 3.3. The spin-boson model. 3.4. Microscopic models. 3.5. Charging and environmental effects in tunnel junctions. 3.6. Nonlinear quantum environments -- 4. Imaginary-time approach and equilibrium dynamics. 4.1. General concepts. 4.2. Effective action and equilibrium density matrix. 4.3. Partition function of the open system. 4.4. Quantum statistical expectation values in phase space -- 5. Real-time path integrals and nonequilibrium dynamics. 5.1. Statement of the problem and general concepts. 5.2. Feynman-Vernon method for a product initial state. 5.3. Decoherence and friction. 5.4. General initial states and preparation function. 5.5. Complex-time path integral for the propagating function. 5.6. Real-time path integral for the propagating function. 5.7. Closed time contour representation. 5.8. Semiclassical regime. 5.9. Stochastic unraveling of influence functionals. 5.10. Non-Markovian dissipative dynamics in the semiclassical limit. 5.11. Brief summary and outlook -- 6. Damped linear quantum mechanical oscillator. 6.1. Fluctuation-dissipation theorem. 6.2. Stochastic modeling. 6.3. Susceptibility. 6.4. The position autocorrelation function. 6.5. Partition function and implications. 6.6. Mean square of position and momentum. 6.7. Equilibrium density matrix. 6.8. Quantum master equations for the reduced density matrix -- 7. Quantum free motion. 7.1. Spectral density, damping function and mass renormalization. 7.2. Displacement correlation and response function. 7.3. Ohmic friction. 7.4. Frequency-dependent friction. 7.5. Partition function and thermodynamic properties -- 8. The thermodynamic variational approach. 8.1. Centroid and the effective classical potential. 8.2. Variational method -- 9. Suppression of quantum coherence. 9.1. Nondynamical versus dynamical environment. 9.2. Suppression of transversal and longitudinal interferences. 9.3. Decoherence in the semiclassical picture. 9.4. Decoherence of electrons -- 10. Introduction -- 11. Classical rate theory: a brief overview. 11.1. Classical transition state theory. 11.2. Moderate-to-strong-damping regime. 11.3. Strong damping regime. 11.4. Weak-damping regime -- 12. Quantum rate theory: basic methods. 12.1. Formal rate expressions in terms of flux operators. 12.2. Quantum transition state theory. 12.3. Semiclassical limit. 12.4. Quantum tunneling regime. 12.5. Free energy method. 12.6. Centroid method -- 13. Multidimensional quantum rate theory. 13.1. The global metastable potential. 13.2. Periodic orbit and bounce -- 14. Crossover from thermal to quantum decay. 14.1. Normal mode analysis at the barrier top. 14.2. Turnover theory for activated rate processes. 14.3. The crossover temperature. ; 8 15. Thermally activated decay. 15.1. Rate formula above the crossover regime. 15.2. Quantum corrections in the pre-exponential factor. 15.3. The quantum Smoluchowski equation approach. 15.4. Multidimensional quantum transition state theory -- 16. The crossover region. 16.1. Beyond steepest descent above T[symbol]. 16.2. Beyond steepest descent below T[symbol]. 16.3. The scaling region -- 17. Dissipative quantum tunneling. 17.1. The quantum rate formula. 17.2. Thermal enhancement of macroscopic quantum tunneling. 17.3. Quantum decay in a cubic potential for Ohmic friction. 17.4. Quantum decay in a tilted cosine potential. 17.5. Concluding remarks -- 18. Introduction. 18.1. Truncation of the double-well to the two-state system. 18.2. Pair interaction in the charge picture -- 19. Thermodynamics. 19.1. Partition function and specific heat. 19.2. Ohmic dissipation. 19.3. Non-Ohmic spectral densities. 19.4. Relation between the Ohmic TSS and the Kondo model. 19.5. Equivalence of the Ohmic TSS with the 1/r[symbol] Ising model -- 20. Electron transfer and incoherent tunneling. 20.1. Electron transfer. 20.2. Incoherent tunneling in the nonadiabatic regime. 20.3. Single charge tunneling -- 21. Two-state dynamics: basics and methods. 21.1. Initial preparation, expectation values, and correlations. 21.2. Exact formal expressions for the system dynamics. 21.3. The noninteracting-blip approximation (NIBA). 21.4. The interacting-blip chain approximation (IBCA) -- 22. Two-state dynamics: sundry topics. 22.1. Symmetric TSS in the NIBA. 22.2. White-noise regime. 22.3. Weak quantum noise in the biased TSS. 22.4. Pure dephasing. 22.5. 1/f noise and decoherence. 22.6. The Ohmic TSS at and close to the Toulouse point. 22.7. Long-time behavior at T = 0 for K < 1: general discussion. 22.8. From weak to strong tunneling: relaxation and decoherence. 22.9. Thermodynamics from dynamics -- 23. The driven two-state system. 23.1. Time-dependent external fields. 23.2. Markovian regime. 23.3. High-frequency regime. 23.4. Quantum stochastic resonance. 23.5. Driving-induced symmetry breaking -- 24. Quantum particle in a washboard potential. 24.1. Introduction. 24.2. Weak- and tight-binding representation -- 25. Multi-state dynamics. 25.1. Quantum transport and quantum-statistical fluctuations. 25.2. Poissonian quantum transport. 25.3. Exact formal expressions for the system dynamics. 25.4. Mobility and diffusion. 25.5. The Ohmic case. 25.6. Exact solution in the Ohmic scaling limit at K = 1/2. 25.7. The effects of a thermal initial state. ; 8 26. Duality symmetry. 26.1. Duality for general spectral density. 26.2. Self-duality in the exactly solvable cases K = 1/2 and K = 2. 26.3. Duality and supercurrent in Josephson junctions. 26.4. Self-duality in the Ohmic scaling limit. 26.5. Exact scaling function at T = 0 for arbitrary K. 26.6. Full counting statistics at zero temperature. 26.7. Low temperature behavior of the characteristic function -- 27. Twisted partition function and nonlinear mobility. 27.1. Solving the imaginary-time Coulomb gas with Jack polynomials. 27.2. Nonlinear mobility -- 28. Charge transport in quantum impurity systems. 28.1. Generic models for transmission of charge through barriers. 28.2. Self-duality between weak and strong tunneling. 28.3. Full counting statistics of charge transfer -- 29. Quantum transport for sub- and super-Ohmic friction. 29.1. Tight-binding representation. 29.2. Weak-binding representation.