Quantum dissipative systems

Quantum dissipative systems / Ulrich Weiss.

Major advances in the quantum theory of macroscopic systems, in combination with stunning experimental achievements, have brightened the field and brought it to the attention of the general community in natural sciences. Today, working knowledge of dissipative quantum mechanics is an essential tool...

Full description

Saved in:
Bibliographic Details
Main Author: Weiss, U. (Ulrich)
Format: eBook
Language:English
Published: Singapore ; Hackensack, N.J. : World Scientific, ©2008.
Edition:3rd ed.
Series:Series in modern condensed matter physics ; v. 13.
Subjects:
Quantum theory.
Mathematical physics.
Thermodynamics.
Path integrals.
thermodynamics.
SCIENCE > Physics > Quantum Theory.
Mathematical physics
Path integrals
Quantum theory
Thermodynamics
Online Access:Click for online access
Table of Contents:
  • I. General theory of open quantum systems. 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. The Spin-Boson model. 3.3. Microscopic models. 3.4. Charging and environmental effects in tunnel junctions. 3.5. Nonlinear quantum environments
  • 4. Imaginary-time path integrals. 4.1. The density matrix: 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 dynamics. 5.1. Feynman-Vernon method for a product initial state. 5.2. Decoherence and friction. 5.3. General initial states and preparation function. 5.4. Complex-time path integral for the propagating function. 5.5. Real-time path integral for the propagating function. 5.6. Stochastic unraveling of influence functionals. 5.7. Brief summary and outlook
  • II. Few simple applications. 6. Damped harmonic oscillator. 6.1. Fluctuation-dissipation theorem. 6.2. Stochastic modeling. 6.3. Susceptibility for Ohmic friction and Drude damping. 6.4. The position autocorrelation function. 6.5. Partition function, internal energy and density of states. 6.6. Mean square of position and momentum. 6.7. Equilibrium density matrix. 7. Quantum Brownian free motion. 7.1. Spectral density. damping function and mass renormalization. 7.2. Displacement correlation and response function. 7.3. Ohmic damping. 7.4. Frequency-dependent damping. 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. Localized bath modes and universal decoherence
  • III. Quantum statistical decay. 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. 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. 15. Thermally activated decay. 15.1. Rate formula above the crossover regime. 15.2. Quantum corrections in the preexponential 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 washboard potential. 17.5. Concluding remarks
  • IV. The dissipative two-state system. 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. 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. Weak-coupling theory beyond the NIBA for a biased system. 21.5. The interacting-blip chain approximation. 21.6. Ohmic dissipation with K at and near [symbol]: exact results. 21.7. Long-time behaviour at T = 0 for K <1: general discussion. 21.8. From weak to strong tunneling: relaxation and decoherence. 21.9. Thermodynamics from dynamics. 22. The driven two-state system. 22.1. Time-dependent external fields. 22.2. Markovian regime. 22.3. High-frequency regime. 22.4. Quantum stochastic resonance. 22.5. Driving-induced symmetry breaking
  • V. The dissipative multi-state system. 23. Quantum Brownian particle in a washboard potential. 23.1. Introduction. 23.2. Weak- and tight-binding representation. 24. Multi-state dynamics. 24.1. Quantum transport and quantum-statistical fluctuations. 24.2. Poissonian quantum transport. 24.3. Exact formal expressions for the system dynamics. 24.4. Mobility and diffusion. 24.5. The Ohmic case. 24.6. Exact solution in the Ohmic scaling limit at K = [symbol]. 24.7. The effects of a thermal initial state. 25. Duality symmetry. 25.1. Duality for general spectral density. 25.2. Self-duality in the exactly solvable cases K = [symbol] and K = 2. 25.3. Duality and supercurrent in Josephson junctions. 25.4. Self-duality in the Ohmic scaling limit. 25.5. Exact scaling function at T = 0 for arbitrary K. 25.6. Full counting statistics at zero temperature. 25.7. Low temperature behaviour of the characteristic function. 25.8. The sub- and super-Ohmic case. 26. Charge transport in quantum impurity systems. 26.1. Generic models for transmission of charge through barriers. 26.2. Self-duality between weak and strong tunneling. 26.3. Full counting statistics.

Similar Items