Path Integrals and Their Application to Dissipative Quantum Systems
Gert-Ludwig Ingold
- Vol. 611, pp 1-53
TLDR
In this article, the authors discuss the effects of entanglement between a quantum system and its environment on the system degree of freedom and the quantum superposition of quantum states in a process referred to as decoherence.Abstract:
The coupling of a system to its environment is a recurrent subject in this collection of lecture notes. The consequences of such a coupling are threefold. First of all, energy may irreversibly be transferred from the system to the environment thereby giving rise to the phenomenon of dissipation. In addition, the fluctuating force exerted by the environment on the system causes fluctuations of the system degree of freedom which manifest itself for example as Brownian motion. While these two effects occur both for classical as well as quantum systems, there exists a third phenomenon which is specific to the quantum world. As a consequence of the entanglement between system and environmental degrees of freedom a coherent superposition of quantum states may be destroyed in a process referred to as decoherence. This effect is of major concern if one wants to implement a quantum computer. Therefore, decoherence is discussed in detail in Chap. 5.read more
Citations
More filters
Journal ArticleDOI
Colloquium: Quantum fluctuation relations: Foundations and applications
TL;DR: In this paper, a self-contained exposition of the theory and applications of quantum fluctuation relations is presented, with a focus on work fluctuation relation for transiently driven closed or open quantum systems.
Journal ArticleDOI
Fluctuation Theorem for Arbitrary Open Quantum Systems
TL;DR: The validity of the Crooks theorem and of the Jarzynski equality is extended to open quantum systems because the thermodynamic equilibrium free energy of an open quantum system in contact with a thermal environment is the difference between thefree energy of the total system and that of the bare environment.
Journal ArticleDOI
Fundamental aspects of quantum Brownian motion
Peter Hänggi,Gert-Ludwig Ingold +1 more
TL;DR: The consequences of the time-reversal symmetry for an open dissipative quantum dynamics and a series of subtleties and possible pitfalls are discussed and the path integral methodology is applied to the decay of metastable states assisted by quantum Brownian noise.
The quantum theory of light.
TL;DR: In this article, the Planck's radiation law and the Einstein coefficients were used to describe the atom-radiation interaction and the quantum mechanics of optical fluctuations and coherence, respectively.
Journal ArticleDOI
Finite quantum dissipation: the challenge of obtaining specific heat
TL;DR: In this paper, a free particle coupled with finite strength to a bath is considered and the evaluation of its specific heat is performed using a harmonic oscillator bath of Drude type with cutoff frequency!D.
References
More filters
Journal ArticleDOI
Handbook of Mathematical Functions
A table of integrals
TL;DR: Basic Forms x n dx = 1 n + 1 x n+1 (1) 1 x dx = ln |x| (2) udv = uv − vdu (3) 1 ax + bdx = 1 a ln|ax + b| (4) Integrals of Rational Functions
Journal ArticleDOI
Statistical-Mechanical Theory of Irreversible Processes : I. General Theory and Simple Applications to Magnetic and Conduction Problems
TL;DR: In this paper, a general type of fluctuation-dissipation theorem is discussed to show that the physical quantities such as complex susceptibility of magnetic or electric polarization and complex conductivity for electric conduction are rigorously expressed in terms of timefluctuation of dynamical variables associated with such irreversible processes.
Journal ArticleDOI
The fluctuation-dissipation theorem
TL;DR: In this article, the linear response of a given system to an external perturbation is expressed in terms of fluctuation properties of the system in thermal equilibrium, which may be represented by a stochastic equation describing the fluctuation, which is a generalization of the familiar Langevin equation in the classical theory of Brownian motion.
Book
Quantum Dissipative Systems
TL;DR: In this paper, the authors present a survey of the various approaches to Quantum-Statistical metastability, including Imaginary-Time and Real-Time Approaches Influence Functional Method Phenomenological and Microscopic System-Plus-Reservoir Models Linear and Nonlinear Quantum Environments Ohmic, Super-Ohmic, and Sub-ohmic Dissipation Quantum Decoherence and Relaxation Correlation Functions, Response Functions, and Fluctuation-Dissipation Theorem Damped Quantum Mechanical Harmonic Oscillator Quantum Brownian Motion Thermodynamic Variational