Our discussion of dissipative phenomena has been based on two distinct examples of stochastic processes, viz., the discrete jump process and the continuous diffusion process. From a microscopic perspective, the jump process is modeled in terms of a single magnetic spin in contact with a heat bath (see Chap. 1). This model is generalizable to the case of an interacting many-body system, described by an Ising model (see Chap. 2). In Chaps. 3–6, we discussed various examples of phase ordering systems, which are described by generalizations of kinetic Ising models and their coarse-grained counterparts. In Chap. 7, we encountered a natural extension of the jump process to the quantum domain, i.e., the spin-boson model, where a single spin is subjected to mutually perpendicular magnetic fields in order to generate non-commuting quantum dynamics. Additionally, the bath is taken to be quantum-mechanical in Chap. 8, and is described by non-interacting bosons.
KeywordsLandau Level Langevin Equation Heat Bath Jump Process Quantum Harmonic Oscillator
Unable to display preview. Download preview PDF.
- 492.G.-L. Ingold, in Quantum Transport and Dissipation ( Wiley-VCH, Weinheim 1998 )Google Scholar
- 494.S. Ichimaru, Basic Principles of Plasma Physics: A Statistical Approach ( Benjamin-Cummings, Reading, MA 1973 )Google Scholar
- 495.J.J. Sakurai, Modern Quantum Mechanics, Second Edition ( Addison-Wesley, Reading, MA 1994 )Google Scholar
- 497.J.H. Van Vleck, Theory of Electric and Magnetic Susceptibilities (Oxford University Press, London 1932 )Google Scholar
- 498.Mesoscopic Phenomena in Solids, ed. by B.L. Altshuler, P.A. Lee and R.A. Webb (North-Holland, Amsterdam 1991)Google Scholar
- 501.N. Bohr, Ph.D. Thesis 1911, in Collected Works Vol. I ( North-Holland, Amsterdam 1972 )Google Scholar
- 502.H.J. van Leeuwen, J. Phys. (Paris) 2, 361 (1921)Google Scholar
- 503.R. Peierls, Surprises in Theoretical Physics ( Princeton University Press, Princeton 1979 )Google Scholar
- 504.C.G. Darwin, Proc. Cambridge Philos. Soc. 27, 86 (1930)Google Scholar
- 506.X.L. Li, G.W. Ford and R.F. O’Connell, Phys. Rev. A 41, 5287 (1990); Phys. Rev. E 53, 3359 (1996)Google Scholar