Abstract:
A non-Markovian treatment of the relaxation of a spin j is developed. The corresponding reduced collision operator admits a discrete spectral representation whose eginevalues are extracted in a high temperature limit. Then, assuming a phonon reservoir with a Debye-like density of phonon states, the time evolution of the collision operator is explicitly given, showing that the corresponding time decay arises from the branch points of its Laplace transform. The extraction of the analytic continuation of the transform allows the memory effects on the relaxation frequencies (resolvent poles) to be analyzed and the validity of the rotating-wave approximation to be tested. © 1990.
Referencias:
- George, Prigogine, Rosenfeld, (1972) Mat. Fys. Medd., 38, p. 12
- Prigogine, George, Henin, Rosenfeld, (1973) Chem. Scripta, 4, p. 5
- George, (1973) Physica, 65, p. 277
- George, Mayné, (1987) J. Stat. Phys., 48, p. 1343
- Courbage, Mathematical problems of irreversible statistical mechanics for quantum systems. I: Analytic continuation of the collision and destruction operators by spectral deformation method (1982) Journal of Mathematical Physics, 23, p. 646
- Courbage, Mathematical problems of irreversible statistical mechanics for quantum systems. II: On the singularities of (Ψ(z)−z)−1 and the pseudo‐Markovian equation. Application to Lee model (1982) Journal of Mathematical Physics, 23, p. 652
- Remarks on a recent article of Ch. Obcemea and E. Brändas on the theory of subdynamics (1986) Annals of Physics, 166, p. 250
- Grecos, Guo, Guo, (1975) Physica A, 80, p. 421
- Linderberg, West, Statistical properties of quantum systems: The linear oscillator (1984) Physical Review A, 30, p. 568
- Cataldo, Hernández, (1988) J. Stat. Phys., 53, p. 673
- Argyres, Kelley, (1964) Phys. Rev., 134, p. A98
- Haake, (1973) Springer Tracts in Modern Physics, 66. , Springer, Berlin
- Willis, Picard, (1974) Phys. Rev. A, 9, p. 1343
- Emptage, Hawrylak, Bose, (1982) Phys. Rev. A, 26, p. 3508
- Haake, (1969) Z. Phys., 223, p. 353
- Dirac, The Quantum Theory of the Emission and Absorption of Radiation (1927) Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 114, p. 243
- Weisskopf, Wigner, (1930) Z. Phys., 63, p. 54
- Oppenheim, (1973) Electron Spin Relaxation in Liquids, , L.T. Muus, P.W. Atkins, Plenum, New York
- Seshadri, Linderberg, (1982) Physica A, 115, p. 501
- Haken, (1978) Synergetics, an Introduction, , Springer, Berlin
- Fox, Physical applications of multiplicative stochastic processes. II. Derivation of the Bloch equations for magnetic relaxation (1974) Journal of Mathematical Physics, 15, p. 217
- Debye, (1929) Polar Molecules, , Dover, New York
- Lindenberg, Mohanty, Seshadri, (1983) Physica A, 119, p. 1
- Hernández, Cataldo, Semiclassical description of harmonic quantal Brownian motion (1989) Physical Review A, 39, p. 2034
- Henin, (1981) Physica A, 108, p. 305
- Metiu, Kitahara, Ross, (1975) J. Chem. Phys., 63, p. 5116
- Haake, (1969) Z. Phys., 223, p. 364
- Cataldo, Hernández, (1988) J. Stat. Phys., 50, p. 383
- H.M. Cataldo, to be published; Muskhelishvili, (1953) Singular Integral Equations, , Noordhoff, Groningen
Citas:
---------- APA ----------
(1990)
. Non-Markovian relaxation of a quantum system. Physica A: Statistical Mechanics and its Applications, 165(2), 249-269.
http://dx.doi.org/10.1016/0378-4371(90)90194-W---------- CHICAGO ----------
Cataldo, H.M.
"Non-Markovian relaxation of a quantum system"
. Physica A: Statistical Mechanics and its Applications 165, no. 2
(1990) : 249-269.
http://dx.doi.org/10.1016/0378-4371(90)90194-W---------- MLA ----------
Cataldo, H.M.
"Non-Markovian relaxation of a quantum system"
. Physica A: Statistical Mechanics and its Applications, vol. 165, no. 2, 1990, pp. 249-269.
http://dx.doi.org/10.1016/0378-4371(90)90194-W---------- VANCOUVER ----------
Cataldo, H.M. Non-Markovian relaxation of a quantum system. Phys A Stat Mech Appl. 1990;165(2):249-269.
http://dx.doi.org/10.1016/0378-4371(90)90194-W