GENERALIZED CUMULANT EXPANSION METHOD
The moment generating function of a set of stochastic variables defines the cumulants or the semi-invariants and the cumulant function. It is possible, simply by formal properties of exponential functions, to generalize to a great extent the concepts of cumulants and cumulant function. The stochastic variables to be considered need not be ordinary c-numbers but they may be q-numbers such as used in quantum mechanics. The exponential function which defines a moment generating function may be any kind of generalized exponential, for example an ordered exponential with a certain prescription for ordering q-number variables. The definition of average may be greatly generalized as far as the condition is fulfilled that the average of unity is unity. After statements of a few basic theorems these generalizations are discussed here with certain examples of application. This generalized cumulant expansion provides us with a point of view from which many existent methods in quantum mechanics and statistical mechanics can be unified. (auth)
- Research Organization:
- Tokyo Univ.
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-17-003365
- OSTI ID:
- 4764483
- Journal Information:
- J. Phys. Soc. Japan, Journal Name: J. Phys. Soc. Japan Vol. Vol: 17
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
Similar Records
The generalized cumulant expansion approach to stochastic reductions in molecular collision dynamics: Applications to collisional energy transfer
Analytical solution of the elastic Boltzmann transport equation in an infinite uniform medium using cumulant expansion
Double stochastic matrices in quantum mechanics
Journal Article
·
Wed Jun 01 00:00:00 EDT 1977
· J. Chem. Phys.; (United States)
·
OSTI ID:7216442
Analytical solution of the elastic Boltzmann transport equation in an infinite uniform medium using cumulant expansion
Journal Article
·
Thu Apr 27 00:00:00 EDT 2000
· Journal of Physical Chemistry B: Materials, Surfaces, Interfaces, amp Biophysical
·
OSTI ID:20050854
Double stochastic matrices in quantum mechanics
Journal Article
·
Fri Aug 01 00:00:00 EDT 1997
· Foundations of Physics
·
OSTI ID:669885