zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The quantum Langevin equation from the independent-oscillator model. (English) Zbl 0656.60074
Quantum probability and applications III, Proc. Conf., Oberwolfach/FRG 1987, Lect. Notes Math. 1303, 103-106 (1988).

[For the entire collection see Zbl 0627.00022.]

Consider the quantum Langevin equation for the position operator x(t) of a Brownian particle in an extended potential V(x)

mx ¨+ - t μ(t-t ' )x ˙(t ' )dt ' +V ' (x)=F(t),

where the coupling to the heat bath is characterized by a friction or radiation- reaction force (with memory function μ (t)) and by a random Gaussian operator force F(t) with (symmetric) correlation

2 -1 <F(t)F(t ' )+F(t ' )F(t)>=π -1 0 [Re(μ ¯(ω+i0 + ))]ωcoth(ω/2kT)cosω(t-t ' )dω·

The term in square brackets completely characterizes the Langevin equation.

The paper shows that this model can be derived on the basis of the independent-oscillator model of the heat bath, where the Brownian particle is coupled with springs to a large number of surrounding bath particles.

Reviewer: C.A.Braumann

MSC:
60H99Stochastic analysis