Abstract
We give a formula in terms of a joint Gibbs measure on Brownian paths and the measure of a random-time Poisson process of the ground state expectations of fractional (in fact, any real) powers of the boson number operator in the Nelson model. We use this representation to obtain tight two-sided bounds. As applications, we discuss the polaron and translation invariant Nelson models.
| Original language | English |
|---|---|
| Pages (from-to) | 437-447 |
| Number of pages | 11 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 395 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Nov 15 2012 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
Cite this
A probabilistic representation of the ground state expectation of fractional powers of the boson number operator. / Hiroshima, Fumio; Lorinczi, József; Takaesu, Toshimitsu.
In: Journal of Mathematical Analysis and Applications, Vol. 395, No. 2, 15.11.2012, p. 437-447.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A probabilistic representation of the ground state expectation of fractional powers of the boson number operator
AU - Hiroshima, Fumio
AU - Lorinczi, József
AU - Takaesu, Toshimitsu
PY - 2012/11/15
Y1 - 2012/11/15
N2 - We give a formula in terms of a joint Gibbs measure on Brownian paths and the measure of a random-time Poisson process of the ground state expectations of fractional (in fact, any real) powers of the boson number operator in the Nelson model. We use this representation to obtain tight two-sided bounds. As applications, we discuss the polaron and translation invariant Nelson models.
AB - We give a formula in terms of a joint Gibbs measure on Brownian paths and the measure of a random-time Poisson process of the ground state expectations of fractional (in fact, any real) powers of the boson number operator in the Nelson model. We use this representation to obtain tight two-sided bounds. As applications, we discuss the polaron and translation invariant Nelson models.
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UR - http://www.scopus.com/inward/citedby.url?scp=84864024443&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2012.04.076
DO - 10.1016/j.jmaa.2012.04.076
M3 - Article
AN - SCOPUS:84864024443
VL - 395
SP - 437
EP - 447
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 2
ER -