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
N1 - Funding Information:
FH acknowledges support of Grant-in-Aid for Science Research (B) 20340032 from JSPS and Grant-in-Aid for Challenging Exploratory Research 22654018 from JSPS . We thank Itaru Sasaki for useful discussions and comments.
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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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 -