Abstract
We give a functional integral representation of the semigroup generated by the spin-boson Hamiltonian by making use of a Poisson point process and a Euclidean field. We present a method of constructing Gibbs path measures indexed by the full real line which can be applied also to more general stochastic processes with jump discontinuities. Using these tools we then show existence and uniqueness of the ground state of the spin-boson, and analyze ground state properties. In particular, we prove super-exponential decay of the number of bosons, Gaussian decay of the field operators, derive expressions for the positive integer, fractional and exponential moments of the field operator, and discuss the field fluctuations in the ground state.
| Original language | English |
|---|---|
| Pages (from-to) | 1165-1198 |
| Number of pages | 34 |
| Journal | Mathematische Zeitschrift |
| Volume | 277 |
| Issue number | 3-4 |
| DOIs | |
| Publication status | Published - Jan 1 2014 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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Spin-boson model through a Poisson-driven stochastic process. / Hirokawa, Masao; Hiroshima, Fumio; Lőrinczi, József.
In: Mathematische Zeitschrift, Vol. 277, No. 3-4, 01.01.2014, p. 1165-1198.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Spin-boson model through a Poisson-driven stochastic process
AU - Hirokawa, Masao
AU - Hiroshima, Fumio
AU - Lőrinczi, József
PY - 2014/1/1
Y1 - 2014/1/1
N2 - We give a functional integral representation of the semigroup generated by the spin-boson Hamiltonian by making use of a Poisson point process and a Euclidean field. We present a method of constructing Gibbs path measures indexed by the full real line which can be applied also to more general stochastic processes with jump discontinuities. Using these tools we then show existence and uniqueness of the ground state of the spin-boson, and analyze ground state properties. In particular, we prove super-exponential decay of the number of bosons, Gaussian decay of the field operators, derive expressions for the positive integer, fractional and exponential moments of the field operator, and discuss the field fluctuations in the ground state.
AB - We give a functional integral representation of the semigroup generated by the spin-boson Hamiltonian by making use of a Poisson point process and a Euclidean field. We present a method of constructing Gibbs path measures indexed by the full real line which can be applied also to more general stochastic processes with jump discontinuities. Using these tools we then show existence and uniqueness of the ground state of the spin-boson, and analyze ground state properties. In particular, we prove super-exponential decay of the number of bosons, Gaussian decay of the field operators, derive expressions for the positive integer, fractional and exponential moments of the field operator, and discuss the field fluctuations in the ground state.
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UR - http://www.scopus.com/inward/citedby.url?scp=85027920326&partnerID=8YFLogxK
U2 - 10.1007/s00209-014-1299-1
DO - 10.1007/s00209-014-1299-1
M3 - Article
VL - 277
SP - 1165
EP - 1198
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
IS - 3-4
ER -