HHL_rev.pdf (221.45 kB)
Spin-boson model through a Poisson-driven stochastic process
journal contribution
posted on 2016-06-07, 11:57 authored by Masao Hirokawa, Fumio Hiroshima, Jozsef LorincziWe 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.
History
School
- Science
Department
- Mathematical Sciences
Published in
MATHEMATISCHE ZEITSCHRIFTVolume
277Issue
3-4Pages
1165 - 1198 (34)Citation
HIROKAWA, M., HIROSHIMA, F. and LORINCZI, J., 2014. Spin-boson model through a Poisson-driven stochastic process. Mathematische Zeitschrift, 277 (3-4), pp.1165-1198Publisher
© Springer HeidelbergVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2014Notes
The final publication is available at Springer via http://dx.doi.org/10.1007/s00209-014-1299-1ISSN
0025-5874eISSN
1432-1823Publisher version
Language
- en