Papers

Peer-reviewed
Aug, 2014

Spin-boson model through a Poisson-driven stochastic process

MATHEMATISCHE ZEITSCHRIFT
  • Masao Hirokawa
  • ,
  • Fumio Hiroshima
  • ,
  • Jozsef Lorinczi

Volume
277
Number
3-4
First page
1165
Last page
1198
Language
English
Publishing type
Research paper (scientific journal)
DOI
10.1007/s00209-014-1299-1
Publisher
SPRINGER HEIDELBERG

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.

Link information
DOI
https://doi.org/10.1007/s00209-014-1299-1
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000339343900031&DestApp=WOS_CPL
URL
http://gateway.isiknowledge.com/gateway/Gateway.cgi?&GWVersion=2&SrcAuth=ShinshuUniv&SrcApp=ShinshuUniv&DestLinkType=FullRecord&DestApp=WOS&KeyUT=000339343900031
ID information
  • DOI : 10.1007/s00209-014-1299-1
  • ISSN : 0025-5874
  • eISSN : 1432-1823
  • Web of Science ID : WOS:000339343900031

Export
BibTeX RIS