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Title: Spin-boson model through a Poisson-driven stochastic process
Authors: Hirokawa, Masao
Hiroshima, Fumio
Lorinczi, Jozsef
Keywords: Poisson process
Cadlag paths
Gibbs measure
Spin-boson operator
Ground state
Issue Date: 2014
Publisher: © Springer Heidelberg
Citation: HIROKAWA, M., HIROSHIMA, F. and LORINCZI, J., 2014. Spin-boson model through a Poisson-driven stochastic process. Mathematische Zeitschrift, 277 (3-4), pp.1165-1198
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.
Description: The final publication is available at Springer via http://dx.doi.org/10.1007/s00209-014-1299-1
Version: Accepted for publication
DOI: 10.1007/s00209-014-1299-1
URI: https://dspace.lboro.ac.uk/2134/21507
Publisher Link: http://dx.doi.org/10.1007/s00209-014-1299-1
ISSN: 0025-5874
Appears in Collections:Published Articles (Maths)

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