Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Stochastic differential equations for models of non-relativistic matter interacting with quantized radiation fields (1402.2242v2)

Published 10 Feb 2014 in math-ph, math.MP, and math.PR

Abstract: We discuss Hilbert space-valued stochastic differential equations associated with the heat semi-groups of the standard model of non-relativistic quantum electrodynamics and of corresponding fiber Hamiltonians for translation invariant systems. In particular, we prove the existence of a stochastic flow satisfying the strong Markov property and the Feller property. To this end we employ an explicit solution ansatz. In the matrix-valued case, i.e., if the electron spin is taken into account, it is given by a series of operator-valued time-ordered integrals, whose integrands are factorized into annihilation, preservation, creation, and scalar parts. The Feynman-Kac formula implied by these results is new in the matrix-valued case. Furthermore, we discuss stochastic differential equations and Feynman-Kac representations for an operator-valued integral kernel of the semi-group. As a byproduct we obtain analogous results for Nelson's model.

Summary

We haven't generated a summary for this paper yet.