### Abstract

We show a mathematical relation between the potential of the rotating wave approximation and an estimation of the fluctuation in Mori′s theory of generalized Brownian motion. We use this relation to prove that, when an autocorrelation function R_{A}(t), t ∈ R concerning the Bogoliubov scalar product is given for a certain quantum observable A in an equilibrium quantum system in finite volume, we can obtain a Hamiltonian H_{RWA} by making the rotating wave approximation from R_{A}(t) such that we reconstruct the autocorrelation function R_{A}(t) in the system governed by H_{RWA}.

Original language | English |
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Pages (from-to) | 185-210 |

Number of pages | 26 |

Journal | Annals of Physics |

Volume | 234 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 1994 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

**A mathematical relation between the potential of the rotating wave approximation and an estimation of the fluctuation in mori′s theory.** / Hirokawa, Masao.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - A mathematical relation between the potential of the rotating wave approximation and an estimation of the fluctuation in mori′s theory

AU - Hirokawa, Masao

PY - 1994/1/1

Y1 - 1994/1/1

N2 - We show a mathematical relation between the potential of the rotating wave approximation and an estimation of the fluctuation in Mori′s theory of generalized Brownian motion. We use this relation to prove that, when an autocorrelation function RA(t), t ∈ R concerning the Bogoliubov scalar product is given for a certain quantum observable A in an equilibrium quantum system in finite volume, we can obtain a Hamiltonian HRWA by making the rotating wave approximation from RA(t) such that we reconstruct the autocorrelation function RA(t) in the system governed by HRWA.

AB - We show a mathematical relation between the potential of the rotating wave approximation and an estimation of the fluctuation in Mori′s theory of generalized Brownian motion. We use this relation to prove that, when an autocorrelation function RA(t), t ∈ R concerning the Bogoliubov scalar product is given for a certain quantum observable A in an equilibrium quantum system in finite volume, we can obtain a Hamiltonian HRWA by making the rotating wave approximation from RA(t) such that we reconstruct the autocorrelation function RA(t) in the system governed by HRWA.

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UR - http://www.scopus.com/inward/citedby.url?scp=0038974648&partnerID=8YFLogxK

U2 - 10.1006/aphy.1994.1078

DO - 10.1006/aphy.1994.1078

M3 - Article

AN - SCOPUS:0038974648

VL - 234

SP - 185

EP - 210

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 2

ER -