### Abstract

We consider a two-state system linearly coupled to a collection of harmonic oscillators, the spin-boson Hamiltonian. Expanding the density matrix in terms of Pauli spin matrices, a set of coupled operator differential equations of motion is obtained by solving the Heisenberg equation. Using the cumulant expansion methods, the expectation values of the Pauli spin matrices are obtained and found to be valid for both coherent and incoherent regimes. The results are compared with other approaches.

Original language | English |
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Pages (from-to) | 593-605 |

Number of pages | 13 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 241 |

Issue number | 3-4 |

Publication status | Published - 1997 Jul 15 |

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### Keywords

- Population inversion
- Spin-boson Hamiltonian
- Two-state system

### ASJC Scopus subject areas

- Mathematical Physics
- Statistical and Nonlinear Physics

### Cite this

**Operator differential equation approach to the dissipative two-state system.** / Cho, Minhaeng.

Research output: Contribution to journal › Article

*Physica A: Statistical Mechanics and its Applications*, vol. 241, no. 3-4, pp. 593-605.

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TY - JOUR

T1 - Operator differential equation approach to the dissipative two-state system

AU - Cho, Minhaeng

PY - 1997/7/15

Y1 - 1997/7/15

N2 - We consider a two-state system linearly coupled to a collection of harmonic oscillators, the spin-boson Hamiltonian. Expanding the density matrix in terms of Pauli spin matrices, a set of coupled operator differential equations of motion is obtained by solving the Heisenberg equation. Using the cumulant expansion methods, the expectation values of the Pauli spin matrices are obtained and found to be valid for both coherent and incoherent regimes. The results are compared with other approaches.

AB - We consider a two-state system linearly coupled to a collection of harmonic oscillators, the spin-boson Hamiltonian. Expanding the density matrix in terms of Pauli spin matrices, a set of coupled operator differential equations of motion is obtained by solving the Heisenberg equation. Using the cumulant expansion methods, the expectation values of the Pauli spin matrices are obtained and found to be valid for both coherent and incoherent regimes. The results are compared with other approaches.

KW - Population inversion

KW - Spin-boson Hamiltonian

KW - Two-state system

UR - http://www.scopus.com/inward/record.url?scp=0031176304&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031176304&partnerID=8YFLogxK

M3 - Article

VL - 241

SP - 593

EP - 605

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 3-4

ER -