### Abstract

For the purpose of understanding the quantum behaviour such as quantum decoherence, fluctuations, dissipation, entanglement and teleportation of a mesoscopic or macroscopic object interacting with a general environment, we derive here a set of exact master equations for the reduced density matrix of N interacting harmonic oscillators in a heat bath with arbitrary spectral density and temperature. Two classes of problems of interest to us which these equations can be usefully applied to are that of the quantum dynamics of nanoelectromechanical oscillators and the entanglement evolution of multipartite macroscopic states such as quantum superposition of mirrors in a high Q cavity. To address a key conceptual issue for macroscopic quantum phenomena we examine the conditions for an assumption often implicitly made in these studies to be valid, namely, that the quantum behaviour of a macroscopic object in an environment can be accurately represented by only treating the dynamics of its centre-of-mass variable. We also mention how these results can be used to calculate the uncertainty principle governing a macroscopic object at finite temperature.

Original language | English |
---|---|

Pages (from-to) | 432-444 |

Number of pages | 13 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 387 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - 2008 Jan 15 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physica A: Statistical Mechanics and its Applications*,

*387*(2-3), 432-444. https://doi.org/10.1016/j.physa.2007.09.025

}

*Physica A: Statistical Mechanics and its Applications*, vol. 387, no. 2-3, pp. 432-444. https://doi.org/10.1016/j.physa.2007.09.025

**Quantum Brownian motion of a macroscopic object in a general environment.** / Chou, Chung-Hsien; Hu, B. L.; Yu, Ting.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Quantum Brownian motion of a macroscopic object in a general environment

AU - Chou, Chung-Hsien

AU - Hu, B. L.

AU - Yu, Ting

PY - 2008/1/15

Y1 - 2008/1/15

N2 - For the purpose of understanding the quantum behaviour such as quantum decoherence, fluctuations, dissipation, entanglement and teleportation of a mesoscopic or macroscopic object interacting with a general environment, we derive here a set of exact master equations for the reduced density matrix of N interacting harmonic oscillators in a heat bath with arbitrary spectral density and temperature. Two classes of problems of interest to us which these equations can be usefully applied to are that of the quantum dynamics of nanoelectromechanical oscillators and the entanglement evolution of multipartite macroscopic states such as quantum superposition of mirrors in a high Q cavity. To address a key conceptual issue for macroscopic quantum phenomena we examine the conditions for an assumption often implicitly made in these studies to be valid, namely, that the quantum behaviour of a macroscopic object in an environment can be accurately represented by only treating the dynamics of its centre-of-mass variable. We also mention how these results can be used to calculate the uncertainty principle governing a macroscopic object at finite temperature.

AB - For the purpose of understanding the quantum behaviour such as quantum decoherence, fluctuations, dissipation, entanglement and teleportation of a mesoscopic or macroscopic object interacting with a general environment, we derive here a set of exact master equations for the reduced density matrix of N interacting harmonic oscillators in a heat bath with arbitrary spectral density and temperature. Two classes of problems of interest to us which these equations can be usefully applied to are that of the quantum dynamics of nanoelectromechanical oscillators and the entanglement evolution of multipartite macroscopic states such as quantum superposition of mirrors in a high Q cavity. To address a key conceptual issue for macroscopic quantum phenomena we examine the conditions for an assumption often implicitly made in these studies to be valid, namely, that the quantum behaviour of a macroscopic object in an environment can be accurately represented by only treating the dynamics of its centre-of-mass variable. We also mention how these results can be used to calculate the uncertainty principle governing a macroscopic object at finite temperature.

UR - http://www.scopus.com/inward/record.url?scp=36448944754&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36448944754&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2007.09.025

DO - 10.1016/j.physa.2007.09.025

M3 - Article

VL - 387

SP - 432

EP - 444

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 2-3

ER -