### Abstract

Ground state of the dissipative two-state system is investigated by means of the Lanczos diagonalization method. We adopted the Hilbert-space-reduction scheme proposed by Zhang, Jeckelmann and White so as to reduce the overwhelming reservoir Hubert space to being tractable in computers. Both the implementation of the algorithm and the precision are reported in detail. We evaluate the dynamical susceptibility (resolvent) with the continued-fraction-expansion formula. Through analysing the resolvent over a frequency range, which is often called "interesting" frequency, we obtain the damping rate and the oscillation frequency. Our results agree with those of a recent quantum Monte-Carlo study, which concludes that the critical dissipation from oscillatory to over-damped behavior decreases as the tunneling amplitude is strengthened.

Original language | English |
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Pages (from-to) | 547-554 |

Number of pages | 8 |

Journal | European Physical Journal B |

Volume | 12 |

Issue number | 4 |

Publication status | Published - Dec 2 1999 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

**Numerical analysis of the dissipative two-state system with the density-matrix Hilbert-space-reduction algorithm.** / Nishiyama, Yoshihiro.

Research output: Contribution to journal › Article

*European Physical Journal B*, vol. 12, no. 4, pp. 547-554.

}

TY - JOUR

T1 - Numerical analysis of the dissipative two-state system with the density-matrix Hilbert-space-reduction algorithm

AU - Nishiyama, Yoshihiro

PY - 1999/12/2

Y1 - 1999/12/2

N2 - Ground state of the dissipative two-state system is investigated by means of the Lanczos diagonalization method. We adopted the Hilbert-space-reduction scheme proposed by Zhang, Jeckelmann and White so as to reduce the overwhelming reservoir Hubert space to being tractable in computers. Both the implementation of the algorithm and the precision are reported in detail. We evaluate the dynamical susceptibility (resolvent) with the continued-fraction-expansion formula. Through analysing the resolvent over a frequency range, which is often called "interesting" frequency, we obtain the damping rate and the oscillation frequency. Our results agree with those of a recent quantum Monte-Carlo study, which concludes that the critical dissipation from oscillatory to over-damped behavior decreases as the tunneling amplitude is strengthened.

AB - Ground state of the dissipative two-state system is investigated by means of the Lanczos diagonalization method. We adopted the Hilbert-space-reduction scheme proposed by Zhang, Jeckelmann and White so as to reduce the overwhelming reservoir Hubert space to being tractable in computers. Both the implementation of the algorithm and the precision are reported in detail. We evaluate the dynamical susceptibility (resolvent) with the continued-fraction-expansion formula. Through analysing the resolvent over a frequency range, which is often called "interesting" frequency, we obtain the damping rate and the oscillation frequency. Our results agree with those of a recent quantum Monte-Carlo study, which concludes that the critical dissipation from oscillatory to over-damped behavior decreases as the tunneling amplitude is strengthened.

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M3 - Article

AN - SCOPUS:0000773013

VL - 12

SP - 547

EP - 554

JO - European Physical Journal B

JF - European Physical Journal B

SN - 1434-6028

IS - 4

ER -