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 |
|---|---|
| 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.
In: European Physical Journal B, Vol. 12, No. 4, 02.12.1999, p. 547-554.Research output: Contribution to journal › Article
}
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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UR - http://www.scopus.com/inward/citedby.url?scp=0000773013&partnerID=8YFLogxK
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 -