T Stauber and A Mielke 2003 J. Phys. A: Math. Gen. 36 2707 doi:10.1088/0305-4470/36/11/305
T Stauber and A Mielke
Show affiliationsTo contrast different generators for flow equations for Hamiltonians and to discuss the dependence of physical quantities on unitarily equivalent, but effectively different, initial Hamiltonians, a numerically solvable model is considered which is structurally similar to impurity models. By this we discuss the question of optimization for the first time. A general truncation scheme is established that produces good results for the Hamiltonian flow as well as for the operator flow. Nevertheless, it is also pointed out that a systematic and feasible scheme for the operator flow on the operator level is missing. For this, an explicit analysis of the operator flow is given for the first time. We observe that truncation of the series of the observable flow after the linear or bilinear terms does not yield satisfactory results for the entire parameter regime as—especially close to resonances—even high orders of the exact series expansion carry considerable weight.
03.65.Yz Decoherence; open systems; quantum statistical methods
02.60.Cb Numerical simulation; solution of equations
65K10 Optimization and variational techniques (See also 49Mxx, 93B40)
Issue 11 (21 March 2003)
Received 29 October 2002, in final form 29 January 2003
Published 6 March 2003
T Stauber and A Mielke 2003 J. Phys. A: Math. Gen. 36 2707
M Vos et al 1999 J. Phys.: Condens. Matter 11 3645
E A Carlen et al 2009 Nonlinearity 22 2919
Stefan Schumann et al 2009 Physiol. Meas. 30 1341
Jon Links et al 2003 J. Phys. A: Math. Gen. 36 R63
A N F Aleixo and A B Balantekin 2007 J. Phys. A: Math. Theor. 40 6433
A J Macfarlane 1989 J. Phys. A: Math. Gen. 22 4581
T Heida et al 2002 J. Phys. D: Appl. Phys. 35 1592
Yuanshui Zheng et al 2009 Phys. Med. Biol. 54 6943
A S Kheifets and Igor Bray 2003 J. Phys. B: At. Mol. Opt. Phys. 36 L211