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Flow equations for Hamiltonians: contrasting different approaches by using a numerically solvable model

T Stauber and A Mielke

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To 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.


PACS

03.65.Yz Decoherence; open systems; quantum statistical methods

02.60.Cb Numerical simulation; solution of equations

02.60.Pn Numerical optimization

02.30.Tb Operator theory

MSC

65K10 Optimization and variational techniques (See also 49Mxx, 93B40)

65P10 Hamiltonian systems including symplectic integrators

81U15 Exactly and quasi-solvable systems

Subjects

Mathematical physics

Computational physics

Quantum information and quantum mechanics

Dates

Issue 11 (21 March 2003)

Received 29 October 2002, in final form 29 January 2003

Published 6 March 2003



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