2004/08/19 by J N Kriel, J. N. Kriel, A. Yu. Morozov +2 · 1 citation
Mathematics · Physics and Astronomy · #Continuous spectrum #Coupling constant #Differential equation #Eigenvalues and eigenvectors #Flow (mathematics) #Hamiltonian (control theory) #Mathematical analysis #Mathematical optimization #Mathematical physics #Mathematics #Nonlinear system #Ordinary differential equation #Partial derivative #Partial differential equation #Physics #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Quantum optics and atomic interactions #Spectroscopy and Quantum Chemical Studies #Spectrum (functional analysis) #Unitary state #Unitary transformation #cond-mat.other #hep-th
paper · pdf · doi:10.1088/0305-4470/38/1/015
published as J.Phys. A38 (2005) 205-226 · 24 pages, 13 figures
arxiv created 2004/08/19 · openalex publication_date 2004/12/09 · arxiv updated 2015/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We use a novel parametrization of the flowing Hamiltonian to show that the flow equations based on continuous unitary transformations, as proposed by Wegner, can be implemented through a nonlinear partial differential equation involving one flow parameter and two system specific auxiliary variables. The implementation is non-perturbative as the partial differential equation involves a systematic expansion in fluctuations, controlled by the size of the system, rather than the coupling constant. The method is applied to the Lipkin model to construct a mapping which maps the non-interacting spectrum onto the interacting spectrum to a very high accuracy. This function is universal in the sense that the full spectrum for any (large) number of particles can be obtained from it. In a similar way expectation values for a large class of operators can be obtained, which also makes it possible to probe the structure of the eigenstates.