On the Geodesic Nature of Wegner's Flow
arXiv:0806.4425 · doi:10.1007/s10701-011-9606-8
Abstract
Wegner's method of flow equations offers a useful tool for diagonalizing a given Hamiltonian and is widely used in various branches of quantum physics. Here, generalizing this method, a condition is derived, under which the corresponding flow of a quantum state becomes geodesic in a submanifold of the projective Hilbert space, independently of specific initial conditions. This implies the geometric optimality of the present method as an algorithm of generating stationary states. The result is illustrated by analyzing some physical examples.
8 pages, no figures. The version published in Foundations of Physics
References in corpus (10)
- Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
- Flow Equations and Normal Ordering. A Survey
- Continuous unitary transformations in two-level boson systems
- Finite-size scaling exponents in the interacting boson model
- Possible Phases of the Two-Dimensional t-t' Hubbard Model
- Remnant superfluid collective phase oscillations in the normal state of systems with resonant pairing
- Effective electron-electron and electron-phonon interactions in the Hubbard-Holstein model
- Tomonaga-Luttinger model with an impurity for a weak two-body interaction
- Light-front Hamiltonians for heavy quarks and gluons
- Stationary photon-atom entanglement and flow equation