On the Geodesic Nature of Wegner's Flow

Details On the Geodesic Nature of Wegner's Flow On the Geodesic Nature of Wegner's Flow

2008-06-27

arxiv.org/abs/0806.4425v3

Foundations of Physics 42, 377 (2012)

Physics

Quantum Physics

8 pages, no figures. The version published in Foundations of Physics

Scientific paper

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.

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