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On the Geodesic Nature of Wegner’s Flow

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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.

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Authors and Affiliations

  1. Science Division, Center for General Education, Aichi Institute of Technology, Aichi, 470-0392, Japan

    Yuichi Itto

  2. Department of Physical Engineering, Mie University, Mie, 514-8507, Japan

    Sumiyoshi Abe

Authors
  1. Yuichi Itto
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  2. Sumiyoshi Abe
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Corresponding author

Correspondence to Sumiyoshi Abe.

Additional information

S.A. was supported in part by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science.

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Itto, Y., Abe, S. On the Geodesic Nature of Wegner’s Flow. Found Phys 42, 377–387 (2012). https://doi.org/10.1007/s10701-011-9606-8

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  • DOI: https://doi.org/10.1007/s10701-011-9606-8

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