The 4D Naimark dilated PT brachistochrone as 2D Hermitian brachistochrone

The 4D Naimark dilated PT brachistochrone as 2D Hermitian brachistochrone

Günther, U.

Abstract

After a brief exposition of the Naimark dilated PT brachistochrone [PRL 101, 230404 (2008)] evidence is provided that the dilation (doubling of the Hilbert space dimension) preserves the brachistochrone features of the model. The dilated PT brachistochrone in 4D-Hilbert space behaves as an effective Hermitian brachistochrone in the 2D subspace spanned by the 4D initial and final states.

Keywords: PT quantum mechanics; non-Hermitian Hamiltonian; Naimark dilation; quantum brachistochrone; dilation invariants

  • Invited lecture (Conferences)
    Analytic and algebraic methods V, 27.-28.05.2009, Prague, Czech Republic

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