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Interactions of Hermitian and non-Hermitian Hamiltonians
Carl M. Bender, Hugh F. Jones
The coupling of non-Hermitian PT-symmetric Hamiltonians to standard Hermitian Hamiltonians, each of which individually has a real energy spectrum, is explored by means of a number…
No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
Carl M. Bender, Philip D. Mannheim
Contrary to common belief, it is shown that theories whose field equations are higher than second order in derivatives need not be stricken with ghosts. In particular, the prototyp…
Complexified Dynamical Systems
Carl M. Bender, Darryl D. Holm, Daniel W. Hook
Many dynamical systems, such as the Lotka-Volterra predator-prey model and the Euler equations for the free rotation of a rigid body, are PT symmetric. The standard and well-known…
Geometry of PT-symmetric quantum mechanics
Carl M. Bender, Dorje C. Brody, Lane P. Hughston +1
Recently, much research has been carried out on Hamiltonians that are not Hermitian but are symmetric under space-time reflection, that is, Hamiltonians that exhibit PT symmetry. I…
Making Sense of Non-Hermitian Hamiltonians
Carl M. Bender
The Hamiltonian H specifies the energy levels and time evolution of a quantum theory. A standard axiom of quantum mechanics requires that H be Hermitian because Hermiticity guarant…
Optimal Shape of a Blob
Carl M. Bender, Michael A. Bender
This paper presents the solution to the following optimization problem: What is the shape of the two-dimensional region that minimizes the average L_p distance between all pairs of…