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The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real bounded below. Replacing this condition by the weaker condition of P T symmetry, one obtains new infiniteâ€¦ (More)

- Carl M. Bender, Dorje C. Brody, H W Francis Jones
- Physical review letters
- 2002

Requiring that a Hamiltonian be Hermitian is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but satisfies the lessâ€¦ (More)

- Carl M. Bender, Dorje C. Brody, H W Francis Jones, Bernhard K. Meister
- Physical review letters
- 2007

Given an initial quantum state |psi(I)> and a final quantum state |psi(F)>, there exist Hamiltonians H under which |psi(I)> evolves into |psi(F)>. Consider the following quantum brachistochroneâ€¦ (More)

This paper shows that there is a correspondence between quasi-exactly solvable models in quantum mechanics and sets of orthogonal polynomials {Pn}. The quantum-mechanical wave function is theâ€¦ (More)

Carl M. Bender, Dorje C. Brody, and Bernhard K. Meister 1Department of Physics, Washington University, St. Louis MO 63130, USA 2Blackett Laboratory, Imperial College, London SW7 2BZ, UK andâ€¦ (More)

If one defines the distance between two points as the Manhattan distance (the sum of the horizontal distance along streets and the vertical distance along avenues) then one can define a city as beingâ€¦ (More)

- Bo Peng, Åžahin Kaya Ã–zdemir, +7 authors Lan Yang
- 2014

Optical systems combining balanced loss and gain provide a unique platform to implement classical analogues of quantum systems described by non-Hermitian parityâ€“time (PT)-symmetric Hamiltonians. Suchâ€¦ (More)

- B Peng, Åžahin Kaya Ã–zdemir, +6 authors Le Yang
- Science
- 2014

Controlling and reversing the effects of loss are major challenges in optical systems. For lasers, losses need to be overcome by a sufficient amount of gain to reach the lasing threshold. In thisâ€¦ (More)

The HamiltonianH = p2+x4+iAx, whereA is a real parameter, is investigated. The spectrum of H is discrete and entirely real and positive for |A| < 3.169. As |A| increases past this point, adjacentâ€¦ (More)

t is possible to extract work from a quantum-mechanical system whose dynamics is governed by a time-dependent cyclic Hamiltonian. An energy bath is required to operate such a quantum engine in placeâ€¦ (More)