Faster than Hermitian time evolution.

Bender, Carl M.

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Three-Hilbert-space formulation of quantum mechanics.

Znojil, Miloslav (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Non-Hermitian quantum systems and time-optimal quantum evolution.

Nesterov, Alexander I. (2009)

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Comment on ”Non-Hermitian quantum mechanics with minimal length uncertainty”.

Bagchi, Bijan, Fring, Andreas (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Properties of non-hermitian quantum field theories

Carl M. Bender (2003)

Annales de l’institut Fourier

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In this paper I discuss quantum systems whose Hamiltonians are non-Hermitian but whose energy levels are all real and positive. Such theories are required to be symmetric under $𝒞 𝒫 𝒯$ , but not symmetric under $𝒫$ and $𝒯$ separately. Recently, quantum mechanical systems having such properties have been investigated in detail. In this paper I extend the results to quantum field theories. Among the systems that I discuss are $- φ^{4}$ and $i φ^{3}$ theories. These theories all have unexpected and remarkable properties....

Conservation of pseudo-norm in $𝒫 𝒯$ symmetric quantum mechanics

Znojil, Miloslav

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On the role of the normalization factors $κ_{n}$ and of the pseudo-metric $𝒫 \neq 𝒫^{†}$ in crypto-Hermitian quantum models.

Znojil, Miloslav (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Supersymmetric extension of non-Hermitian $s u (2)$ Hamiltonian and supercoherent states.

Cherbal, Omar, Drir, Mahrez, Maamache, Mustapha, Trifonov, Dimitar A. (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Hamiltonian systems inspired by the Schrödinger equation.

Kovalchuk, Vasyl, Slawianowski, Jan Jerzy (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Supersymmetry and Ghosts in Quantum Mechanics

Robert, Didier (2008)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 81Q60, 35Q40. A standard supersymmetric quantum system is defined by a Hamiltonian [^H] = ½([^Q]*[^Q] +[^Q][^Q]*), where the super-charge [^Q] satisfies [^Q]2 = 0, [^Q] commutes with [^H]. So we have [^H] ≥ 0 and the quantum spectrum of [^H] is non negative. On the other hand Pais-Ulhenbeck proposed in 1950 a model in quantum-field theory where the d'Alembert operator [¯] = [(∂2)/( ∂t2)] − Δx is replaced by fourth order operator [¯]([¯]...

Re-establishing supersymmetry between harmonic oscillators in $D \neq 1$ dimensions

Znojil, Miloslav

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