Non-Hermitian noncommutative quantum mechanics

Abstract

In this work we present a general formalism to treat non-Hermitian and noncommutative Hamiltonians. This is done employing the phase-space formalism of quantum mechanics, which allows to write a set of robust maps connecting the Hamitonians and the associated Wigner functions to the different Hilbert space structures, namely, those describing the non-Hermitian and noncommutative, Hermitian and noncommutative, and Hermitian and commutative systems. A general recipe is provided to obtain the expected values of the more general Hamiltonian. Finally, we apply our method to the harmonic oscillator under linear amplification and discuss the implications of both non-Hermitian and noncommutative effects.

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Cited by in corpus (7)

• Heat flow and noncommutative quantum mechanics in phase-space
• Non-Commutative space: boon or bane for quantum engines and refrigerators
• Effects of quantum deformation on the Jaynes-Cummings and anti-Jaynes-Cummings models
• Quantum thermodynamics aspects with a thermal reservoir based on $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians
• $\mathcal{P}\mathcal{T}$-Symmetric Generalized Extended Momentum Operator
• Thermostatistical analysis and negative heat capacities of Yukawa and Lee-Wick potentials in noncommutative phase spaces
• Hilbert space representation for quasi-Hermitian position-deformed Heisenberg algebra and Path integral formulation