Pseudo-Boson Coherent and Fock States
D. A. Trifonov
- pp 241-250
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TLDR
In this paper, coherent states for non-Hermitian systems are introduced as eigenstates of pseudo-hermitian boson annihilation operators, and the wave functions of the eigen states of the two complementary number operators are found to be proportional to new polynomials, that are bi-orthogonal and can be regarded as a generalization of standard Hermite polynomial.Abstract:
Coherent states (CS) for non-Hermitian systems are introduced as eigenstates of pseudo-Hermitian boson annihilation operators. The set of these CS includes two subsets which form bi-normalized and bi-overcomplete system of states. The subsets consist of eigenstates of two complementary lowering pseudo-Hermitian boson operators. Explicit constructions are provided on the example of one-parameter family of pseudo-boson ladder operators. The wave functions of the eigenstates of the two complementary number operators, which form a bi-orthonormal system of Fock states, are found to be proportional to new polynomials, that are bi-orthogonal and can be regarded as a generalization of standard Hermite polynomials.read more
Citations
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Pseudo-bosons, Riesz bases and coherent states
TL;DR: In this paper, the same authors re-consider the same model and extend the same construction paying particular attention to all the subtle mathematical points, such as Riesz bases and coherent states associated to the model.
Journal ArticleDOI
Pseudobosons, Riesz bases, and coherent states
TL;DR: In this paper, the same authors revisited the same model and repeated and extended the same construction paying particular attention to all the subtle mathematical points, including the crucial role of Riesz bases.
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More mathematics for pseudo-bosons
TL;DR: In this article, an alternative definition for pseudo-bosons is proposed, which simplifies the mathematical structure, minimizing the required assumptions, and some physical examples are discussed, as well as some mathematical results related to the biorthogonal sets arising out of their framework.
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Construction of pseudo-bosons systems
TL;DR: A general construction of pseudobosons based on an explicit coordinate representation is considered, extending what is usually done in ordinary supersymmetric quantum mechanics.
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Modified Landau levels, damped harmonic oscillator, and two-dimensional pseudo-bosons
TL;DR: In this article, a generalized version of the two-dimensional Hamiltonian describing Landau levels has been applied to a class of elementary excitations called pseudo-bosons, which arise from a special deformation of the canonical commutation relation [a, a†] = 11, with b not necessarily equal to a†.
References
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Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
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