Analytic representations with theta functions for systems on ℤ(<i>d</i>) and on 𝕊

Evangelides, Pavlos; Lei, Ci; Vourdas, A.

doi:10.1063/1.4927256

Cited by 3 publications

(3 citation statements)

References 47 publications

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“…( 9) have the coherence properties described in proposition 1, and have been studied using the language of analytic functions (and in particular Theta functions) in refs. [11,12]. These states are not (in general) minimum uncertainty states.…”

Section: ) the Displacement Transformations D(κ λ) Exp(iμ)mentioning

confidence: 99%

Coherent states with minimum Gini uncertainty for finite quantum systems

Lei¹,

Vourdas²

2022

EPL

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Uncertainty relations ∆(ρ) ≥ ηdin terms of the Gini index are studied. The ‘Gini uncertainty constant’ ηdis estimated numerically and compared to an upper bound η̃d ≥ ηd. It is shown that for large d we get η̃d ≈ ηd. States |g〉 with minimum Gini uncertainty and displacement transformations are used to deﬁne coherent states |α, β〉g (where α, β ∈ ℤd) with minimum Gini uncertainty (∆[|α, β〉g g〈α, β|] ≈ ηd). The |α, β〉g resolve the identity, and therefore an arbitrary state can be expanded in terms of them.

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Section: ) the Displacement Transformations D(κ λ) Exp(iμ)mentioning

confidence: 99%

Coherent states with minimum Gini uncertainty for finite quantum systems

Lei¹,

Vourdas²

2022

EPL

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“…We used here the fact that the |P; m is represented by [25]. Let ζ n (t) where n = 0, ..., d − 1 be the zeros of G(z; t), i.e.,…”

Section: Zeros Of the Analytic Representation Of X T |Gmentioning

confidence: 99%

“…Refs. [21,22,25,23,24] have represented their quantum states with analytic functions on a torus, using Theta functions. It has been shown that these functions have exactly d zeros, which determine uniquely the state of the system.…”

Section: Introductionmentioning

confidence: 99%

Paths of zeros of analytic functions describing finite quantum systems

et al. 2016

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Quantum systems with positions and momenta in Z(d), are described by the d zeros of analytic functions on a torus. The d paths of these zeros on the torus, describe the time evolution of the system. A semi-analytic method for the calculation of these paths of the zeros, is discussed. Detailed analysis of the paths for periodic systems, is presented. A periodic system which has the displacement operator to a real power t, as time evolution operator, is studied. Several numerical examples, which elucidate these ideas, are presented.

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Quantum Systems with Variables in $${\mathbb Z}(d)$$

Vourdas

2017

Quantum Science and Technology

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Analytic representations with theta functions for systems on ℤ(d) and on 𝕊

Cited by 3 publications

References 47 publications

Coherent states with minimum Gini uncertainty for finite quantum systems

Coherent states with minimum Gini uncertainty for finite quantum systems

Paths of zeros of analytic functions describing finite quantum systems

Quantum Systems with Variables in $${\mathbb Z}(d)$$

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