Wigner function for a particle in an infinite lattice

Hinarejos, M.; Perez, A.; Bañuls, Mari Carmen

doi:10.1088/1367-2630/14/10/103009

Cited by 26 publications

(54 citation statements)

References 36 publications

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“…for complex arguments q, z, with| | < q 1 [42]. As in the previous example, we find an important difference with the WF for the case without spin [32], since the components in the scalar function appear to be distributed here as the components of the matrix WF. In the limit…”

Section: • Superposition Of Two Gaussian Statessupporting

confidence: 55%

“…The marginal distributions of (2) are related to matrix elements of the density operator As already discussed in [32], these equations reflect the distinction between the coordinates of the phase space points,…”

Section: Particle With Spin On a One-dimensional Latticementioning

confidence: 99%

“…It is interesting to compare the structure provided by equation (16) with the corresponding superposition of two localized states without spin [32], given by…”

Section: • Product Statementioning

confidence: 99%

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Wigner formalism for a particle on an infinite lattice: dynamics and spin

2015

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The recently proposed Wigner function for a particle in an infinite lattice (Hinarejos M, Bañuls M C and Pérez A 2012 New J. Phys. 14 103009) is extended here to include an internal degree of freedom as spin. This extension is made by introducing a Wigner matrix. The formalism is developed to account for dynamical processes, with or without decoherence. We show explicit solutions for the case of Hamiltonian evolution under a position-dependent potential, and for evolution governed by a master equation under some simple models of decoherence, for which the Wigner matrix formalism is well suited. Discrete processes are also discussed. Finally, we discuss the possibility of introducing a negativity concept for the Wigner function in the case where the spin degree of freedom is included.

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Section: • Superposition Of Two Gaussian Statessupporting

confidence: 55%

Section: Particle With Spin On a One-dimensional Latticementioning

confidence: 99%

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Wigner formalism for a particle on an infinite lattice: dynamics and spin

2015

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“…Note that any Wigner function should have the properties described by (3.6)-(3.8) [3,7,16]. It is worthwhile noticing that the discrete Wigner functions have been also extensively studied from the general point of view [29][30][31][32][33][34]. Moreover, a class of discrete-time Wigner functions has been introduced in signal processing [35], where Wigner distributions have been used for time-frequency analysis [36].…”

Section: Wigner Functionmentioning

confidence: 99%

From the Weyl quantization of a particle on the circle to number–phase Wigner functions

Przanowski¹,

Brzykcy²,

Tosiek³

2014

Annals of Physics

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a b s t r a c tA generalized Weyl quantization formalism for a particle on the circle is shown to supply an effective method for defining the number-phase Wigner function in quantum optics. A Wigner function for the stateρ and the kernel K for a particle on the circle is defined and its properties are analysed. Then it is shown how this Wigner function can be easily modified to give the number-phase Wigner function in quantum optics. Some examples of such number-phase Wigner functions are considered.

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“…The present definition of W t ( k, x) can be proved to be equivalent to the definition using phase-point operators in finite systems [39][40][41]. We remark the prescription that…”

Section: Phase-space (Lattice) Representationmentioning

confidence: 94%

Bath-induced correlations in an infinite-dimensional Hilbert space

Nizama

Cáceres

2017

Eur. Phys. J. B

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Quantum correlations between two free spinless dissipative distinguishable particles (interacting with a thermal bath) are studied analytically using the quantum master equation and tools of quantum information. Bath-induced coherence and correlations in an infinite-dimensional Hilbert space are shown. We show that for temperature T > 0 the time-evolution of the reduced density matrix cannot be written as the direct product of two independent particles. We have found a time-scale that characterizes the time when the bath-induced coherence is maximum before being wiped out by dissipation (purity, relative entropy, spatial dispersion, and mirror correlations are studied). The Wigner function associated to the Wannier lattice (where the dissipative quantum walks move) is studied as an indirect measure of the induced correlations among particles. We have supported the quantum character of the correlations by analyzing the geometric quantum discord.

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Wigner function for a particle in an infinite lattice

Cited by 26 publications

References 36 publications

Wigner formalism for a particle on an infinite lattice: dynamics and spin

Wigner formalism for a particle on an infinite lattice: dynamics and spin

From the Weyl quantization of a particle on the circle to number–phase Wigner functions

Bath-induced correlations in an infinite-dimensional Hilbert space

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