Information and thermodynamic properties of a <scp>non‐Hermitian</scp> particle ensemble

Lima, F. C. E.; Moreira, A. R. P.; Almeida, C. A. S.

doi:10.1002/qua.26645

Cited by 13 publications

(6 citation statements)

References 61 publications

(79 reference statements)

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“…Research was expanded to the Rényi and Tsallis entropies [39] which are one-parameter generalizations of their Shannon counterpart. Functionals S ρ and S γ of a spinless non-Hermitian particle in the presence of a magnetic field were studied [40]. The measures' dependencies on the uniform field were calculated for the particle moving in the Yukawa-type potential [41,42].…”

Section:  Y =mentioning

confidence: 99%

Quantum-information theory of magnetic field influence on circular dots with different boundary conditions

Shafeekali,

Olendski

2023

Phys. Scr.

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Influence of the transverse uniform magnetic field Β on position (subscript ρ) and momentum (γ) Shannon quantum-information entropies S ρ,γ, Fisher informations I ρ,γ and Onicescu energies O ρ,γ is studied theoretically for the 2D circular quantum dots (QDs) whose circumference supports homogeneous either Dirichlet or Neumann boundary condition (BC). Comparative analysis reveals similarities and differences of the influence on the properties of the structure of the surface interaction with the magnetic field. A conspicuous distinction between the two spectra are crossings at the increasing induction of the Neumann energies with the same radial quantum number n and adjacent non-positive angular indices m. At the growing B, either system undergoes Landau condensation when its characteristics turn into their uniform field counterparts. It is shown that for the Dirichlet system this transformation takes place at the smaller magnetic intensities; e.g., the Dirichlet sum S ρ00 +S γ00 on its approach from above to a fundamental limit 2(1+lnπ) is at any B smaller than the corresponding Neumann quantity what physically means that the former geometry provides more total information about the position and motion of the particle. It is pointed out that the widely accepted Onicescu uncertainty relation OρOγ≤(2π)-d , with d being a dimensionality of the system, is violated by the Neumann QD in the magnetic field. Comparison with electrostatic harmonic confinement is performed; in particular, contrary to the hard-wall QDs, for this configuration the sums S ρ+S γ and the products I ρ I γ and O ρ O γ do not depend on the field. Physical interpretation is based on the different roles of the two BCs and their interplay with the field: Dirichlet (Neumann) surface is a repulsive (attractive) interface.

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Section:  Y =mentioning

confidence: 99%

Quantum-information theory of magnetic field influence on circular dots with different boundary conditions

Shafeekali,

Olendski

2023

Phys. Scr.

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“…Some conceptual applications of Shannon’s entropy help us understand the information and uncertainty measurement of quantum systems, e.g., Shannon entropy gives us the uncertainty of non-Hermitian particle systems [ 65 ]. Furthermore, Shannon formalism allowed the study of fermionic particles [ 66 ], problems with effective mass distribution [ 67 , 68 ], and mechanical-quantum models with double-well potential [ 69 ].…”

Section: Shannon’s Entropymentioning

confidence: 99%

“…The entropic quantities of Equations ( 19 ) and ( 20 ) play a role analogous to the Heisenberg uncertainty measures [ 65 , 66 ]. An entropic uncertainty relation that relates to the entropic uncertainties was obtained by Beckner [ 71 ] and Bialynicki–Birula and Mycielski (BBM) [ 73 ].…”

Section: Shannon’s Entropymentioning

confidence: 99%

Quantum Information of the Aharanov–Bohm Ring with Yukawa Interaction in the Presence of Disclination

Edet

Lima

Almeida

et al. 2022

Entropy

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We investigate quantum information by a theoretical measurement approach of an Aharanov–Bohm (AB) ring with Yukawa interaction in curved space with disclination. We obtained the so-called Shannon entropy through the eigenfunctions of the system. The quantum states considered come from Schrödinger theory with the AB field in the background of curved space. With this entropy, we can explore the quantum information at the position space and reciprocal space. Furthermore, we discussed how the magnetic field, the AB flux, and the topological defect influence the quantum states and the information entropy.

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“…The Swanson oscillator [43] is a very peculiar system that combines both profiles since it is non-Hermitian and time-dependent. Formulated to study transitions of probability amplitudes that are generated by non-unitary time evolutions, the model developed by Swanson has been revisited and studied in different branches of physics and mathematical physics [44][45][46][47][48][49][50]. Quite remarkably, the Swanson Hamiltonian can be connected with the Hamiltonian of the harmonic oscillator by the appropriate rotation in configuration space [51], which clarifies the solvability of the model.…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions for Time-Dependent Non-Hermitian Oscillators: Classical and Quantum Pictures

Zelaya

Rosas-Ortiz

2021

Quantum Reports

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We associate the stationary harmonic oscillator with time-dependent systems exhibiting non-Hermiticity by means of point transformations. The new systems are exactly solvable, with all-real spectra, and transit to the Hermitian configuration for the appropriate values of the involved parameters. We provide a concrete generalization of the Swanson oscillator that includes the Caldirola–Kanai model as a particular case. Explicit solutions are given in both the classical and quantum pictures.

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Information and thermodynamic properties of a non‐Hermitian particle ensemble

Cited by 13 publications

References 61 publications

Quantum-information theory of magnetic field influence on circular dots with different boundary conditions

Quantum-information theory of magnetic field influence on circular dots with different boundary conditions

Quantum Information of the Aharanov–Bohm Ring with Yukawa Interaction in the Presence of Disclination

Exact Solutions for Time-Dependent Non-Hermitian Oscillators: Classical and Quantum Pictures

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