Magnetocaloric Effect in an Antidot: The Effect of the Aharonov-Bohm Flux and Antidot Radius

Negrete, Oscar; Peña, Francisco J.; Vargas, P.

doi:10.3390/e20110888

Cited by 18 publications

(11 citation statements)

References 59 publications

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“…In the limit α → 1 (and, accordingly, β → 1) Eqs. (48) and (49a) degenerate into their Shannon counterparts, Eqs. (4) and (5), respectively, whereas the Tsallis inequality turns into the identity with each of its sides equal to π −l/4 .…”

Section: Discussionmentioning

confidence: 99%

“…(10) In this Letter, an exact analysis of the above mentioned quantum-information measures is provided for the QR in the superposition of the transverse uniform magnetic field B and the Aharonov-Bohm flux φ AB . For the azimuthally symmetric 2D potential profile U (r) of the ring [with r = (r, ϕ r ) being position polar coordinates with the origin of this frame of reference coinciding with the geometrical center of the structure] we use a combination of the quadratic and inverse quadratic depedendencies on the radius r [38][39][40][41][42][43][44][45][46][47][48]:…”

Section: Introductionmentioning

confidence: 99%

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Quantum information measures of the Aharonov–Bohm ring in uniform magnetic fields

Olendski

2019

Physics Letters A

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Shannon quantum information entropies S ρ,γ , Fisher informations I ρ,γ , Onicescu energies O ρ,γ and complexities e S O are calculated both in the position (subscript ρ) and momentum (γ) spaces for the azimuthally symmetric twodimensional nanoring that is placed into the combination of the transverse uniform magnetic field B and the Aharonov-Bohm (AB) flux φ AB and whose potential profile is modeled by the superposition of the quadratic and inverse quadratic dependencies on the radius r. The increasing intensity B flattens momentum waveforms Φ nm (k) and in the limit of the infinitely large fields they turn to zero: Φ nm (k) → 0 at B → ∞, what means that the position wave functions Ψ nm (r), which are their Fourier counterparts, tend in this limit to the δ-functions. Position (momentum) Shannon entropy depends on the field B as a negative (positive) logarithm of ω ef f ≡ ω 2 0 + ω 2 c /4 1/2 , where ω 0 determines the quadratic steepness of the confining potential and ω c is a cyclotron frequency. This makes the sum S ρ nm + S γ nm a field-independent quantity that increases with the principal n and azimuthal m quantum numbers and does satisfy entropic uncertainty relation. Position Fisher information does not depend on m, linearly increases with n and varies as ω ef f whereas its n and m dependent Onicescu counterpart O ρ nm changes as ω −1 ef f . The products I ρ nm I γ nm and O ρ nm O γ nm are B-independent quantities. A dependence of the measures on the ring geometry is discussed. It is argued that a variation of the position Shannon entropy or Onicescu energy with the AB field uniquely determines an associated persistent current as a function of φ AB at B = 0. An inverse statement is correct too.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum information measures of the Aharonov–Bohm ring in uniform magnetic fields

Olendski

2019

Physics Letters A

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“…where the formulas for the disequilibria O ρ,γ are given in Equations (15). For example, this was very recently done for a noncommutative anisotropic oscillator in a homogeneous magnetic field [73].…”

Section: Discussionmentioning

confidence: 99%

“…In an attempt to expand quantum-information theory to the study of the quantum rings (QRs) [1], a recent analysis [2] addressed an influence of the combination of the transverse uniform magnetic field B and the AB flux φ AB [3] on the position and momentum components of, among others, Shannon entropy [4] of the one-particle orbitals of the flat 2D annulus whose rotationally symmetric potential profile U(r) is modeled in the position of polar coordinates (r, ϕ r ) by the superposition of the quadratic and inverse quadratic dependencies on the radius r [5][6][7][8][9][10][11][12][13][14][15]:…”

Section: Introductionmentioning

confidence: 99%

Rényi and Tsallis Entropies of the Aharonov–Bohm Ring in Uniform Magnetic Fields

Olendski

2019

Entropy

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One-parameter functionals of the Rényi R ρ,γ (α) and Tsallis T ρ,γ (α) types are calculated both 1 in the position (subscript ρ) and momentum (γ) spaces for the azimuthally symmetric 2D nanoring that 2 is placed into the combination of the transverse uniform magnetic field B and the Aharonov-Bohm (AB) 3 flux φ AB and whose potential profile is modelled by the superposition of the quadratic and inverse 4 quadratic dependencies on the radius r. Position (momentum) Rényi entropy depends on the field B as 5 a negative (positive) logarithm of ω e f f ≡ ω 2 0 + ω 2 c /4 1/2 , where ω 0 determines the quadratic steepness 6 of the confining potential and ω c is a cyclotron frequency. This makes the sum R ρ nm (α)field-independent quantity that increases with the principal n and azimuthal m quantum numbers and 8 does satisfy corresponding uncertainty relation. In the limit α → 1 both entropies in either space tend to 9 their Shannon counterparts along, however, different paths. Analytic expression for the lower boundary 10 of the semi-infinite range of the dimensionless coefficient α where the momentum entropies exist reveals 11 that it depends on the ring geometry, AB intensity and quantum number m. It is proved that there is the 12 only orbital for which both Rényi and Tsallis uncertainty relations turn into the identity at α = 1/2 and 13 which is not necessarily the lowest-energy level. At any coefficient α, the dependence of the position 14 Rényi entropy on the AB flux mimics the energy variation with φ AB what, under appropriate scaling, can 15 be used for the unique determination of the associated persistent current. Similarities and differences 16 between the two entropies and their uncertainty relations are discussed too. 17 Note that, as it follows from Eqs. (49a) and (49c), the sum of the entropies of the generalized Gaussian 111 approaches its edge values (which are equal to each other due to the fact that each item in it has the 112 same dependence on the Rényi parameter and, as a result, due to the condition from Eq. (18), at the rims 113 α and β simply interchange their places) from above and since the expression in the square brackets in 114 Eq. (49b) is always positive, left-hand side of Eq. (21) reaches its maximum at the Shannon entropy. Also, 115 the leading terms in all three cases are increasing functions of the magnetic index what means that at 116 the greater |m| the corresponding curve lies higher satisfying, of course, the uncertainty relation. As our 117 numerical results show, the same statement holds true at the fixed quantum number m and the increasing 118 principal index n. 119For the QR, a > 0, a comparison of Eqs. (25), (39) and (48) proves that the n = m = 0 orbital does 120 convert at α = 1/2 the Rényi uncertainty into the identity, as it did for the Tsallis inequality too. This is 121 also exemplified in Fig. 2(a), which shows that its sum R ρ (α) + R γ (β) at any parameter α is the smallest 122 one as compared to other levels. Dependence of the left-hand side of Eq. (21) on n and |m| is...

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“…Among the physical properties, there are some studies on thermodynamic properties of different systems [25][26][27][28][29][30][31][32][33][34]. Tan et al [35] have studied the magnetization and persistent currents in mesoscopic rings and dots by use of an exactly soluble model to calculate the structures of large number of electrons over a wide range of magnetic field strengths.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic properties of a charged particle in non-uniform magnetic field

2021

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We solve the Schrödinger equation for a charged particle in the non-uniform magnetic field by using the Nikiforov-Uvarov method. We find the energy spectrum and the wave function, and present an explicit relation for the partition function. We give analytical expressions for the thermodynamic properties such as mean energy and magnetic susceptibility, and analyze the entropy, free energy and specific heat of this system numerically. It is concluded that the specific heat and magnetic susceptibility increase with external magnetic field strength and different values of the non-uniformity parameter, α, in the low temperature region, while the mentioned quantities are decreased in high temperature regions due to increasing the occupied levels at these regions. The non-uniformity parameter has the same effect with a constant value of the magnetic field on the behavior of thermodynamic properties.On the other hand, the results show that transition from positive to negative magnetic susceptibility depends on the values of non-uniformity parameter in the constant external magnetic field.

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Magnetocaloric Effect in an Antidot: The Effect of the Aharonov-Bohm Flux and Antidot Radius

Cited by 18 publications

References 59 publications

Quantum information measures of the Aharonov–Bohm ring in uniform magnetic fields

Quantum information measures of the Aharonov–Bohm ring in uniform magnetic fields

Rényi and Tsallis Entropies of the Aharonov–Bohm Ring in Uniform Magnetic Fields

Thermodynamic properties of a charged particle in non-uniform magnetic field

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