Exact trace formulas for two-dimensional electron magnetism

Gazeau, Jean‐Pierre; Hsiao, Pai‐Yi; Jellal, Ahmed

doi:10.1103/physrevb.65.094427

Cited by 24 publications

(45 citation statements)

References 8 publications

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“…While the study of Landau operators has its roots in the construction of coherent states for relativistic Klein-Gordon and Dirac equations (see [7] and references given there), the surge of interest in these operators arose in the study of the possible occurrence of orbital electromagnetism (cf [19]) as well as in the study of pseudo-differential operators on modulation spaces (cf [13]) and quantum representations of Gabor-windowed Fourier analysis (cf [5]). …”

Section: The Scope Of Problemsmentioning

confidence: 99%

“…Here, we would like to stress that when restricted to dimension 2 or 4, the spherical Dirac operator is equivalent to the orbital angular momentum operators that appear in [19,39].…”

Section: The Scope Of Problemsmentioning

confidence: 99%

“…In this subsection we will obtain a derivation of Landau operators that describe symmetries in electromagnetism (cf [19]) in terms of osp(1|2) symmetries. Moreover, we are able to derive series representations that involve the solutions of the time-harmonic Maxwell equations with angular part i.e.…”

Section: Relation With Landau Operatorsmentioning

confidence: 99%

“…Physically speaking, Xu's approach describes an electromagnetic field without the action of orbital electromagnetic sources (cf [7,19]). …”

Section: Theorem 42mentioning

confidence: 99%

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Fock spaces, Landau operators and the time-harmonic Maxwell equations

Constales¹,

Faustino²,

Kraußhar³

2011

J. Phys. A: Math. Theor.

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We investigate the representations of the solutions to Maxwell's equations based on the combination of hypercomplex function-theoretical methods with quantum mechanical methods. Our approach provides us with a characterization for the solutions to the time-harmonic Maxwell system in terms of series expansions involving spherical harmonics resp. spherical monogenics. Also, a thorough investigation for the series representation of the solutions in terms of eigenfunctions of Landau operators that encode n-dimensional spinless electrons is given. This new insight should lead to important investigations in the study of regularity and hypo-ellipticity of the solutions to Schrödinger equations with natural applications in relativistic quantum mechanics concerning massive spinor fields.

show abstract

Section: The Scope Of Problemsmentioning

confidence: 99%

“…Here, we would like to stress that when restricted to dimension 2 or 4, the spherical Dirac operator is equivalent to the orbital angular momentum operators that appear in [19,39].…”

Section: The Scope Of Problemsmentioning

confidence: 99%

Section: Relation With Landau Operatorsmentioning

confidence: 99%

“…Physically speaking, Xu's approach describes an electromagnetic field without the action of orbital electromagnetic sources (cf [7,19]). …”

Section: Theorem 42mentioning

confidence: 99%

See 2 more Smart Citations

Fock spaces, Landau operators and the time-harmonic Maxwell equations

Constales¹,

Faustino²,

Kraußhar³

2011

J. Phys. A: Math. Theor.

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show abstract

“…The obtained form of M nc lo can deeply be investigated to make contact with early works on the magnetization [9,10,11]. With this, one may have a full picture on the magnetism of the system at low temperature.…”

Section: Low Temperature Regimementioning

confidence: 99%

Thermodynamical Properties of Hall Systems

Jellal

Khedif

2008

Int. J. Geom. Methods Mod. Phys.

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We study quantum Hall effect within the framework of a newly proposed approach, which captures the principal results of some proposals. This can be established by considering a system of particles living on the non-commutative plane in the presence of an electromagnetic field and quantum statistical mechanically investigate its basic features. Solving the eigenvalue equation, we analytically derive the energy levels and the corresponding wavefunctions. These will be used, at low temperature and weak electric field, to determine the thermodynamical potential Ω nc and related physical quantities.Varying Ω nc with respect to the non-commutativity parameter θ, we define a new function that can be interpreted as a Ω nc density. Evaluating the particle number, we show that the Hall conductivity of the system is θ-dependent. This allows us to make contact with quantum Hall effect by offering different interpretations. We study the high temperature regime and discuss the magnetism of the system. We finally show that at θ = 2l 2 B , the system is sharing some common features with the Laughlin theory.

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Exact traveling wave solutions in the coupled plane-base rotator model of DNA

Torres

Agüero

2016

International Journal of Non-Linear Mechanics

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Exact trace formulas for two-dimensional electron magnetism

Cited by 24 publications

References 8 publications

Fock spaces, Landau operators and the time-harmonic Maxwell equations

Fock spaces, Landau operators and the time-harmonic Maxwell equations

Thermodynamical Properties of Hall Systems

Exact traveling wave solutions in the coupled plane-base rotator model of DNA

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