Ground state of a spin-1/2 charged particle in a two-dimensional magnetic field

Masao Hirokawa; Osamu Ogurisu

doi:10.1063/1.1379312

Ground state of a spin-1/2 charged particle in a two-dimensional magnetic field

Masao Hirokawa, Osamu Ogurisu

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8 Citations (Scopus)

Abstract

It is investigated that the structure of the kernel of the Dirac-Weyl operator D of a charged particle in the magnetic-field B = B₀ + B₁, given by the sum of a strongly singular magnetic field B₀ (·) = Σ_vγ^v δ(· - a_v with some singular points a_v and a magnetic-field B₁ with a bounded support. Here the magnetic field B₁ may have some singular points with the order of the singularity less than 2. At a glance, it seems that, following "Aharonov-Casher Theorem" [Phys. Rev. A 19, 2461 (1979)], the dimension of the kernel of D, dimker D, is a function of one variable of the total magnetic flux ( = Σ_vγ_v + ∫_R2B₁dxdy) of B. However, since the influence of the strongly singular points works, dim ker D indeed is a function of several variables of the total magnetic flux and each of y_v's.

Original language	English
Pages (from-to)	3334-3343
Number of pages	10
Journal	Journal of Mathematical Physics
Volume	42
Issue number	8
DOIs	https://doi.org/10.1063/1.1379312
Publication status	Published - Aug 2001
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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abstract = "It is investigated that the structure of the kernel of the Dirac-Weyl operator D of a charged particle in the magnetic-field B = B0 + B1, given by the sum of a strongly singular magnetic field B0 (·) = Σvγv δ(· - av with some singular points av and a magnetic-field B1 with a bounded support. Here the magnetic field B1 may have some singular points with the order of the singularity less than 2. At a glance, it seems that, following {"}Aharonov-Casher Theorem{"} [Phys. Rev. A 19, 2461 (1979)], the dimension of the kernel of D, dimker D, is a function of one variable of the total magnetic flux ( = Σvγv + ∫R2B1dxdy) of B. However, since the influence of the strongly singular points works, dim ker D indeed is a function of several variables of the total magnetic flux and each of yv's.",

author = "Masao Hirokawa and Osamu Ogurisu",

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T1 - Ground state of a spin-1/2 charged particle in a two-dimensional magnetic field

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AU - Ogurisu, Osamu

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N2 - It is investigated that the structure of the kernel of the Dirac-Weyl operator D of a charged particle in the magnetic-field B = B0 + B1, given by the sum of a strongly singular magnetic field B0 (·) = Σvγv δ(· - av with some singular points av and a magnetic-field B1 with a bounded support. Here the magnetic field B1 may have some singular points with the order of the singularity less than 2. At a glance, it seems that, following "Aharonov-Casher Theorem" [Phys. Rev. A 19, 2461 (1979)], the dimension of the kernel of D, dimker D, is a function of one variable of the total magnetic flux ( = Σvγv + ∫R2B1dxdy) of B. However, since the influence of the strongly singular points works, dim ker D indeed is a function of several variables of the total magnetic flux and each of yv's.

AB - It is investigated that the structure of the kernel of the Dirac-Weyl operator D of a charged particle in the magnetic-field B = B0 + B1, given by the sum of a strongly singular magnetic field B0 (·) = Σvγv δ(· - av with some singular points av and a magnetic-field B1 with a bounded support. Here the magnetic field B1 may have some singular points with the order of the singularity less than 2. At a glance, it seems that, following "Aharonov-Casher Theorem" [Phys. Rev. A 19, 2461 (1979)], the dimension of the kernel of D, dimker D, is a function of one variable of the total magnetic flux ( = Σvγv + ∫R2B1dxdy) of B. However, since the influence of the strongly singular points works, dim ker D indeed is a function of several variables of the total magnetic flux and each of yv's.

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Ground state of a spin-1/2 charged particle in a two-dimensional magnetic field

Abstract

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