On moments of negative eigenvalues for the Pauli operator

Zhongwei Shen

doi:10.1006/jdeq.1998.3483

On moments of negative eigenvalues for the Pauli operator

Zhongwei Shen

Producción científica: Article › revisión exhaustiva

4 Citas (Scopus)

Resumen

This paper concerns the three-dimensional Pauli operator P=(σ·(p-A(x)))²+V(x) with a non-homogeneous magnetic field B=curl A. The following Lieb-Thirring type inequality for the moment of negative eigenvalues is established, ∑λ_j<0λ_j≤C₁∫_R³V(x)^5/2_-dx+C2∫_R³[b_p(x)]^3/2V(x)_-dx where p>3/2 and b_p(x) is the L^p average of B over a certain cube centered at x with a side length scaling like B^-1/2. We also show that, ifBhas a constant direction, ∑λ_j<0λ_j^γ≤C_1,γ∫_R³V(x)^γ+3/2_-dx+C_2,γ∫_R³b_p(x)V(x)^γ+1/2_-dx where γ>1/2 and p>1.

Idioma original	English
Páginas (desde-hasta)	420-455
Número de páginas	36
Publicación	Journal of Differential Equations
Volumen	151
N.º	2
DOI	https://doi.org/10.1006/jdeq.1998.3483
Estado	Published - ene 20 1999

Nota bibliográfica

Funding Information:
* Research supported in part by the AMS Centennial Research Berkeley, California, and the NSF grant DMS-9596266.

Financiación

* Research supported in part by the AMS Centennial Research Berkeley, California, and the NSF grant DMS-9596266.

Financiadores	Número del financiador
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	DMS-9596266

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1006/jdeq.1998.3483

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title = "On moments of negative eigenvalues for the Pauli operator",

abstract = "This paper concerns the three-dimensional Pauli operator P=(σ·(p-A(x)))2+V(x) with a non-homogeneous magnetic field B=curl A. The following Lieb-Thirring type inequality for the moment of negative eigenvalues is established, ∑λj<0λj≤C1∫R3V(x)5/2-dx+C2∫R3[bp(x)]3/2V(x)-dx where p>3/2 and bp(x) is the Lp average of B over a certain cube centered at x with a side length scaling like B-1/2. We also show that, ifBhas a constant direction, ∑λj<0λjγ≤C1,γ∫R3V(x)γ+3/2-dx+C2,γ∫R3bp(x)V(x)γ+1/2-dx where γ>1/2 and p>1.",

author = "Zhongwei Shen",

note = "Funding Information: * Research supported in part by the AMS Centennial Research Berkeley, California, and the NSF grant DMS-9596266.",

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AU - Shen, Zhongwei

N1 - Funding Information: * Research supported in part by the AMS Centennial Research Berkeley, California, and the NSF grant DMS-9596266.

PY - 1999/1/20

Y1 - 1999/1/20

N2 - This paper concerns the three-dimensional Pauli operator P=(σ·(p-A(x)))2+V(x) with a non-homogeneous magnetic field B=curl A. The following Lieb-Thirring type inequality for the moment of negative eigenvalues is established, ∑λj<0λj≤C1∫R3V(x)5/2-dx+C2∫R3[bp(x)]3/2V(x)-dx where p>3/2 and bp(x) is the Lp average of B over a certain cube centered at x with a side length scaling like B-1/2. We also show that, ifBhas a constant direction, ∑λj<0λjγ≤C1,γ∫R3V(x)γ+3/2-dx+C2,γ∫R3bp(x)V(x)γ+1/2-dx where γ>1/2 and p>1.

AB - This paper concerns the three-dimensional Pauli operator P=(σ·(p-A(x)))2+V(x) with a non-homogeneous magnetic field B=curl A. The following Lieb-Thirring type inequality for the moment of negative eigenvalues is established, ∑λj<0λj≤C1∫R3V(x)5/2-dx+C2∫R3[bp(x)]3/2V(x)-dx where p>3/2 and bp(x) is the Lp average of B over a certain cube centered at x with a side length scaling like B-1/2. We also show that, ifBhas a constant direction, ∑λj<0λjγ≤C1,γ∫R3V(x)γ+3/2-dx+C2,γ∫R3bp(x)V(x)γ+1/2-dx where γ>1/2 and p>1.

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DO - 10.1006/jdeq.1998.3483

M3 - Article

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JO - Journal of Differential Equations

JF - Journal of Differential Equations

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On moments of negative eigenvalues for the Pauli operator

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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