Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields

Akira Iwatsuka; Hideo Tamura

Displaying similar documents to “Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields”

Eigenvalue asymptotics for the Pauli operator in strong nonconstant magnetic fields

Georgi D. Raikov (1999)

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We consider the Pauli operator $H (μ) : = {(\sum_{j = 1}^{m} σ_{j} (- i \frac{\partial}{\partial x_{j}} - μ A_{j}))}^{2} + V$ selfadjoint in $L^{2} (ℝ^{m}; ℂ^{2})$ , $m = 2, 3$ . Here $σ_{j}$ , $j = 1, ..., m$ , are the Pauli matrices, $A : = (A_{1}, ..., A_{m})$ is the magnetic potential, $μ > 0$ is the coupling constant, and $V$ is the electric potential which decays at infinity. We suppose that the magnetic field generated by $A$ satisfies some regularity conditions; in particular, its norm is lower-bounded by a positive constant, and, in the case $m = 3$ , its direction is constant. We investigate the asymptotic behaviour as $μ \to \infty$ of the number of the eigenvalues of $H (μ)$ smaller...

Eigenvalue asymptotics for Schrödinger and Dirac operators with the constant magnetic field and with electric potential decreasing at infinity

Victor Ivrii (1991)

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Zhongwei Shen (1996)

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Semiclassical expansion for the thermodynamic limit of the ground state energy of Kac's operator

Bernard Helffer, Thierry Ramond (2000)

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We continue the study started by the first author of the semiclassical Kac Operator. This kind of operator has been obtained for example by M. Kac as he was studying a 2D spin lattice by the so-called “transfer operator method”. We are interested here in the thermodynamical limit $Λ (h)$ of the ground state energy of this operator. For Kac’s spin model, $Λ (h)$ is the free energy per spin, and the semiclassical regime corresponds to the mean-field approximation. Under suitable assumptions, which...

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George D. Raikov (1994)

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Eigenvalue asymptotics of the even-dimensional exterior Landau-Neumann Hamiltonian.

Persson, Mikael (2009)

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Domain perturbations, capacity and shift of eigenvalues

André Noll (1999)

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After introducing the notion of capacity in a general Hilbert space setting we look at the spectral bound of an arbitrary self-adjoint and semi-bounded operator $H$ . If $H$ is subjected to a domain perturbation the spectrum is shifted to the right. We show that the magnitude of this shift can be estimated in terms of the capacity. We improve the upper bound on the shift which was given in (, 24:759–775, 1999) and obtain a lower bound which leads to a generalization of Thirring’s inequality...