Displaying similar documents to “Semiclassical expansion for the thermodynamic limit of the ground state energy of Kac's operator”

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

Akira Iwatsuka, Hideo Tamura (1998)

Annales de l'institut Fourier

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This article studies the asymptotic behavior of the number N ( λ ) of the negative eigenvalues < - λ as λ → + 0 of the two dimensional Pauli operators with electric potential V ( x ) decaying at ∞ and with nonconstant magnetic field b ( x ) , which is assumed to be bounded or to decay at ∞ . In particular, it is shown that N ( λ ) = ( 1 / 2 π ) ∫ V ( x ) > λ b ( x ) d x ( 1 + o ( 1 ) ) , when V ( x ) decays faster than b ( x ) under some additional conditions.

On the eigenvalues of a class of hypo-elliptic operators. IV

Johannes Sjöstrand (1980)

Annales de l'institut Fourier

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Let P be a selfadjoint classical pseudo-differential operator of order > 1 with non-negative principal symbol on a compact manifold. We assume that P is hypoelliptic with loss of one derivative and semibounded from below. Then exp ( - t P ) , t ≥ 0 , is constructed as a non-classical Fourier integral operator and the main contribution to the asymptotic distribution of eigenvalues of P is computed. This paper is a continuation of a series of joint works with A. Menikoff.

Eigenvalue asymptotics for the Pauli operator in strong nonconstant magnetic fields

Georgi D. Raikov (1999)

Annales de l'institut Fourier

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We consider the Pauli operator H ( μ ) : = ∑ j = 1 m σ j - i ∂ ∂ 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 → ∞ of the number of the eigenvalues of H ( μ ) smaller...

Accurate Spectral Asymptotics for periodic operators

Victor Ivrii (1999)

Journées équations aux dérivées partielles

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Asymptotics with sharp remainder estimates are recovered for number 𝐍 ( τ ) of eigenvalues of operator A ( x , D ) - t W ( x , x ) crossing level E as t runs from 0 to τ , τ → ∞ . Here A is periodic matrix operator, matrix W is positive, periodic with respect to first copy of x and decaying as second copy of x goes to infinity, E either belongs to a spectral gap of A or is one its ends. These problems are first treated in papers of M. Sh. Birman, M. Sh. Birman-A. Laptev and M. Sh. Birman-T. Suslina.