Spectral Asymptotics of Nonselfadjoint Elliptic Systems of Differential Operators in Bounded Domains

Abstract

We calculate exactly matrix elements between non-equilibrium excitations of the quantum XY model for general anisotropy. These matrix elements are expressed as a sum of Pfaffians. For single particle excitations on the ground state, the Pfaffians in the sum simplify to determinants.

Spectral properties of degenerate elliptic operators with matrix coefficients

“…This paper as [1] sides with [2,3,7], among them more general results were obtained in [7] where it was assumed that a leading coefficient of operator A a(t) ∈ C m ([0, 1]; EndC l ) (0.1) and has simple different eigenvalues (e.v.) for any t ∈ [0, 1].…”

“…Spectral asymptotics of degenerate elliptic operators far from selfadjoint ones were studied in [2][3][4][5][6][7] in a case when eigenvalues of an operator are divided into two series, one lies out of the angle | arg z| ≤ ϕ, ϕ < π and another localizes to the ray R + = (0, +∞). This paper as [1] sides with [2,3,7], among them more general results were obtained in [7] where it was assumed that a leading coefficient of operator A a(t) ∈ C m ([0, 1]; EndC l ) (0.1) and has simple different eigenvalues (e.v.)…”

“…and p.d.o. that are far from selfadjoint were studied in [3,4,[13][14][15][16][17][18]; only [3,4,13] are devoted to degenerate elliptic problems.…”