Spectral shift function of the schrödinger operator in the large coupling constant limit

Pushnitski, Alexander

doi:10.1080/03605300008821528

Cited by 22 publications

(29 citation statements)

References 15 publications

(12 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[59], and the study of surface potentials, see [10,36]. Various of its properties are discussed in the literature: monotonicity and concavity in [20,22,35], the asymptotic behaviour in the large coupling constant [43,46,44] and semiclassical limit [42,40]. See [5,34] for surveys.…”

Section: Introduction and Resultsmentioning

confidence: 99%

Bounds on the Spectral Shift Function and the Density of States

Hundertmark

Killip²,

Nakamura

et al. 2005

Commun. Math. Phys.

View full text Add to dashboard Cite

Abstract. We study spectra of Schrödinger operators on R d . First we consider a pair of operators which differ by a compactly supported potential, as well as the corresponding semigroups. We prove almost exponential decay of the singular values µn of the difference of the semigroups as n → ∞ and deduce bounds on the spectral shift function of the pair of operators.Thereafter we consider alloy type random Schrödinger operators. The single site potential u is assumed to be non-negative and of compact support. The distributions of the random coupling constants are assumed to be Hölder continuous. Based on the estimates for the spectral shift function, we prove a Wegner estimate which implies Hölder continuity of the integrated density of states.

show abstract

Section: Introduction and Resultsmentioning

confidence: 99%

Bounds on the Spectral Shift Function and the Density of States

Hundertmark

Killip²,

Nakamura

et al. 2005

Commun. Math. Phys.

View full text Add to dashboard Cite

show abstract

“…Also they allow one to study the strong coupling limit. In particular, in Section 3 we will prove For other results related to the strong coupling limit we refer to [20,21,23]. Most of the results of the present note have appeared previously in [13] in a slightly less general form.…”

Section: Introduction and Main Resultsmentioning

confidence: 91%

Concavity of Eigenvalue Sums and the Spectral Shift Function

Kostrykin

2000

Journal of Functional Analysis

View full text Add to dashboard Cite

It is well known that the sum of negative (positive) eigenvalues of some finite Hermitian matrix $V$ is concave (convex) with respect to $V$. Using the theory of the spectral shift function we generalize this property to self-adjoint operators on a separable Hilbert space with an arbitrary spectrum. More precisely, we prove that the spectral shift function integrated with respect to the spectral parameter from $-\infty$ to $\lambda$ (from $\lambda$ to $+\infty$) is concave (convex) with respect to trace class perturbations. The case of relative trace class perturbations is also considered

show abstract

“…(*, :) as : Ä and typically it does not depend on *. A similar`i ndependancy'' theorem for negative V=&V & was obtained in [17]. In this paper we treat the more difficult case of no-signdefinite perturbations of the form (0.1).…”

mentioning

confidence: 87%

“…(*, :) is monotone decreasing in : (for a fixed *=* ) and coincides with a certain integral of the counting function of the spectrum of an auxiliary compact selfadjoint operator. A suitable version of the corresponding representation formula can be found in [16,17]. These arguments have allowed Pushnitski [17] to prove for V<0 that the leading term in the asymptotics is independent of *.…”

mentioning

confidence: 97%

Spectral Shift Function in the Large Coupling Constant Limit

Safronov

2001

Journal of Functional Analysis

View full text Add to dashboard Cite

Spectral shift function of the schrödinger operator in the large coupling constant limit

Cited by 22 publications

References 15 publications

Bounds on the Spectral Shift Function and the Density of States

Bounds on the Spectral Shift Function and the Density of States

Concavity of Eigenvalue Sums and the Spectral Shift Function

Spectral Shift Function in the Large Coupling Constant Limit

Contact Info

Product

Resources

About