The Lp-Theory of the Spectral Shift Function,¶the Wegner Estimate, and the Integrated Density¶of States for Some Random Operators

2001 ◽  
Vol 218 (1) ◽  
pp. 113-130 ◽  
Author(s):  
J. M. Combes ◽  
P. D. Hislop ◽  
Shu Nakamura
Keyword(s):  
Density Of States ◽  
Spectral Shift ◽  
Integrated Density Of States ◽  
Shift Function ◽  
Random Operators ◽  
Spectral Shift Function ◽  
Wegner Estimate ◽  
Lp Theory

The Wegner estimate and the integrated density of states for some random operators

2002 ◽  
Vol 112 (1) ◽  
pp. 31-53 ◽  
Author(s):  
J. M. Combes ◽  
P. D. Hislop ◽  
Frédéric Klopp ◽  
Shu Nakamura
Keyword(s):  
Density Of States ◽  
Integrated Density Of States ◽  
Random Operators ◽  
Wegner Estimate

scholarly journals THE DENSITY OF STATES AND THE SPECTRAL SHIFT DENSITY OF RANDOM SCHRÖDINGER OPERATORS

2000 ◽  
Vol 12 (06) ◽  
pp. 807-847 ◽  
Author(s):  
VADIM KOSTRYKIN ◽  
ROBERT SCHRADER
Keyword(s):  
Density Of States ◽  
Arbitrary Dimension ◽  
Schrödinger Operators ◽  
Spectral Shift ◽  
Random Schrödinger Operators ◽  
Shift Function ◽  
Schrodinger Operators ◽  
Spectral Shift Function ◽  
Arbitrary Dimensions ◽  
The Difference

In this article we continue our analysis of Schrödinger operators with a random potential using scattering theory. In particular the theory of Krein's spectral shift function leads to an alternative construction of the density of states in arbitrary dimensions. For arbitrary dimension we show existence of the spectral shift density, which is defined as the bulk limit of the spectral shift function per unit interaction volume. This density equals the difference of the density of states for the free and the interaction theory. This extends the results previously obtained by the authors in one dimension. Also we consider the case where the interaction is concentrated near a hyperplane.

scholarly journals Bounds on the Spectral Shift Function and the Density of States

2005 ◽  
Vol 262 (2) ◽  
pp. 489-503 ◽  
Author(s):  
Dirk Hundertmark ◽  
Rowan Killip ◽  
Shu Nakamura ◽  
Peter Stollmann ◽  
Ivan Veselić
Keyword(s):  
Density Of States ◽  
Spectral Shift ◽  
Shift Function ◽  
Spectral Shift Function

scholarly journals RESONANCES AND SPECTRAL SHIFT FUNCTION FOR THE SEMI-CLASSICAL DIRAC OPERATOR

2007 ◽  
Vol 19 (10) ◽  
pp. 1071-1115 ◽  
Author(s):  
ABDALLAH KHOCHMAN
Keyword(s):  
Dirac Operator ◽  
Upper Bound ◽  
Selfadjoint Operator ◽  
Energy Levels ◽  
Critical Energy ◽  
Spectral Shift ◽  
Approximation Formula ◽  
Shift Function ◽  
Spectral Shift Function ◽  
Electro Magnetic

We consider the selfadjoint operator H = H0+ V, where H0is the free semi-classical Dirac operator on ℝ3. We suppose that the smooth matrix-valued potential V = O(〈x〉-δ), δ > 0, has an analytic continuation in a complex sector outside a compact. We define the resonances as the eigenvalues of the non-selfadjoint operator obtained from the Dirac operator H by complex distortions of ℝ3. We establish an upper bound O(h-3) for the number of resonances in any compact domain. For δ > 3, a representation of the derivative of the spectral shift function ξ(λ,h) related to the semi-classical resonances of H and a local trace formula are obtained. In particular, if V is an electro-magnetic potential, we deduce a Weyl-type asymptotics of the spectral shift function. As a by-product, we obtain an upper bound O(h-2) for the number of resonances close to non-critical energy levels in domains of width h and a Breit–Wigner approximation formula for the derivative of the spectral shift function.

Spectral shift function and trace formula for unitaries?A new proof

1996 ◽  
Vol 24 (3) ◽  
pp. 285-297 ◽  
Author(s):  
A. Mohapatra ◽  
Kakyan B. Sinha
Keyword(s):  
Trace Formula ◽  
Spectral Shift ◽  
Shift Function ◽  
Spectral Shift Function
Sign in / Sign up

Export Citation Format

Share Document