#### Filter Results:

- Full text PDF available (42)

#### Publication Year

2000

2016

- This year (0)
- Last 5 years (5)
- Last 10 years (21)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

- IVAN VESELIĆ
- 2004

We study the family of Hamiltonians which corresponds to the adjacency operators on a percolation graph. We characterise the set of energies which are almost surely eigenvalues with finitely supported eigenfunctions. This set of energies is a dense subset of the algebraic integers. The integrated density of states has discontinuities precisely at this set… (More)

- Ivan Veselić
- 2002

We study Schrödinger operators with a random potential of alloy type. The single site potentials are allowed to change sign. For a certain class of them we prove a Wegner estimate. This is a key ingredient in an existence proof of pure point spectrum of the considered random Schrödinger operators. Our estimate is valid for all bounded energy intervals and… (More)

- Dirk Hundertmark, Rowan Killip, Shu Nakamura, Peter Stollmann, Ivan Veselić
- 2004

We study spectra of Schrödinger operators on R . 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.… (More)

- IVAN VESELIĆ
- 2003

We consider the quantum site percolation model on graphs with an amenable group action. It consists of a random family of Hamiltonians. Basic spectral properties of these operators are derived: non-randomness of the spectrum and its components, existence of an self-averaging integrated density of states and an associated trace-formula.

We analyze Schrödinger operators whose potential is given by a singular interaction supported on a sub-manifold of the ambient space. Under the assumption that the operator has at least two eigenvalues below its essential spectrum we derive estimates on the lowest spectral gap. In the case where the sub-manifold is a finite curve in two dimensional… (More)

In this paper we study spectral properties of adjacency and Laplace operators on percolation subgraphs of Cayley graphs of amenable, finitely generated groups. In particular we describe the asymptotic behaviour of the integrated density of states (spectral distribution function) of these random Hamiltonians near the spectral minimum. The first part of the… (More)

We study homogeneous, independent percolation on general quasi-transitive graphs. We prove that in the disorder regime where all clusters are finite almost surely, in fact the expectation of the cluster size is finite. This extends a well-known theorem by Menshikov and Aizenman & Barsky to all quasi-transitive graphs. Moreover we deduce that in this… (More)

- IVAN VESELIĆ
- 2009

We study discrete alloy type random Schrödinger operators on `(Z). Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of operators. If the single site potential is compactly supported and the distribution of the coupling constant is of bounded variation a Wegner estimate holds.… (More)

- Ivan Veselić, IVAN VESELIĆ
- 2006

We give a survey on results on spectral properties of random Schrödinger operators. The focus is set on the integrated density of states (IDS). First we present a proof of the existence of a self-averaging IDS which is general enough to be applicable to random Schrödinger and Laplace-Beltrami operators on manifolds. Subsequently we study more specific… (More)

- Ivan Veselić
- 2008

We prove a localization theorem for continuous ergodic Schrödinger operators Hω := H0+Vω, where the random potential Vω is a nonnegative Anderson-type perturbation of the periodic operator H0. We consider a lower spectral band edge of σ(H0), say E = 0, at a gap which is preserved by the perturbation Vω . Assuming that all Floquet eigenvalues of H0, which… (More)