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Showing 1 to 5 of 5 for “"Schrodinger operator"”.
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Two Random Multiplicative Processes: Multiplicative Cascades and Eigenvectors of the Random Schrodinger Operator
… of the one-dimensional discrete random Schrodinger operator. This is the Hamiltonian operator on the lattice of integers given by the discrete Laplacian plus an independent, identically distributed delta potential at each point. We restrict this operator to a finite box, pick an …
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A study of the computation and convergence behavior of eigenvalue bounds for self-adjoint operators
… problems. An example of a one dimensional Schrodinger operator with a potential is presented which arises in quantum mechanics. Examples using the recent eigenvector-free (EVF) method of Beattie and Goerisch are considered. Since the EVF method uses finite element trial functions as …
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Intrinsic Ultracontractivity and Other Properties of Mixed Barrier Brownian Motions
… also intrinsic ultracontractivity (IU) for some Schrodinger operator H. IU was introduced by E. B. Davies and B. Simon in 1984 and states that pt,x,y≤Ct 41x4 1y, where 41 is the ground state of H on D with mixed boundary conditions. Logarithmic Sobolev inequality and the theory of Dirichlet …
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Mean curvature flow self-shrinkers with genus and asymptotically conical ends
… in weighted Hölder spaces for the stability operator, which is a Schrodinger operator of Ornstein-Uhlenbeck type, on the self-shrinkers viewed as minimal surfaces. This material is, for the special case of graphs over the plane, included as part of the thesis. The results in (1)-(1') are …
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Eigenvalue Statistics for Random Block Operators
The Schrodinger Hamiltonian for a single electron in a crystalline solid with independent, identically distributed (i.i.d.) single-site potentials has been well studied. It has the form of a diagonal potential energy operator, which contains the random variables, plus a kinetic energy operator, …