Spectral properties of a short-range impurity in a quantum dot

The spectral properties of the quantum mechanical system consisting of a quantum dot with a short-range attractive impurity inside the dot are investigated in the zero-range limit. The Green function of the system is obtained in an explicit form. In the case of a spherically symmetric quantum dot, the dependence of the spectrum on the impurity position and the strength of the impurity potential is analyzed in detail. It is proven that the confinement potential of the dot can be recovered from the spectroscopy data. The consequences of the hidden symmetry breaking by the impurity are considered. The effect of the positional disorder is studied.Comment: 30 pages, 6 figures, Late

Spectra of self-adjoint extensions and applications to solvable Schroedinger operators

We give a self-contained presentation of the theory of self-adjoint extensions using the technique of boundary triples. A description of the spectra of self-adjoint extensions in terms of the corresponding Krein maps (Weyl functions) is given. Applications include quantum graphs, point interactions, hybrid spaces, singular perturbations.Comment: 81 pages, new references added, subsection 1.3 extended, typos correcte

Zero modes in a system of Aharonov-Bohm fluxes

We study zero modes of two-dimensional Pauli operators with Aharonov--Bohm fluxes in the case when the solenoids are arranged in periodic structures like chains or lattices. We also consider perturbations to such periodic systems which may be infinite and irregular but they are always supposed to be sufficiently scarce

Localization on quantum graphs with random vertex couplings

We consider Schr\"odinger operators on a class of periodic quantum graphs with randomly distributed Kirchhoff coupling constants at all vertices. Using the technique of self-adjoint extensions we obtain conditions for localization on quantum graphs in terms of finite volume criteria for some energy-dependent discrete Hamiltonians. These conditions hold in the strong disorder limit and at the spectral edges

Topological effects in ring polymers: A computer simulation study

Unconcatenated, unknotted polymer rings in the melt are subject to strong interactions with neighboring chains due to the presence of topological constraints. We study this by computer simulation using the bond-fluctuation algorithm for chains with up to N=512 statistical segments at a volume fraction \Phi=0.5 and show that rings in the melt are more compact than gaussian chains. A careful finite size analysis of the average ring size R \propto N^{\nu} yields an exponent \nu \approx 0.39 \pm 0.03 in agreement with a Flory-like argument for the topologica interactions. We show (using the same algorithm) that the dynamics of molten rings is similar to that of linear chains of the same mass, confirming recent experimental findings. The diffusion constant varies effectively as D_{N} \propto N^{-1.22(3) and is slightly higher than that of corresponding linear chains. For the ring sizes considered (up to 256 statistical segments) we find only one characteristic time scale \tau_{ee} \propto N^{2.0(2); this is shown by the collapse of several mean-square displacements and correlation functions onto corresponding master curves. Because of the shrunken state of the chain, this scaling is not compatible with simple Rouse motion. It applies for all sizes of ring studied and no sign of a crossover to any entangled regime is found.Comment: 20 Pages,11 eps figures, Late

Entangled Polymer Rings in 2D and Confinement

The statistical mechanics of polymer loops entangled in the two-dimensional array of randomly distributed obstacles of infinite length is discussed. The area of the loop projected to the plane perpendicular to the obstacles is used as a collective variable in order to re-express a (mean field) effective theory for the polymer conformation. It is explicitly shown that the loop undergoes a collapse transition to a randomly branched polymer with $R\propto lN^\frac{1}{4}$.Comment: 17 pages of Latex, 1 ps figure now available upon request, accepted for J.Phys.A:Math.Ge

Self-diffusion in binary blends of cyclic and linear polymers

A lattice model is used to estimate the self-diffusivity of entangled cyclic and linear polymers in blends of varying compositions. To interpret simulation results, we suggest a minimal model based on the physical idea that constraints imposed on a cyclic polymer by infiltrating linear chains have to be released, before it can diffuse beyond a radius of gyration. Both, the simulation, and recently reported experimental data on entangled DNA solutions support the simple model over a wide range of blend compositions, concentrations, and molecular weights.Comment: 10 pages, 2 figure