Searcharxiv⌕ Search

arXiv subjects

W. D. Heiss

Publications and source records attributed to W. D. Heiss.

31 records · Page 2Linked to original sources
arXiv2000

Higher Order Effects in the Dielectric Constant of Percolative Metal-Insulator Systems above the Critical Point

The dielectric constant of a conductor-insulator mixture shows a pronounced maximum above the critical volume concentration. Further experimental evidence is presented as well as a theoretical consideration based on a phenomenological equation. Explicit expressions are given for the position of the maximum in terms of scaling parameters and the (complex) conductances of the conductor and insulator. In order to fit some of the data, a volume fraction dependent expression for the conductivity of the more highly conductive component is introduced.

cond-mat↗
arXiv1999

Repulsion of Resonance States and Exceptional Points

Level repulsion is associated with exceptional points which are square root singularities of the energies as functions of a (complex) interaction parameter. This is also valid for resonance state energies. Using this concept it is argued that level anti-crossing (crossing) must imply crossing (anti-crossing) of the corresponding widths of the resonance states. Further, itis shown that an encircling of an exceptional point induces a phase change of one wave function but not of the other. An experimental setup is discussed where this phase behaviour which differs from the one encountered at a diabolic point can be observed.

quant-ph↗
arXiv1999

Tri-axial Octupole Deformations and Shell Structure

Manifestations of pronounced shell effects are discovered when adding nonaxial octupole deformations to a harmonic oscillator model. The degeneracies of the quantum spectra are in a good agreement with the corresponding main periodic orbits and winding number ratios which are found by classical analysis.

nucl-th↗
arXiv1999

Phases of Wave Functions and Level Repulsion

Avoided level crossings are associated with exceptional points which are the singularities of the spectrum and eigenfunctions, when they are considered as functions of a coupling parameter. It is shown that the wave function of {\it one} state changes sign but not the other, if the exceptional point is encircled in the complex plane. An experimental setup is suggested where this peculiar phase change could be observed.

quant-ph↗
arXiv1998

Orbital Magnetism in Small Quantum Dots with Closed Shells

It is found that various kind of shell structure which occurs at specific values of the magnetic field leads to the disappearance of the orbital magnetization for particular magic numbers of small quantum dots with an electron number $A < 30$.

cond-mat↗
arXiv1998

Analytic Scaling Functions Applicable to Dispersion Measurements

Scaling functions, $F_+(ω/ω_c^+)$ and $F_-(ω/ω_c^-)$ for $ϕ>ϕ_c$ and $ϕ<ϕ_c$, respectively, are derived from an equation for the complex conductivity of binary conductor-insulator composites. It is shown that the real and imaginary parts of $F_{\pm}$ display most properties required for the percolation scaling functions. One difference is that, for $ω/ω_c<1$, $\Re F_-(ω/ω_c)$ has an $ω$-dependence of $(1+t)/t $ and not $ω^2$ as previously predicted, but never conclusively observed. Experimental results on a Graphite-Boron Nitride system are given which are in reasonable agreement with the $ω^{(1+t)/t}$ behaviour for $\Re F_-$. Anomalies in the real dielectric constant just above $ϕ_c$ are also discussed.

cond-mat↗
arXiv1998

Collectivity, Phase Transitions and Exceptional Points in Open Quantum Systems

Phase transitions in open quantum systems, which are associated with the formation of collective states of a large width and of trapped states with rather small widths, are related to exceptional points of the Hamiltonian. Exceptional points are the singularities of the spectrum and eigenfunctions, when they are considered as functions of a coupling parameter. In the present paper this parameter is the coupling strength to the continuum. It is shown that the positions of the exceptional points (their accumulation point in the thermodynamical limit) depend on the particular type and energy dependence of the coupling to the continuum in the same way as the transition point of the corresponding phase transition.

quant-ph↗
arXiv1997

Electronic shell structure of large metallic clusters in the modified harmonic oscillator

Shell structure in the single particle spectrum of deformed harmonic oscillator potentials when a term proportional to $(\vec L)^2$ is added is analyzed for a large particle number. A scaling law which gives a dividing line between regular and chaotic behavior in terms of energy, deformation and strength of the $(\vec L)^2$ term has been found. According to this law, shell structure survives for higher particle numbers only with lesser deformation.

cond-mat↗
arXiv1997

Shell Effects in Mesoscopic Systems

The main aim of the results presented here is to demonstrate and analyse the importance of shell effects in nuclei, metallic clusters and quantum dots.

nucl-th↗
arXiv1997

A Simple Shell Model for Quantum Dots in a Tilted Magnetic Field

A model for quantum dots is proposed, in which the motion of a few electrons in a three-dimensional harmonic oscillator potential under the influence of a homogeneous magnetic field of arbitrary direction is studied. The spectrum and the wave functions are obtained by solving the classical problem. The ground state of the Fermi-system is obtained by minimizing the total energy with regard to the confining frequencies. From this a dependence of the equilibrium shape of the quantum dot on the electron number, the magnetic field parameters and the slab thickness is found.

cond-mat.mes-hall↗
arXiv1997

Deformation of Quantum Dots in the Coulomb Blockade Regime

We extend the theory of Coulomb blockade oscillations to quantum dots which are deformed by the confining potential. We show that shape deformations can generate sequences of conductance resonances which carry the same internal wavefunction. This fact may cause strong correlations of neighboring conductance peaks. We demonstrate the relevance of our results for the interpretation of recent experiments on semiconductor quantum dots.

cond-mat.mes-hall↗
arXiv1994

Classical Analysis of Phenomenological Potentials for Metallic Clusters

The classical trajectories of single particle motion in a Wodds-Saxon and a modified Nilsson potential are studied for axial quadrupole deformation. Both cases give rise to chaotic behaviour when the deformation in the Woods-Saxon and the l**2 term in the modified Nilsson potential are turned on. Important similarities, in particular with regard to the shortest periodic orbits, have been found.

cond-mat↗