Transport properties of a lateral semiconductor quantum dot defined by a single connected metallic front-gate

We present studies on the electric transport in a lateral GaAs/AlGaAs quantum dot defined by a patterned single connected metallic front-gate. This gate design allows to easily couple a large number of quantum dots and therefore holds high potential in the design of new materials with tailor-made band structures based on quantum dot superlattices of controlled shape. Clear Coulomb diamond structures and well pronounced tunneling peaks observed in experiment indicate that single-electron control has been achieved. However, the dependence on electron density in the heterostructure embedding the dot, which is controlled by an additional back-gate, reveals that transport characteristics are strongly influenced supposedly by potential fluctuations in the dot and lead regions.     

On the Dynamics of the Classical Transverse Field Ising Chain

We investigate stationary and travelling wave solutions of a special lattice differential equation in one space dimension. Depending on a parameter λ, results are given on the existence, shape and stability for these kind of solutions. The analysis of travelling wave solutions leads us to a functional differential equation with both forward and backward shifts. The existence of solutions of this equation will be proved by use of the implicit function theorem. In particular, we consider kink solutions and periodic solutions.     

The homotopy limit problem for two-primary algebraic K-theory

We solve the homotopy limit problem for two-primary algebraic K-theory of fields, that is, the Quillen-Lichtenbaum conjecture at the prime 2.     

Top condensation without fine-tuning

Quadratic divergencies which lead to the usual fine-tuning or hierarchy problem are discussed in top condensation models. As in the Standard Model a cancellation of quadratic divergencies is not possible without the boson contributions in the radiative corrections which are absent in lowest order of an 1/N_c-expansion. To deal with the cancellation of quadratic divergencies we propose therefore an expansion in the flavor degrees of freedom. In leading order we find the remarkable result that quadratic divergencies automatically disappear.     

Maximal regularity for the non-stationary Stokes system in an aperture domain

We prove estimates in L^s (0, T; L_w^q (W)) L^s (0, T; L_w^q (\Omega)) for the solution of the non-stationary Stokes system in an aperture domain, where 1 <s, q< ￥ \infty and the weight function w \omega is in the Muckenhoupt class A_q A_q .¶The result is achieved by combining a characterisation of maximal regularity by R {\mathcal R} -bounded operator families with the fact that R {\mathcal R} -boundedness follows from weighted estimates for Muckenhoupt weights.     

Sum-rule conserving spectral functions from the numerical renormalization group

We show how spectral functions for quantum impurity models can be calculated very accurately using a complete set of discarded numerical renormalization group eigenstates, recently introduced by Anders and Schiller. The only approximation is to judiciously exploit energy scale separation. Our derivation avoids both the overcounting ambiguities and the single-shell approximation for the equilibrium density matrix prevalent in current methods, ensuring that relevant sum rules hold rigorously and spectral features at energies below the temperature can be described accurately.     

Extension of the Jones matrix formalism to higher-order transverse modes

The well-known Jones matrix formalism, which can be directly applied to the propagation of the polarization of fundamental (TEM(00)) laser resonator modes, has to be modified for higher-order transverse modes. It is shown that this can be done in straightforward manner by using N x N matrices instead of the 2 x 2 Jones matrices, where N denotes the number of orthogonal polarization states of the transverse mode under consideration. The most common case of TEM(01) Hermite-Gaussian modes, where N is four, is discussed in detail.