Michael Dzierzawa

Scaling Behavior in the Stable Marriage Problem

We study the optimization of the stable marriage problem. All individuals attempt to optimize their own satisfaction, subject to mutually conflicting constraints. We find that the stable solutions are generally not the globally best solution, but reasonably close to it. All the stable solutions form a special sub-set of the meta-stable states, obeying interesting scaling laws. Both numerical and analytical tools are used to derive our results.

Statistics of stable marriages.

In the stable marriage problem N men and N women have to be matched by pairs under the constraint that the resulting matching is stable. We study the statistical properties of stable matchings in the large N limit using both numerical and analytical methods. Generalizations of the model including singles and unequal numbers of men and women are also investigated.

Phase diagram of the three-dimensional Hubbard model at half filling

Abstract:We investigate the phase diagram of the three-dimensional Hubbard model at half filling using quantum Monte Carlo (QMC) simulations. The antiferromagnetic Néel temperature is determined from the specific heat maximum in combination with finite-size scaling of the magnetic structure factor. Our results interpolate smoothly between the asymptotic solutions for weak and strong coupling, respectively, in contrast to previous QMC simulations. The location of the metal-insulator transition in the paramagnetic phase above is determined using the electronic compressibility as criterion.

Quasiclassical approach to the spin-Hall effect in the two-dimensional electron gas

We study the spin-charge coupled transport in a two-dimensional electron system using the method of quasiclassical (

Slave-Boson Approach to Spiral Magnetic Order in the Hubbard Model

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Spin polarizations and spin Hall currents in a two-dimensional electron gas with magnetic impurities

-integrated) Greens functions. In particular we derive the Eilenberger equation in the presence of a generic spin-orbit field. The method allows us to study spin and charge transport from ballistic to diffusive regimes and continuity equations for spin and charge are automatically incorporated. In the clean limit we establish the connection between the spin Hall conductivity and the Berry phase in momentum space. For finite systems we solve the Eilenberger equation numerically for the special case of the Rashba spin-orbit coupling and a two-terminal geometry. In particular, we calculate explicitly the spin Hall induced spin polarization in the corners, predicted by Mishchenko et al. [Phys. Rev. Lett. 93, 226602 (2004)]. Furthermore we find universal spin currents in the short-time dynamics after switching on the voltage across the sample, and calculate the corresponding spin Hall polarization at the edges. Where available, we find perfect agreement with analytical results.

Spin relaxation in narrow wires of a two-dimensional electron gas

We show that for the Hubbard model on the square lattice a spiral magnetic state characterized by a wave vector Q = (π - δQx, π), where δQx increases with the concentration δ of holes in the half-filled band, is lowest in energy within this class of states. This is obtained from a saddle point approximation of a spin-rotation-invariant form of the slave-boson representation introduced by Kotliar and Ruckenstein. The energy is within 2 percent of quantum Monte Carlo results.

Density functional theory for a model quantum dot: Beyond the local-density approximation

We consider a two-dimensional electron gas in the presence of Rashba spin-orbit coupling, and study the effects of magnetic s-wave and long-range nonmagnetic impurities on the spin-charge dynamics of the system. We focus on voltage induced spin polarizations and their relation to spin Hall currents. Our results are obtained using the quasiclassical Green function technique, and hold in the full range of the disorder parameter αpFτ.

Successes and failures of Bethe Ansatz Density Functional Theory

How does an initially homogeneous spin polarization in a confined two-dimensional electron gas with Rashba spin-orbit coupling evolve in time? How does the relaxation time depend on system size? We study these questions for systems of a size that is much larger than the Fermi wavelength, but comparable and even shorter than the spin relaxation length. Depending on the confinement spin relaxation may become faster or slower than in the bulk. An initially homogeneously polarized spin system evolves into a spiral pattern.

Hartree-Fock theory of spiral magnetic order in the 2-d Hubbard model

We study both static and transport properties of model quantum dots, employing density functional theory as well as (numerically) exact methods. For the lattice model under consideration the accuracy of the local-density approximation generally is poor. For weak interaction, however, accurate results are achieved within the optimized effective potential method, while for intermediate interaction strengths a method combining the exact diagonalization of small clusters with density functional theory is very successful. Results obtained from the latter approach yield very good agreement with density matrix renormalization group studies, where the full Hamiltonian consisting of the dot and the attached leads has to be diagonalized. Furthermore we address the question whether static density functional theory is able to predict the exact linear conductance through the dot correctly - with, in general, negative answer.