The complex Busemann-Petty problem on sections of convex bodies

The complex Busemann-Petty problem asks whether origin symmetric convex bodies in \C^n with smaller central hyperplane sections necessarily have smaller volume. We prove that the answer is affirmative if $n\le 3$ and negative if $n\ge 4.$Comment: 18 page

Magnetic domains in III-V magnetic semiconductors

Recent progress in theoretical understanding of magnetic anisotropy and stiffness in III-V magnetic semiconductors is exploited for predictions of magnetic domain characteristics and methods of their tuning. We evaluate the width and the energy of domain walls as well as the period of stripe domains in perpendicular films. The computed stripe width d = 1.1 um for Ga_0.957Mn_0.043As/In_0.16Ga_0.84As compares favorably to the experimental value 1.5 um, as determined by Shono et al. [Appl. Phys. Lett. 77, 1363 (2000)].Comment: 4 RevTex pages, 2 figures spelling of author's names corrected in abstract pag

Non-perturbative gadget for topological quantum codes

Many-body entangled systems, in particular topologically ordered spin systems proposed as resources for quantum information processing tasks, often involve highly non-local interaction terms. While one may approximate such systems through two-body interactions perturbatively, these approaches have a number of drawbacks in practice. Here, we propose a scheme to simulate many-body spin Hamiltonians with two-body Hamiltonians non-perturbatively. Unlike previous approaches, our Hamiltonians are not only exactly solvable with exact ground state degeneracy, but also support completely localized quasi-particle excitations, which are ideal for quantum information processing tasks. Our construction is limited to simulating the toric code and quantum double models, but generalizations to other non-local spin Hamiltonians may be possible.Comment: 13 pages, 8 figures, PRL Accepte

Influence of spin waves on transport through a quantum-dot spin valve

We study the influence of spin waves on transport through a single-level quantum dot weakly coupled to ferromagnetic electrodes with noncollinear magnetizations. Side peaks appear in the differential conductance due to emission and absorption of spin waves. We, furthermore, investigate the nonequilibrium magnon distributions generated in the source and drain lead. In addition, we show how magnon-assisted tunneling can generate a fullly spin-polarized current without an applied transport voltage. We discuss the influence of spin waves on the current noise. Finally, we show how the magnonic contributions to the exchange field can be detected in the finite-frequency Fano factor.Comment: published version, 15 pages, 10 figure

Acoustic Properties of Amorphous Solids at Very Low Temperatures: The Quest for Interacting Tunneling States

We discuss the strain dependence of the acoustic properties of amorphous metals in both normal and superconducting states, in the temperature range 0.1 mK $\le T \le 1$K. A crossover is found when the strain energy is of the order of the effective interaction energy between tunneling systems at the corresponding temperature. Our results provide clear evidence for the interaction between tunneling systems, whose energy is in quantitative agreement with theoretical expectations, and reveal that without the knowledge of the corresponding strain dependences, the measured temperature dependences below $\sim 50$mK of the acoustic properties of disordered solids are rather meaningless.Comment: 13 pages, 3 figure

Super-poissonian noise, negative differential conductance, and relaxation effects in transport through molecules, quantum dots and nanotubes

We consider charge transport through a nanoscopic object, e.g. single molecules, short nanotubes, or quantum dots, that is weakly coupled to metallic electrodes. We account for several levels of the molecule/quantum dot with level-dependent coupling strengths, and allow for relaxation of the excited states. The current-voltage characteristics as well as the current noise are calculated within first-order perturbation expansion in the coupling strengths. For the case of asymmetric coupling to the leads we predict negative-differential-conductance accompanied with super-poissonian noise. Both effects are destroyed by fast relaxation processes. The non-monotonic behavior of the shot noise as a function of bias and relaxation rate reflects the details of the electronic structure and level-dependent coupling strengths.Comment: 8 pages, 7 figures, submitted to Phys. Rev. B, added reference

Nonmonotonic charge occupation in double dots

We study the occupation of two electrostatically-coupled single-level quantum dots with spinless electrons as a function of gate voltage. While the total occupation of the double-dot system varies monotonically with gate voltage, we predict that the competition between tunneling and Coulomb interaction can give rise to a nonmonotonic filling of the individual quantum dots. This non-monotonicity is a signature of the correlated nature of the many-body wavefunction in the reduced Hilbert space of the dots. We identify two mechanisms for this nonmonotonic behavior, which are associated with changes in the spectral weights and the positions, respectively, of the excitation spectra of the individual quantum dots. An experimental setup to test these predictions is proposed.Comment: 4 pages, 5 figure

Probing the exchange field of a quantum-dot spin valve by a superconducting lead

Electrons in a quantum-dot spin valve, consisting of a single-level quantum dot coupled to two ferromagnetic leads with magnetizations pointing in arbitrary directions, experience an exchange field that is induced on the dot by the interplay of Coulomb interaction and quantum fluctuations. We show that a third, superconducting lead with large superconducting gap attached to the dot probes this exchange field very sensitively. In particular, we find striking signatures of the exchange field in the symmetric component of the supercurrent with respect to the bias voltage applied between the ferromagnets already for small values of the ferromagnets' spin polarization.Comment: published version, 10 pages, 7 figure

Collective Molecular Dynamics in Proteins and Membranes

The understanding of dynamics and functioning of biological membranes and in particular of membrane embedded proteins is one of the most fundamental problems and challenges in modern biology and biophysics. In particular the impact of membrane composition and properties and of structure and dynamics of the surrounding hydration water on protein function is an upcoming hot topic, which can be addressed by modern experimental and computational techniques. Correlated molecular motions might play a crucial role for the understanding of, for instance, transport processes and elastic properties, and might be relevant for protein function. Experimentally that involves determining dispersion relations for the different molecular components, i.e., the length scale dependent excitation frequencies and relaxation rates. Only very few experimental techniques can access dynamical properties in biological materials on the nanometer scale, and resolve dynamics of lipid molecules, hydration water molecules and proteins and the interaction between them. In this context, inelastic neutron scattering turned out to be a very powerful tool to study dynamics and interactions in biomolecular materials up to relevant nanosecond time scales and down to the nanometer length scale. We review and discuss inelastic neutron scattering experiments to study membrane elasticity and protein-protein interactions of membrane embedded proteins