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

Classification of topologically protected gates for local stabilizer codes

Given a quantum error correcting code, an important task is to find encoded operations that can be implemented efficiently and fault-tolerantly. In this Letter we focus on topological stabilizer codes and encoded unitary gates that can be implemented by a constant-depth quantum circuit. Such gates have a certain degree of protection since propagation of errors in a constant-depth circuit is limited by a constant size light cone. For the 2D geometry we show that constant-depth circuits can only implement a finite group of encoded gates known as the Clifford group. This implies that topological protection must be "turned off" for at least some steps in the computation in order to achieve universality. For the 3D geometry we show that an encoded gate U is implementable by a constant-depth circuit only if the image of any Pauli operator under conjugation by U belongs to the Clifford group. This class of gates includes some non-Clifford gates such as the \pi/8 rotation. Our classification applies to any stabilizer code with geometrically local stabilizers and sufficiently large code distance.Comment: 6 pages, 2 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

Topological insulator and the Dirac equation

We present a general description of topological insulators from the point of view of Dirac equations. The Z_{2} index for the Dirac equation is always zero, and thus the Dirac equation is topologically trivial. After the quadratic B term in momentum is introduced to correct the mass term m or the band gap of the Dirac equation, the Z_{2} index is modified as 1 for mB>0 and 0 for mB<0. For a fixed B there exists a topological quantum phase transition from a topologically trivial system to a non-trivial one system when the sign of mass m changes. A series of solutions near the boundary in the modified Dirac equation are obtained, which is characteristic of topological insulator. From the solutions of the bound states and the Z_{2} index we establish a relation between the Dirac equation and topological insulators.Comment: 9 pages, published versio

Income and distance elasticities of values of travel time savings: New Swiss results

This paper presents the findings of a study looking into the valuation of travel time savings (VTTS) in Switzerland, across modes as well as across purpose groups. The study makes several departures from the usual practice in VTTS studies, with the main one being a direct representation of the income and distance elasticity of the VTTS measures. Here, important gains in model performance and significantly different results are obtained through this approach. Additionally, the analysis shows that the estimation of robust coefficients for congested car travel time is hampered by the low share of congested time in the overall travel time, and the use of an additional rate-of-congestion coefficient, in addition to a generic car travel time coefficient, is preferable. Finally, the analysis demonstrates that the population mean of the indicators calculated is quite different from the sample means and presents methods to calculate those, along with the associated variances. These variances are of great interest as they allow the generation of confidence intervals, which can be extremely useful in cost-benefit analyses

Frequency-Dependent Current Noise through Quantum-Dot Spin Valves

We study frequency-dependent current noise through a single-level quantum dot connected to ferromagnetic leads with non-collinear magnetization. We propose to use the frequency-dependent Fano factor as a tool to detect single-spin dynamics in the quantum dot. Spin precession due to an external magnetic and/or a many-body exchange field affects the Fano factor of the system in two ways. First, the tendency towards spin-selective bunching of the transmitted electrons is suppressed, which gives rise to a reduction of the low-frequency noise. Second, the noise spectrum displays a resonance at the Larmor frequency, whose lineshape depends on the relative angle of the leads' magnetizations.Comment: 12 pages, 15 figure