Theory of anisotropic exchange in laterally coupled quantum dots

The effects of spin-orbit coupling on the two-electron spectra in lateral coupled quantum dots are investigated analytically and numerically. It is demonstrated that in the absence of magnetic field the exchange interaction is practically unaffected by spin-orbit coupling, for any interdot coupling, boosting prospects for spin-based quantum computing. The anisotropic exchange appears at finite magnetic fields. A numerically accurate effective spin Hamiltonian for modeling spin-orbit-induced two-electron spin dynamics in the presence of magnetic field is proposed.Comment: 4 pages, 3 figures; paper rewritte

Self-sustained magnetoelectric oscillations in magnetic resonant tunneling structures

The dynamic interplay of transport, electrostatic, and magnetic effects in the resonant tunneling through ferromagnetic quantum wells is theoretically investigated. It is shown that the carrier-mediated magnetic order in the ferromagnetic region not only induces, but also takes part in intrinsic, robust, and sustainable high-frequency current oscillations over a large window of nominally steady bias voltages. This phenomenon could spawn a new class of quantum electronic devices based on ferromagnetic semiconductors.Comment: 5 pages, 4 figure

The Ebers-Moll model for magnetic bipolar transistors

The equivalent electrical circuit of the Ebers-Moll type is introduced for magnetic bipolar transistors. In addition to conventional diodes and current sources, the new circuit comprises two novel elements due to spin-charge coupling. A classification scheme of the operating modes of magnetic bipolar transistors in the low bias regime is presented.Comment: 4 pages, 2 figure

State-Dependent Approach to Entropic Measurement-Disturbance Relations

Heisenberg's intuition was that there should be a tradeoff between measuring a particle's position with greater precision and disturbing its momentum. Recent formulations of this idea have focused on the question of how well two complementary observables can be jointly measured. Here, we provide an alternative approach based on how enhancing the predictability of one observable necessarily disturbs a complementary one. Our measurement-disturbance relation refers to a clear operational scenario and is expressed by entropic quantities with clear statistical meaning. We show that our relation is perfectly tight for all measurement strengths in an existing experimental setup involving qubit measurements.Comment: 9 pages, 2 figures. v4: published versio

Non-thermal X-rays, a high abundance ridge and fossil bubbles in the core of the Perseus cluster of galaxies

Using a deep Chandra observation of the Perseus cluster of galaxies, we find a high-abundance shell 250 arcsec (93 kpc) from the central nucleus. This ridge lies at the edge of the Perseus radio mini-halo. In addition we identify two Halpha filaments pointing towards this shell. We hypothesise that this ridge is the edge of a fossil radio bubble, formed by entrained enriched material lifted from the core of the cluster. There is a temperature jump outside the shell, but the pressure is continuous indicating a cold front. A non-thermal component is mapped over the core of the cluster with a morphology similar to the mini-halo. Its total luminosity is 4.8x10^43 erg/s, extending in radius to ~75 kpc. Assuming the non-thermal emission is the result of inverse Compton scattering of the CMB and infrared emission from NGC 1275, we map the magnetic field over the core of the cluster.Comment: 8 pages, colour, accepted by MNRA

Beating the Generator-Enumeration Bound for pp-Group Isomorphism

We consider the group isomorphism problem: given two finite groups G and H specified by their multiplication tables, decide if G cong H. For several decades, the n^(log_p n + O(1)) generator-enumeration bound (where p is the smallest prime dividing the order of the group) has been the best worst-case result for general groups. In this work, we show the first improvement over the generator-enumeration bound for p-groups, which are believed to be the hard case of the group isomorphism problem. We start by giving a Turing reduction from group isomorphism to n^((1 / 2) log_p n + O(1)) instances of p-group composition-series isomorphism. By showing a Karp reduction from p-group composition-series isomorphism to testing isomorphism of graphs of degree at most p + O(1) and applying algorithms for testing isomorphism of graphs of bounded degree, we obtain an n^(O(p)) time algorithm for p-group composition-series isomorphism. Combining these two results yields an algorithm for p-group isomorphism that takes at most n^((1 / 2) log_p n + O(p)) time. This algorithm is faster than generator-enumeration when p is small and slower when p is large. Choosing the faster algorithm based on p and n yields an upper bound of n^((1 / 2 + o(1)) log n) for p-group isomorphism.Comment: 15 pages. This is an updated and improved version of the results for p-groups in arXiv:1205.0642 and TR11-052 in ECC

Spin-orbit coupling and anisotropic exchange in two-electron double quantum dots

The influence of the spin-orbit interactions on the energy spectrum of two-electron laterally coupled quantum dots is investigated. The effective Hamiltonian for a spin qubit pair proposed in F. Baruffa et al., Phys. Rev. Lett. 104, 126401 (2010) is confronted with exact numerical results in single and double quantum dots in zero and finite magnetic field. The anisotropic exchange Hamiltonian is found quantitatively reliable in double dots in general. There are two findings of particular practical importance: i) The model stays valid even for maximal possible interdot coupling (a single dot), due to the absence of a coupling to the nearest excited level, a fact following from the dot symmetry. ii) In a weak coupling regime, the Heitler-London approximation gives quantitatively correct anisotropic exchange parameters even in a finite magnetic field, although this method is known to fail for the isotropic exchange. The small discrepancy between the analytical model (which employes the linear Dresselhaus and Bychkov-Rashba spin-orbit terms) and the numerical data for GaAs quantum dots is found to be mostly due to the cubic Dresselhaus term.Comment: 15 pages, 11 figure

Band-Structure Effects in the Spin Relaxation of Conduction Electrons

Spin relaxation of conduction electrons in metals is significantly influenced by the Fermi surface topology. Electrons near Brillouin zone boundaries, special symmetry points, or accidental degeneracy lines have spin flip rates much higher than an average electron. A realistic calculation and analytical estimates show that these regions dominate the spin relaxation, explaining why polyvalent metals have much higher spin relaxation rates (up to three orders of magnitude) than similar monovalent metals. This suggests that spin relaxation in metals can be tailored by band-structure modifications like doping, alloying, reducing the dimensionality, etc.Comment: 10 pages, 2 figures; to appear in the 43rd MMM Conference Proceedings published in the JA