Unexpected systematic degeneracy in a system of two coupled Gaudin models with homogeneous couplings

We report an unexpected systematic degeneracy between different multiplets in an inversion symmetric system of two coupled Gaudin models with homogeneous couplings, as occurring for example in the context of solid state quantum information processing. We construct the full degenerate subspace (being of macroscopic dimension), which turns out to lie in the kernel of the commutator between the two Gaudin models and the coupling term. Finally we investigate to what extend the degeneracy is related to the inversion symmetry of the system and find that indeed there is a large class of systems showing the same type of degeneracy.Comment: 13 pages, 4 figure

Hyperfine induced spin and entanglement dynamics in Double Quantum Dots: A homogeneous coupling approach

We investigate hyperfine induced electron spin and entanglement dynamics in a system of two quantum dot spin qubits. We focus on the situation of zero external magnetic field and concentrate on approximation-free theoretical methods. We give an exact solution of the model for homogeneous hyperfine coupling constants (with all coupling coefficients being equal) and varying exchange coupling, and we derive the dynamics therefrom. After describing and explaining the basic dynamical properties, the decoherence time is calculated from the results of a detailed investigation of the short time electron spin dynamics. The result turns out to be in good agreement with experimental data.Comment: 10 pages, 8 figure

Perturbative regimes in central spin models

Central spin models describe several types of solid state nanostructures which are presently considered as possible building blocks of future quantum information processing hardware. From a theoretical point of view, a key issue remains the treatment of the flip-flop terms in the Hamiltonian in the presence of a magnetic field. We systematically study the influence of these terms, both as a function of the field strength and the size of the spin baths. We find crucial differences between initial states with central spin configurations of high and such of low polarizations. This has strong implications with respect to the influence of a magnetic field on the flip-flop terms in central spin models of a single and more than one central spin. Furthermore, the dependencies on bath size and field differ from those anticipated so far. Our results might open the route for the systematic search for more efficient perturbative treatments of central spin problems.Comment: 7 pages, 3 figure

Lane reduction in driven 2d-colloidal systems through microchannels

The transport behavior of a system of gravitationally driven colloidal particles is investigated. The particle interactions are determined by the superparamagnetic behavior of the particles. They can thus be arranged in a crystalline order by application of an external magnetic field. Therefore the motion of the particles through a narrow channel occurs in well-defined lanes. The arrangement of the particles is perturbed by diffusion and the motion induced by gravity. Due to these combined influences a density gradient forms along the direction of motion of the particles. A reconfiguration of the crystal is observed leading to a reduction of the number of lanes. In the course of the lane reduction transition a local melting of the quasi-crystalline phase to a disordered phase and a subsequent crystallization along the motion of the particles is observed. This transition is characterized experimentally and using Brownian dynamics (BD) simulations.Comment: 4 pages, 4 figure

Different types of integrability and their relation to decoherence in central spin models

We investigate the relation between integrability and decoherence in central spin models with more than one central spin. We show that there is a transition between integrability ensured by the Bethe ansatz and integrability ensured by complete sets of commuting operators. This has a significant impact on the decoherence properties of the system, suggesting that it is not necessarily integrability or nonintegrability which is related to decoherence, but rather its type or a change from integrability to nonintegrability.Comment: 4 pages, 3 figure

Swapping and entangling hyperfine coupled nuclear spin baths

We numerically study the hyperfine induced nuclear spin dynamics in a system of two coupled quantum dots in zero magnetic field. Each of the electron spins is considered to interact with an individual bath of nuclear spins via homogeneous coupling constants (all coupling coefficients being equal). In order to lower the dimension of the problem, the two baths are approximated by two single long spins. We demonstrate that the hyperfine interaction enables to utilize the nuclear baths for quantum information purposes. In particular, we show that it is possible to swap the nuclear ensembles on time scales of seconds and indicate that it might even be possible to fully entangle them. As a key result, it turns out that the larger the baths are, the more useful they become as a resource of quantum information. Interestingly, the nuclear spin dynamics strongly benefits from combining two quantum dots of different geometry to a double dot set up.Comment: 6 pages, 7 figure

Non-diffractive mechanisms in the ϕ\phi meson photoproduction on nucleons

We examine the non-diffractive mechanisms in the $\phi$ meson photoproduction from threshold up to a few GeV using an effective Lagrangian in a constituent quark model. The new data from CLAS at large angles can be consistently accounted for in terms of {\it s}- and {\it u}-channel processes. Isotopic effects arising from the reactions $\gamma p\to \phi p$ and $\gamma n\to \phi n$, are investigated by comparing the cross sections and polarized beam asymmetries. Our result highlights an experimental means of studying non-diffractive mechanisms in $\phi$ meson photoproduction.Comment: 4 eps figures, version accepted by Phys. Lett.

Binary trees, coproducts, and integrable systems

We provide a unified framework for the treatment of special integrable systems which we propose to call "generalized mean field systems". Thereby previous results on integrable classical and quantum systems are generalized. Following Ballesteros and Ragnisco, the framework consists of a unital algebra with brackets, a Casimir element, and a coproduct which can be lifted to higher tensor products. The coupling scheme of the iterated tensor product is encoded in a binary tree. The theory is exemplified by the case of a spin octahedron.Comment: 15 pages, 6 figures, v2: minor correction in theorem 1, two new appendices adde