The generalized Kupershmidt deformation for constructing new integrable systems from integrable bi-Hamiltonian systems

Based on the Kupershmidt deformation for any integrable bi-Hamiltonian systems presented in [4], we propose the generalized Kupershmidt deformation to construct new systems from integrable bi-Hamiltonian systems, which provides a nonholonomic perturbation of the bi-Hamiltonian systems. The generalized Kupershmidt deformation is conjectured to preserve integrability. The conjecture is verified in a few representative cases: KdV equation, Boussinesq equation, Jaulent-Miodek equation and Camassa-Holm equation. For these specific cases, we present a general procedure to convert the generalized Kupershmidt deformation into the integrable Rosochatius deformation of soliton equation with self-consistent sources, then to transform it into a $t$-type bi-Hamiltonian system. By using this generalized Kupershmidt deformation some new integrable systems are derived. In fact, this generalized Kupershmidt deformation also provides a new method to construct the integrable Rosochatius deformation of soliton equation with self-consistent sources.Comment: 21 pages, to appear in Journal of Mathematical Physic

Quantum convolutional data-syndrome codes

We consider performance of a simple quantum convolutional code in a fault-tolerant regime using several syndrome measurement/decoding strategies and three different error models, including the circuit model.Comment: Abstract submitted for The 20th IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC 2019

Crossing point phenomena (T* = 2.7 K) in specific heat curves of superconducting ferromagnets RuSr2Gd1.4Ce0.6Cu2O10-{\delta}

Crossing point phenomena are one of the interesting and still puzzling effects in strongly correlated electron systems. We have synthesized RuSr2Gd1.4Ce0.6Cu2O10-{\delta} (GdRu-1222) magneto-superconductor through standard solid state reaction route and measured its magnetic, transport and thermal properties. We also synthesized RuSr2Eu1.4Ce0.6Cu2O10-{\delta} (EuRu-1222) then measured its heat capacity in zero magnetic fields for reference. The studied compounds crystallized in tetragonal structure with space group I4/mmm. GdRu-1222 is a reported magneto-superconductor with Ru spins magnetic ordering at temperature around 110 K and superconductivity in Cu-O2 planes below around 40 K. To explore the crossing point phenomena, the specific heat [Cp (T)] was investigated in temperature range 1.9-250 K, under magnetic field of up to 70 kOe. Unfortunately though no magnetic and superconducting transitions are observed in specific heat, a Schottky type anomaly is observed at low temperatures below 20 K. This low temperature Schottky type anomaly can be attributed to splitting of the ground state spectroscopic term 8S7/2 of paramagnetic Gd3+ ions by both internal and external magnetic fields. It was also observed that Cp (T) being measured for different values of magnetic field, possesses the same crossing point (T* = 2.7 K), up to the applied magnetic field 70 kOe. A quantitative explanation of this phenomenon, based on its shape and temperature dependence of the associated generalized heat capacity (Cp), is presented. This effect supports the crossing point phenomena, which is supposed to be inherent for strongly correlated systems.Comment: 12 pages Text+Figs ([email protected]

SCAN+rVV10: A promising van der Waals density functional

The newly developed "strongly constrained and appropriately normed" (SCAN) meta-generalized-gradient approximation (meta-GGA) can generally improve over the non-empirical Perdew-Burke-Ernzerhof (PBE) GGA not only for strong chemical bonding, but also for the intermediate-range van der Waals (vdW) interaction. However, the long-range vdW interaction is still missing. To remedy this, we propose here pairing SCAN with the non-local correlation part from the rVV10 vdW density functional, with only two empirical parameters. The resulting SCAN+rVV10 yields excellent geometric and energetic results not only for molecular systems, but also for solids and layered-structure materials, as well as the adsorption of benzene on coinage metal surfaces. Especially, SCAN+rVV10 outperforms all current methods with comparable computational efficiencies, accurately reproducing the three most fundamental parameters---the inter-layer binding energies, inter-, and intra-layer lattice constants---for 28 layered-structure materials. Hence, we have achieved with SCAN+rVV10 a promising vdW density functional for general geometries, with minimal empiricism