37,448 research outputs found
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 -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
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