Crystal nucleation mechanism in melts of short polymer chains under quiescent conditions and under shear flow

We present a molecular dynamics simulation study of crystal nucleation from undercooled melts of n-alkanes, and we identify the molecular mechanism of homogeneous crystal nucleation under quiescent conditions and under shear flow. We compare results for n-eicosane(C20) and n-pentacontahectane(C150), i.e. one system below the entanglement length and one above. Under quiescent conditions, we observe that entanglement does not have an effect on the nucleation mechanism. For both chain lengths, the chains first align and then straighten locally. Then the local density increases and finally positional ordering sets in. At low shear rates the nucleation mechanism is the same as under quiescent conditions, while at high shear rates the chains align and straighten at the same time. We report on the effects of shear rate and temperature on the nucleation rates and estimate the critical shear rates, beyond which the nucleation rates increase with the shear rate. We show that the viscosity of the system is not affected by the crystalline nuclei.Comment: 9 page

The Early Crystal Nucleation Process in Hard Spheres shows Synchronised Ordering and Densification

We investigate the early part of the crystal nucleation process in the hard sphere fluid using data produced by computer simulation. We find that hexagonal order manifests continuously in the overcompressed liquid, beginning approximately one diffusion time before the appearance of the first `solid-like' particle of the nucleating cluster, and that a collective influx of particles towards the nucleation site occurs simultaneously to the ordering process: the density increases leading to nucleation are generated by the same individual particle displacements as the increases in order. We rule out the presence of qualitative differences in the early nucleation process between medium and low overcompressions, and also provide evidence against any separation of translational and orientational order on the relevant lengthscales

Qudit Colour Codes and Gauge Colour Codes in All Spatial Dimensions

Two-level quantum systems, qubits, are not the only basis for quantum computation. Advantages exist in using qudits, d-level quantum systems, as the basic carrier of quantum information. We show that color codes, a class of topological quantum codes with remarkable transversality properties, can be generalized to the qudit paradigm. In recent developments it was found that in three spatial dimensions a qubit color code can support a transversal non-Clifford gate, and that in higher spatial dimensions additional non-Clifford gates can be found, saturating Bravyi and K\"onig's bound [Phys. Rev. Lett. 110, 170503 (2013)]. Furthermore, by using gauge fixing techniques, an effective set of Clifford gates can be achieved, removing the need for state distillation. We show that the qudit color code can support the qudit analogues of these gates, and show that in higher spatial dimensions a color code can support a phase gate from higher levels of the Clifford hierarchy which can be proven to saturate Bravyi and K\"onig's bound in all but a finite number of special cases. The methodology used is a generalisation of Bravyi and Haah's method of triorthogonal matrices [Phys. Rev. A 86 052329 (2012)], which may be of independent interest. For completeness, we show explicitly that the qudit color codes generalize to gauge color codes, and share the many of the favorable properties of their qubit counterparts.Comment: Authors' final cop