Second-layer nucleation in coherent Stranski-Krastanov growth of quantum dots

We have studied the monolayer-bilayer transformation in the case of the coherent Stranski-Krastanov growth. We have found that the energy of formation of a second layer nucleus is largest at the center of the first-layer island and smallest on its corners. Thus nucleation is expected to take place at the corners (or the edges) rather than at the center of the islands as in the case of homoepitaxy. The critical nuclei have one atom in addition to a compact shape, which is either a square of i*i or a rectangle of i*(i-1) atoms, with i>1 an integer. When the edge of the initial monolayer island is much larger than the critical nucleus size, the latter is always a rectangle plus an additional atom, adsorbed at the longer edge, which gives rise to a new atomic row in order to transform the rectangle into the equilibrium square shape.Comment: 6 pages, 4 figures. Accepted version, minor change

The Boltzmann equation for colourless plasmons in hot QCD plasma. Semiclassical approximation

Within the framework of the semiclassical approximation, we derive the Boltzmann equation describing the dynamics of colorless plasmons in a hot QCD plasma. The probability of the plasmon-plasmon scattering at the leading order in the coupling constant is obtained. This probability is gauge-independent at least in the class of the covariant and temporal gauges. It is noted that the structure of the scattering kernel possesses important qualitative difference from the corresponding one in the Abelian plasma, in spite of the fact that we focused our study on the colorless soft excitations. It is shown that four-plasmon decay is suppressed by the power of $g$ relative to the process of nonlinear scattering of plasmons by thermal particles at the soft momentum scale. It is stated that the former process becomes important in going to the ultrasoft region of the momentum scale.Comment: 41, LaTeX, minor changes, identical to published versio

Minimal Universal Two-qubit Quantum Circuits

We give quantum circuits that simulate an arbitrary two-qubit unitary operator up to global phase. For several quantum gate libraries we prove that gate counts are optimal in worst and average cases. Our lower and upper bounds compare favorably to previously published results. Temporary storage is not used because it tends to be expensive in physical implementations. For each gate library, best gate counts can be achieved by a single universal circuit. To compute gate parameters in universal circuits, we only use closed-form algebraic expressions, and in particular do not rely on matrix exponentials. Our algorithm has been coded in C++.Comment: 8 pages, 2 tables and 4 figures. v3 adds a discussion of asymetry between Rx, Ry and Rz gates and describes a subtle circuit design problem arising when Ry gates are not available. v2 sharpens one of the loose bounds in v1. Proof techniques in v2 are noticeably revamped: they now rely less on circuit identities and more on directly-computed invariants of two-qubit operators. This makes proofs more constructive and easier to interpret as algorithm