Angular distribution of radiation by relativistic electrons in a thin crystal

The results of theoretical investigation of angular distributions of radiation from a relativistic electron passing through a thin crystal at a small angle to the crystal axis are presented. The electron trajectories in crystal were simulated using the binary collision model which takes into account both coherent and incoherent effects at scattering. The angular distribution of radiation was calculated as a sum of radiation from each electron. It is shown that there are nontrivial angular distributions of the emitted photons, which is connected to the superposition of the coherent scattering of electrons by atomic rows (doughnut scattering effect) and the suppression of the radiation due to the multiple scattering effect (similar to the Landau-Pomeranchuk-Migdal effect in an amorphous matter). The orientation dependence of angular distribution of radiation is also analyzed

Influence of the confinement geometry on surface superconductivity

The nucleation field for surface superconductivity, $H_{c3}$, depends on the geometrical shape of the mesoscopic superconducting sample and is substantially enhanced with decreasing sample size. As an example we studied circular, square, triangular and wedge shaped disks. For the wedge the nucleation field diverges as $H_{c3}/H_{c2}=\sqrt{3}/\alpha$ with decreasing angle ($\alpha$) of the wedge, where $H_{c2}$ is the bulk upper critical field.Comment: 4 pages, 3 figures. Accepted for publication in Phys. Rev.

Phase transition curves for mesoscopic superconducting samples

We compute the phase transition curves for mesoscopic superconductors. Special emphasis is given to the limiting shape of the curve when the magnetic flux is large. We derive an asymptotic formula for the ground state of the Schr\"odinger equation in the presence of large applied flux. The expansion is shown to be sensitive to the smoothness of the domain. The theoretical results are compared to recent experiments.Comment: 8 pages, 1 figur

Critical temperature oscillations in magnetically coupled superconducting mesoscopic loops

We study the magnetic interaction between two superconducting concentric mesoscopic Al loops, close to the superconducting/normal phase transition. The phase boundary is measured resistively for the two-loop structure as well as for a reference single loop. In both systems Little-Parks oscillations, periodic in field are observed in the critical temperature Tc versus applied magnetic field H. In the Fourier spectrum of the Tc(H) oscillations, a weak 'low frequency' response shows up, which can be attributed to the inner loop supercurrent magnetic coupling to the flux of the outer loop. The amplitude of this effect can be tuned by varying the applied transport current.Comment: 9 pages, 7 figures, accepted for publication in Phys. Rev.

Waterlike thermodynamic anomalies in a repulsive-step potential system

We report a computer-simulation study of the equilibrium phase diagram of a three-dimensional system of particles with a repulsive step potential. The phase diagram is obtained using free-energy calculations. At low temperatures, we observe a number of distinct crystal phases. We show that at certain values of the potential parameters the system exhibits the water-like thermodynamic anomalies: density anomaly and diffusion anomaly. The anomalies disappear with increasing the repulsive step width: their locations move to the region inside the crystalline phase.Comment: 6 pages, 5 figure

Resonant nature of phonon-induced damping of Rabi oscillations in quantum dots

Optically controlled coherent dynamics of charge (excitonic) degrees of freedom in a semiconductor quantum dot under the influence of lattice dynamics (phonons) is discussed theoretically. We show that the dynamics of the lattice response in the strongly non-linear regime is governed by a semiclassical resonance between the phonon modes and the optically driven dynamics. We stress on the importance of the stability of intermediate states for the truly coherent control.Comment: 4 pages, 2 figures; final version; moderate changes, new titl

Associahedra via spines

An associahedron is a polytope whose vertices correspond to triangulations of a convex polygon and whose edges correspond to flips between them. Using labeled polygons, C. Hohlweg and C. Lange constructed various realizations of the associahedron with relevant properties related to the symmetric group and the classical permutahedron. We introduce the spine of a triangulation as its dual tree together with a labeling and an orientation. This notion extends the classical understanding of the associahedron via binary trees, introduces a new perspective on C. Hohlweg and C. Lange's construction closer to J.-L. Loday's original approach, and sheds light upon the combinatorial and geometric properties of the resulting realizations of the associahedron. It also leads to noteworthy proofs which shorten and simplify previous approaches.Comment: 27 pages, 11 figures. Version 5: minor correction

Mean parameter model for the Pekar-Fr\"{o}hlich polaron in a multilayered heterostructure

The polaron energy and the effective mass are calculated for an electron confined in a finite quantum well constructed of $GaAs/Al_x Ga_{1-x} As$ layers. To simplify the study we suggest a model in which parameters of a medium are averaged over the ground-state wave function. The rectangular and the Rosen-Morse potential are used as examples. To describe the confined electron properties explicitly to the second order of perturbations in powers of the electron-phonon coupling constant we use the exact energy-dependent Green function for the Rosen-Morse confining potential. In the case of the rectangular potential, the sum over all intermediate virtual states is calculated. The comparison is made with the often used leading term approximation when only the ground-state is taken into account as a virtual state. It is shown that the results are quite different, so the incorporation of all virtual states and especially those of the continuous spectrum is essential. Our model reproduces the correct three-dimensional asymptotics at both small and large widths. We obtained a rather monotonous behavior of the polaron energy as a function of the confining potential width and found a peak of the effective mass. The comparison is made with theoretical results by other authors. We found that our model gives practically the same (or very close) results as the explicit calculations for potential widths $L \geq 10 \AA$.Comment: 12 pages, LaTeX, including 5 PS-figures, subm. to Phys. Rev. B, new data are discusse

Dephasing times in quantum dots due to elastic LO phonon-carrier collisions

Interpretation of experiments on quantum dot (QD) lasers presents a challenge: the phonon bottleneck, which should strongly suppress relaxation and dephasing of the discrete energy states, often seems to be inoperative. We suggest and develop a theory for an intrinsic mechanism for dephasing in QD's: second-order elastic interaction between quantum dot charge carriers and LO-phonons. The calculated dephasing times are of the order of 200 fs at room temperature, consistent with experiments. The phonon bottleneck thus does not prevent significant room temperature dephasing.Comment: 4 pages, 1 figure, accepted for Phys. Rev. Let