Memory effects in the two-level model for glasses

We study an ensemble of two-level systems interacting with a thermal bath. This is a well-known model for glasses. The origin of memory effects in this model is a quasistationary but nonequilibrium state of a single two-level system, which is realized due to a finite-rate cooling and slow thermally activated relaxation. We show that single-particle memory effects, such as negativity of the specific heat under reheating, vanish for a sufficiently disordered ensemble. In contrast, a disordered ensemble displays a collective memory effect [similar to the Kovacs effect], where nonequilibrium features of the ensemble are monitored via a macroscopic observable. An experimental realization of the effect can be used to further assess the consistency of the model.     

Efficient power scaling of laser radiation by spectral beam combining

The possibility of achieving multikilowatt laser radiation by spectrally combining beams using volume Bragg gratings (VBGs) is shown. The VBGs recorded in a photothermorefractive glass exhibit long-term stability of all its parameters in high-power laser beams with power density >1 MW/cm2 in the cw beam of total power on a kilowatt level. We consider an architecture-specific beam-combining scheme and address the cross-talk minimization problem based on optimal channel positioning. Five-channel high efficiency spectral beam combining resulted in a >750 W near-diffraction-limited cw beam has been demonstrated experimentally.     

Multi-phonon capture of charge carriers by dislocation kinks in semiconductors

In view of the problem of recombination-enhanced motion of dislocations in semiconductors, we studied the thermal capture of an electron by a smooth dislocation kink. Multi-phonon capture becomes possible due to localization of the carrier on the kink. The localized state on the smooth kink is studied in the deformation potential approximation. In this case the potential created by the kink is described by Poschl-Teller function, which enables to find the analytical expressions for the eigenstates and the corresponding wave functions. With the use of the ground state wave function we find the multi-phonon capture cross-section for two limiting temperature cases, corresponding to the thermally activated and quantum transitions between vibronic terms.     

The Crystal Structure of Kx(MgxIn1–x)F3 (x = 0.38): a New Magnéli‐Bronze Type Fluoride

K_x(Mg_xIn_1–x)F₃ (x = 0.38) is monoclinic, pseudo tetragonal: a = 12.781(2) Å, b = 12.787(2) Å, c = 7.930(1) Å, β = 90,00(1)°, Z = 20. The crystal structure was solved in the space group P2₁/a (No. 14), subgroup of the tetragonal space group P4/mbm (No. 127), from X‐ray single crystal data using 4302 unique reflections (1770 with F_o/σ(F_o) > 4). The final observed R factor is 0.053. K_x(Mg_xIn_1–x)F₃ has the Magnéli‐bronze structural type, which consists in a tridimensional framework of mixed [(Mg_xIn_1–x)F₆] octahedra linked together by corners. The potassium ions are mainly located in large almost fully occupied 15‐coordinated sites and in practically empty 12‐coordinated cavities.     

Direct Deprotonative Functionalization of α,α-Difluoromethyl Ketones using a Catalytic Organosuperbase

The deprotonative functionalization of α,α-difluoromethyl ketones is described herein. Using a catalytic organosuperbase and a silane additive, the corresponding difluoroenolate could be generated and trapped with aldehydes to deliver various α,α-difluoro-β-hydroxy ketones in high yields. This new strategy tolerates numerous functional groups and represents the access to the difluoroenolate by direct deprotonation of the difluoromethyl unit. The diastereoselective version of the reaction was also investigated with d.r. up to 93 : 7. Several transformations were performed to demonstrate the synthetic potential of these α,α-difluoro-β-hydroxy ketones. In addition, this method has been extended to the use of other electrophiles such as imines and chalcogen derivatives, and a difluoromethyl sulfoxide as nucleophile, thus leading to a diversity of difluoromethylene compounds.     

Enumeration of Łukasiewicz paths modulo some patterns

For any pattern $\alpha$ of length at most two, we enumerate equivalence classes of ?ukasiewicz paths of length $n\ge 0$ where two paths are equivalent whenever the occurrence positions of $\alpha$ are identical on these paths. As a byproduct, we give a constructive bijection between Motzkin paths and some equivalence classes of ?ukasiewicz paths.