$HC_*(A rtimes G)$ is the cyclic homology of the crossed product algebra $A rtimes G.$ For any $g epsilon G$ we will define a homomorphism from $HC_*^g(A),$ the twisted cylic homology of $A$ with respect to $g,$ to $HC_*(A rtimes G).$ If $G$ is the f
inite cyclic group generated by $g$ and $|G|=r$ is invertible in $k,$ then $HC_*(A rtimes G)$ will be isomorphic to a direct sum of $r$ copies of $HC_*^g(A).$ For the case where $|G|$ is finite and $Q subset k$ we will generalize the Karoubi and Connes periodicity exact sequences for $HC_*^g(A)$ to Karoubi and Connes periodicity exact sequences for $HC_*(A rtimes G)$ .
Measurements of the phonon density of states by inelastic neutron emph{time-of-flight} scattering and specific heat measurements along with first principles calculations, provide compelling evidence for the existence of an Einstein oscillator (emph{r
attler}) at ${omega}_{E1} approx$ 5.0 meV in the filled skutterudite Yb$_{0.2}$Co$_{4}$Sb$_{12}$. Multiple dispersionless modes in the measured density of states of Yb$_{0.2}$Co$_{4}$Sb$_{12}$ at intermediate transfer energies (14 meV $leq$ emph{$omega$} $leq$ 20 meV) are exhibited in both the experimental and theoretical emph{density-of-states} of the Yb-filled specimen. A peak at 12.4 meV is shown to coincide with a second Einstein mode at emph{$omega_{E2} approx$} 12.8 meV obtained from heat capacity data. The local modes at intermediate transfer energies are attributed to altered properties of the host CoSb$_{3}$ cage as a result of Yb-filling. It is suggested that these modes are owed to a complementary mechanism for the scattering of heat-carrying phonons in addition to the mode observed at ${omega}_{E1} , approx$ 5.0 meV. Our observations offer a plausible explanation for the significantly-higher textit{dimensionless figures of merit} of filled skutterudites, compared to their parent compounds.
Elastic neutron-scattering, inelastic x-ray scattering, specific-heat, and pressure-dependent electrical transport measurements have been made on single crystals of AuZn and Au_{0.52}Zn_{0.48} above and below their martensitic transition temperatures
(T_M=64K and 45K, respectively). In each composition, elastic neutron scattering detects new commensurate Bragg peaks (modulation) appearing at Q = (1.33,0.67,0) at temperatures corresponding to each samples T_M. Although the new Bragg peaks appear in a discontinuous manner in the Au_{0.52}Zn_{0.48} sample, they appear in a continuous manner in AuZn. Surprising us, the temperature dependence of the AuZn Bragg peak intensity and the specific-heat jump near the transition temperature are in favorable accord with a mean-field approximation. A Landau-theory-based fit to the pressure dependence of the transition temperature suggests the presence of a critical endpoint in the AuZn phase diagram located at T_M*=2.7K and p*=3.1GPa, with a quantum saturation temperature theta_s=48.3 +/- 3.7K.
We propose and demonstrate the method of population transfer by piecewise adiabatic passage between two quantum states. Coherent excitation of a two-level system with a train of ultrashort laser pulses is shown to reproduce the effect of an adiabatic
passage, conventionally achieved with a single frequency-chirped pulse. By properly adjusting the amplitudes and phases of the pulses in the excitation pulse train, we achieve complete and robust population transfer to the target state. The effect is demonstrated experimentally by observing piecewise excitation of Rubidium atoms from 5s_1/2 to 5p_1/2 electronic state. We show that similarly to the conventional adiabatic passage, the piecewise process is insensitive to the total excitation energy as long as the adiabaticity conditions are satisfied. The piecewise nature of the process suggests that robust and selective population transfer could be implemented in a variety of complex quantum systems beyond the two-level approximation.
Ti50 Pd50-xCrx is a high temperature shape memory alloy with a martensitic transformation temperature strongly dependent on the Cr composition. Prior to the transformation a premartensitic phase is present with an incommensurate modulated cubic latti
ce with wave vector of q0=(0.22, 0.22, 0). The temperature dependence of the diffuse scattering in the cubic phase is measured as a function temperature for x=6.5, 8.5, and 10 at. %. The lattice dynamics has been studied and reveals anomalous temperature and q-dependence of the [110]-TA2 transverse phonon branch. The phonon linewidth is broad over the entire Brillouin zone and increases with decreasing temperature, contrary to the behavior expected for anharmonicity. No anomaly is observed at q0. The results are compared with first principles calculation of the phonon structure.
