Low-temperature lattice thermal expansion of the II-VI semiconductor ZnSe

The low-temperature lattice thermal expansion of the wide gap semiconductor ZnSe is investigated using the quasi-harmonic theory of thermal expansion. The generalized Grüneisen parameters (GPs) of the elastic waves propagating in different directions with respect to the [001] crystallographic axis are calculated using the second-and third-order elastic constants. The values of the generalized GPs γ_j are generally positive except for γ₂ from θ=25 to 65°. The Brugger gamma is calculated and the low-temperature limit of the Grüneisen gamma is determined using the procedure of Menon and Rao. The low-temperature limit has been obtained as 0.46 for ZnSe. The volume expansion is expected to be positive down to absolute zero for ZnSe, since is positive.     

Geometrical properties of local dynamics in Hamiltonian systems: The Generalized Alignment Index (GALI) method

We investigate the detailed dynamics of multi-dimensional Hamiltonian systems by studying the evolution of volume elements formed by unit deviation vectors about their orbits. The behavior of these volumes is strongly influenced by the regular or chaotic nature of the motion, the number of deviation vectors, their linear (in)dependence and the spectrum of Lyapunov exponents. The different time evolution of these volumes can be used to identify rapidly and efficiently the nature of the dynamics, leading to the introduction of quantities that clearly distinguish between chaotic behavior and quasiperiodic motion on N-dimensional tori. More specifically we introduce the Generalized Alignment Index of order k () as the volume of a generalized parallelepiped, whose edges are k initially linearly independent unit deviation vectors with respect to the orbit studied whose magnitude is normalized to unity at every time step. We show analytically and verify numerically on particular examples of N-degree-of-freedom Hamiltonian systems that, for chaotic orbits, tends exponentially to zero with exponents that involve the values of several Lyapunov exponents. In the case of regular orbits, fluctuates around non-zero values for 2≤k≤N and goes to zero for N<k≤2N following power laws that depend on the dimension of the torus and the number m of deviation vectors initially tangent to the torus: ∝t^{−2(k−N)+m} if 0≤m<k−N, and ∝t^−(k−N) if m≥k−N. The is a generalization of the Smaller Alignment Index (SALI) (). However, provides significantly more detailed information on the local dynamics, allows for a faster and clearer distinction between order and chaos than SALI and works even in cases where the SALI method is inconclusive.     

Crystal field effect and geometric frustration in Er2Ti2O7 —an XY antiferromagnetic pyrochlore

Magnetic susceptibility of powder Er₂Ti₂O₇ (ErT) is measured between 300 K and 80 K. shows a Curie-Weiss (CW) type behaviour with   ErTiO_3.5 and . A crystal field (CF) analysis of our experimental data, g-values (g_∥=0.27 and g_⊥=7.8) and the positions of two CF levels (reported earlier from an inelastic neutron scattering study) provide CF parameters and CF levels of the ground ⁴I_15/2 and excited multiplets of ErT. The theoretical follows a CW-type behaviour, with . Single-ion magnetic anisotropy (χ_⊥−χ_∥) is 9500×10⁻⁶ emu/mol ErTiO_3.5 at 300 K, which increases by ∼54 times at 10 K and ErT resembles an XY planar system. It can be inferred from CF analysis that the earlier observed change of from −13 K to −22 K below 50 K is not due to the CF effect. Nuclear hyperfine (HF) levels of ¹⁶⁷ErT and ¹⁶⁶ErT are calculated and the theoretical curve of vs. T (K) for T<T_N matches the observed results. Mössbauer lines expected for ¹⁶⁶ErT are also predicted.     

The q-gamma and (q,q)-polygamma functions of Tsallis statistics

An axiomatic definition is given for the q-gamma function of Tsallis (non-extensive) statistical physics, the continuous analogue of the q-factorial of Suyari [H. Suyari, Physica A 368 (1) (2006) 63], and the q-analogue of the gamma function of Euler and Gauss. A working definition in closed form, based on the Hurwitz and Riemann zeta functions (including their analytic continuations), is shown to satisfy this definition. Several relations involving the q-gamma and other functions are obtained. The (q,q)-polygamma functions , defined by successive derivatives of , where ln_qa=(1−q)⁻¹(a^1−q−1),a>0 is the q-logarithmic function, are also reported. The new functions are used to calculate the inferred probabilities and multipliers for Tsallis systems with finite numbers of particles N?∞.     

EPR and optical study of Mn-doped bis(l-Asparaginato)Zn(II)

EPR and optical studies of single crystals of Mn²⁺: bis(l-Asparaginato)Zn(II) are reported. The spin-Hamiltonian parameters are determined employing the positions of a large number of resonance lines for various orientations of the external magnetic field. The best-fit zero-field parameters to the observed EPR spectra are obtained as, D=(228±2)×10⁻⁴ cm⁻¹, E=(58±2)×10⁻⁴ cm⁻¹ and a=(−12±1)×10⁻⁴ cm⁻¹,whereas g=2.0002±0.0002, , and . From the optical absorption study, the lattice distortion is suggested. The electron repulsion parameters (B and C) and crystal field parameters (Dq and α) evaluated from the fitting of observed optical spectra are: B=858 cm⁻¹, C=2620 cm⁻¹, Dq=950 cm⁻¹, and α=76 cm⁻¹.     

Anomalous thermostat and intraband discrete breathers

We investigate the dynamics of a macroscopic system which consists of an anharmonic subsystem embedded in an arbitrary harmonic lattice, including quenched disorder. The coupling between both parts is bilinear. Elimination of the harmonic degrees of freedom leads to a nonlinear Langevin equation with memory kernels and noise term for the anharmonic coordinates . For zero temperature, i.e. for , we prove that the support of the Fourier transform of and of the time averaged velocity-velocity correlation functions of the anharmonic system cannot overlap. As a consequence, the asymptotic solutions can be constant, periodic, quasiperiodic or almost periodic, and possibly weakly chaotic. For a sinusoidal trajectory with frequency we find that the energy E_T transferred to the harmonic system up to time T is proportional to T^α. If equals one of the phonon frequencies ω_ν, it is α=2. We prove that there is a zero measure set L such that for in its full measure complement R?L, it is α=0, i.e. there is no energy dissipation. Under certain conditions L contains a subset L^′ such that for the dissipation rate is nonzero and may be subdissipative (0≤α<1) or superdissipative (1<α≤2), compared to ordinary dissipation (α=1). Consequently, the harmonic bath does act as an anomalous thermostat, in variance with the common belief that elimination of a macroscopically large number of degrees of freedom always generates dissipation, forcing convergence to equilibrium. Intraband discrete breathers are such solutions which do not relax. We prove for arbitrary anharmonicity and small but finite coupling that intraband discrete breathers with frequency exist for all in a Cantor set C(k) of finite Lebesgue measure. This is achieved by estimating the contribution of small denominators appearing for , related to . For the small denominators do not lead to divergencies such that is a smooth and bounded function in t.     

Controlled Stark shifts in Er-doped crystalline and amorphous waveguides for quantum state storage

We present measurements of the linear Stark effect on the ⁴I_15/2 → ⁴I_13/2 transition in an Er³⁺-doped proton-exchanged LiNbO₃ crystalline waveguide and an Er³⁺-doped silicate fiber. The measurements were made using spectral hole burning techniques at temperatures below 4 K. We measured an effective Stark coefficient (Δμ_eχ)/(h) = 25 ± 1 kHz/V cm⁻¹ in the crystalline waveguide and  kHz/V cm⁻¹ in the silicate fiber. These results confirm the potential of erbium-doped waveguides for quantum state storage based on controlled reversible inhomogeneous broadening.     

Energy confinement and high-k turbulence on HT-7 tokamak

A CO₂ collective scattering system has been developed to measure medium and high-k density fluctuation on HT-7 tokamak. Energy confinement and high-k density fluctuation are studied in ohmic discharges. The saturation of confinement was observed at approximately . For kθ=23 cm⁻¹ turbulence, it is found that fluctuation levels have great increase for , and simultaneously a high frequency turbulence feature appear in the frequency spectra. For kθ=14 cm⁻¹ turbulence, it is observed that fluctuation levels have no changes in uncertainties and the spectra are similar at all discharges in this experiment.     

Spin-glass behavior and magnetocaloric effect in melt-spun TbCuAl alloys

Magnetic properties and magnetocaloric effects of amorphous and crystalline TbCuAl ribbons are investigated by measuring their ac susceptibilities including a nonlinear term and dc magnetizations. The in-phase third harmonic ac susceptibility is found to be negative. It can be well fitted by the expression at high temperatures, indicating a spin-glass behavior in amorphous TbCuAl alloy. ΔT_f(ω)/[T_f(ω)Δlog₁₀ω], a possible distinguishing criterion to judge the presence of a spin-glass behavior is ∼0.011. The frequency-dependent data can be well fitted by the conventional critical slowing down law and the spin-glass transition temperature is obtained to be 20.1 K. The maximum of magnetic entropy change reaches 4.5 J kg⁻¹ K⁻¹ for a field change of 0-50 000 Oe, while the crystalline TbCuAl compound experiences a simple ferromagnetic-to-paramagnetic phase transition. The peak value of magnetic entropy change is obtained at the Curie temperature and reaches 14.4 J kg⁻¹ K⁻¹ for the same field change, which is much larger than that of amorphous TbCuAl alloy.     

Young's modulus surface and Poisson's ratio curve for cubic metals

The general expressions for the compliance , Young's modulus E(h k l) and Poisson's ratio υ(h k l, θ) along arbitrary loading direction [h k l] are given for cubic crystals. The representation surface for which the length of the radius vector in the [h k l] direction equals to E(h k l) and representation curve for which the length of the radius vector with angle θ deviated from the reference directions , and equals to υ(100, θ), υ(110, θ) and υ(111, θ) for example, are constructed for six FCC metals Ag, Al, Au, Cu, Ni, Pb and seven BCC metals Cr, Fe, Mo, Nb, Ta, V, W.     

Manley-Rowe relations for an arbitrary discrete system

Manley-Rowe relations are formulated for a discrete Hamiltonian system with an arbitrary number of resonances. Assuming that the resonances are defined as , where is an n×n integer matrix of rank r<n, and |ω〉≡T(ω₁,…,ωn) is the frequency vector, the projection of the action vector |J〉 on is an adiabatic invariant. Hence n−r independent integrals, from where the conventional Manley-Rowe relations for a single resonance follow as a particular case.     

Density and well width dependences of the effective mass of two-dimensional holes in (100) GaAs quantum wells measured using cyclotron resonance at microwave frequencies

Cyclotron resonance at microwave frequencies is used to measure the band mass (m_b) of the two-dimensional holes (2DHs) in carbon-doped (100) GaAs/ Al_xGa_1−xAs heterostructures. The measured m_b shows strong dependences on both the 2DH density (p) and the GaAs quantum well width (W). For a fixed W, in the density range (0.4×10¹¹ to 1.1×10¹¹ cm⁻²) studied here, m_b increases with p, consistently with previous studies of the 2DHs on the (311)A surface. For a fixed , m_b increases from 0.22m_e at to 0.50m_e at , and saturates around 0.51m_e for .     

Laser excitation spectrum of C3 in the region 26 000-30 700 cm

The vibrational structure of the electronic state of C₃ in the region 26 000-30 775 cm⁻¹ has been re-examined, using laser excitation spectra of jet-cooled molecules. Rotational constants and vibrational energies have been determined for over 60 previously-unreported vibronic levels; a number of other levels have been re-assigned. The vibrational structure is complicated by interactions between levels of the upper and lower Born-Oppenheimer components of the state, and by the effects of the double minimum potential in the Q₃ coordinate, recognized by Izuha and Yamanouchi [16]. The present work shows that there is also strong anharmonic resonance between the overtones of the ν₁ and ν₃ vibrations. For instance, the levels 2 1⁺ 1 and 0 1 ⁺ 3 are nearly degenerate in zero order, but as a result of the resonance they give rise to two levels 139 cm⁻¹ apart, centered about the expected position of the 2 1⁺ 1 level. With these irregularities recognized, every observed vibrational level up to 30 000 cm⁻¹ (a vibrational energy of over 5000 cm⁻¹) can now be assigned. A vibronic level at 30181.4 cm⁻¹, which has a much lower B′ rotational constant than nearby levels of the state, possibly represents the onset of vibronic perturbations by the electronic state; this state is so far unknown, but is predicted by the ab initio calculations of Ahmed et al. [36].     

Quadratic temperature dependence of electron-phonon scattering in disordered V1−xPdx alloys

We report the results of a comprehensive study of weak localization and electron-electron interaction effects in disordered V_1−xPd_x alloys whose compositions are close to the (low T_c) A15 V₃Pd compound. Magnetoresistivity and zero field resistivity have been measured within the temperature range 1.5≤T≤300 K. The low-temperature resistivity obeys a law, which is explained by electron-electron interaction. We have determined the electron-phonon scattering time (τ_e-ph) for V_1−xPd_x alloys. Our results indicate an anomalous electron-phonon scattering rate obeying quadratic temperature dependence. This observation is interpreted by the existing theories of electron-phonon interactions.