The rule for a subdiffusive particle in an extremely diverse environment

We consider a subdiffusive continuous time random walker in an inhomogeneous environment. Each microscopic random time is drawn from a waiting time probability density function (WT-PDF) of the form: , 0<β?1. The parameter k is a random quantity also, and is drawn from a PDF, , 0?γ<1, for a cutoff parameter . We show that the effective WT-PDF, ψ(t), obtained by averaging φ(t;k) with p(k), exhibits a transition in the rule that governs the power of ψ(t). ψ(t) obeys, , and μ is given by two different formula. When, 1−γ>β, μ=β, but otherwise, μ=1−γ. The rule for the scaling of ψ(t) reflects the competition between two different mechanisms for subdiffusion: subdiffusion due to the heavily tailed φ(t;k) for individual jumps, and subdiffusion due to the collective effect of an environment made of many slow local regions. These two different mechanisms for subdiffusion are not additive, and compete each other. The reported transition is dimension independent, and disappears when the power β is also distributed, in the range, 0<β?1. Simulations exemplified the transition, and implications are discussed.     

Finite and infinite dynamical systems of identical interacting particles

A dynamical system of infinite volume and of infinite number of identical interacting particles occupying energy levels has been constructed as the limit of an infinite sequence of finite, equivalent systems of increasing size and particle number. Systems both in equilibrium and in non-equilibrium state (designated S_∞=limS_k, , respectively, k=1,2,…) were investigated. The main results are:(i) The values in the T-limit (thermodynamic limit) of the physical quantities characterizing these systems are determined.(ii) The time evolution process both in and in systems is governed by the non-linear rate equations with common initial conditions p_i(t₀), where p_i(t)=n_i(t)/N are the occupation probabilities at time t. The time evolution process in the and systems is the same. The asymptotic approach to the equilibrium state is proved.(iii) For the case of the equilibrium state, the Boltzmann probability distribution p_i is given by the equation −lnp_i+a+e_ib=0 common to S_k and S_∞ systems with the same value of a and b. The term a=β⁻¹a_e, where a_e is the free energy per particle, and .(iv) The conditions for the equivalence of the systems being in equilibrium and also of the ones in non-equilibrium are stated.     

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.     

The nature of the rectilinear diameter singularity

The rigorous explanation for the term |t|^2β in the rectilinear diameter equation is given (t=(T_c−T)/T_c, β is the critical exponent for the asymptotic form of the equation of state). The optimal order parameter, for which the branches of binodal are symmetric, is constructed within the canonical formalism. It is shown that the ratio of the amplitudes for the diameter singularity of the order parameter before |t|^1−α and |t|^2β, where α determines the behavior of the heat capacity and β is the critical exponent of the order parameter, takes the universal character modulo non-universal factor which depends on the thermodynamic class of the corresponding states. The analysis of entropy for argon and water leads to β=0.33 and the corresponding amplitude ratio .     

Calorimetric and single crystal X-ray study of the phase transition of (PyH)2PdCl4

Polymorphic transition of pyridinium tetrachloropalladate(II) was investigated by heat capacity measurements and by single crystal X-ray structural analysis. A large λ-type anomaly was detected at 240 K in the temperature dependence of the heat capacity. The low-temperature phase (LTP) belongs to the triclinic space group with a=6.856(1), b=7.293(1), c=7.721(1) Å, α=75.180(2)°, β=71.081(2)°, γ=81.109(3)° at 100 K, and the high-temperature phase (HTP) to the same space group with a=7.217(2), b=7.470(2), c=7.880(2) Å, α=73.438(3)°, β=65.195(3)°, γ=82.727(4)° at 293 K. The pyridinium cations are ordered antiferroelectrically in LTP. In HTP, however, an orientational disorder of the cation was observed. The energy difference between potential wells for the reorientation of pyridinium ion in HTP is discussed referring to the results of the present single crystal X-ray and heat capacity as well as the previous ¹H NMR measurements. A five-site disorder model is shown to be consistent with both of the observations of ¹H NMR and X-ray study.     

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.     

Renewal-anomalous-heterogeneous files

Renewal-anomalous-heterogeneous files are solved. A simple file is made of Brownian hard spheres that diffuse stochastically in an effective 1D channel. Generally, Brownian files are heterogeneous: the spheres' diffusion coefficients are distributed and the initial spheres' density is non-uniform. In renewal-anomalous files, the distribution of waiting times for individual jumps is not exponential as in Brownian files, yet obeys: ψα(t)∼t−1−α, 0<α<1. The file is renewal as all the particles attempt jumping at the same time. It is shown that the mean square displacement (MSD) in a renewal-anomalous-heterogeneous file, 〈r²〉, obeys, , where nrml〈r²〉 is the MSD in the corresponding Brownian file. This scaling is an outcome of an exact relation (derived here) connecting probability density functions of Brownian files and renewal-anomalous files. It is also shown that non-renewal-anomalous files are slower than the corresponding renewal ones.     

Substantially low desorption barriers in recombinative desorption of deuterium from a Si(1 0 0) surface

We have studied desorption kinetics of deuterium molecules from a Si(1 0 0) surface by means of temperature-programmed desorption (TPD) spectra and isothermal desorptions.Three desorption components, denoted as β_1,A,β_1,B, and C, can be distinguished in semi-logarithmic plots of the TPD spectra.Their peak positions and intensities are strongly affected by the surface preparation methods employed, either with or without annealing to control the initial D coverage .Peak C appears at the leading edge of the TPD peak.It accounts for only about 5% of the TPD peak at and it diminishes rapidly with decreasing , vanishing at .In contrast, together the β_1,A and β_1,B peaks account for the whole TPD peak at any less than 1.0 ML. The maximum of the β_1,A peak is nearly constant at around the maximum temperature of the TPD peak.On the other hand, the β_1,B peak appears on the high-temperature side of the TPD peak and it systematically shifts to higher temperatures with decreasing .These results imply that first- and second-order kinetics are operating for the β_1,A and β_1,B desorptions, respectively.Isothermal desorption experiments confirm the above predicted kinetics for a limited region, namely .From the results for the rate curve analysis, the desorption barriers are evaluated to be 1.6 ± 0.1 eV and 1.8 ± 0.1 eV for the β_1,A and β_1,B desorptions, respectively.These values are substantially lower than the widely accepted value of ∼2.5 eV. To reproduce the measured TPD spectra we take the Arrhenius-type rate equation containing the first- and second-order rate terms for the β_1,A and β_1,B desorptions.The TPD spectra measured for can be reasonably fit with the proposed rate equation when the values given above for E_d,A and E_d,B are used. For , however, the TPD curves are not fit with the same values; rather, the best-fit curves require values for E_d,A and E_d,B larger than those given above. Combining the present kinetics results with those obtained by STM along with the studies, the β_1,A and β_1,B peaks may be attributed to desorption along the 2H path, while peak C may be attributed to desorption along the 4H path. The atomistic desorption mechanism as well as the energy relationship between the desorption barrier and isosteric heat of adsorption are discussed.     

Nuclear reactions and the double beta decay

Charge-exchange reactions of (n,p) and (p,n) types at intermediate energies are introduced as a tool for the study of nuclear matrix element in ββ decay. Here, the (n,p) type reactions are realized through , where ²He refers to two protons in a singlet ¹S₀ state and where both of these are momentum analyzed and detected by the same spectrometer and detector. These reactions have been developed and performed exclusively at KVI, Groningen (NL), using an incident deuteron energy of 183 MeV. The  reaction is of (p,n) type and was developed at the RCNP facility in Osaka (JP) at incident energies of 420 MeV. Using both reaction types one can extract the Gamow-Teller transition strengths B(GT⁺) and , which define the two “legs” of the ββ decay matrix elements for the 2νββ decay. The high resolution available in both reactions allows a detailed insight into the excitations of the intermediate odd-odd nuclei and, as will be shown, some unexpected features are being unveiled.     

On the symmetry and structure of the double perovskites Ba2LnRuO6 (Ln=La, Pr and Nd)

The structures of the double perovskites Ba₂LnRuO₆ (Ln=La, Pr and Nd) at room temperature were re-investigated by profile analysis of X-ray diffraction data. It has been shown that neither the triclinic nor the monoclinic P2₁/n space group correctly describes their structures. Ba₂LaRuO₆ is actually rhombohedral, space group , cell parameters a=6.03196(10) Å and α=60.298(2)°. On the other hand, both Ba₂PrRuO₆ and Ba₂NdRuO₆ are found to be cubic, space group , with the cell parameters a=8.48416(6) and 8.47061(5) Å, respectively.     

Structure of a high temperature phase of potassium dideuteriophosphate (DKDP)

We previously determined the crystal structures of the high temperature phases of KH₂PO₄ [J.A. Subramony, S. Lovell, B. Kahr, Chem. Mater. 10 (1998) 2053. [6]]. These triclinic and monoclinic phases were obtained by heating the room temperature tetragonal form until new crystal phases were identified by polarization microscopy. These samples were subsequently cooled to room temperature thereby preserving the metastable high temperature phases for analysis. KD₂PO₄ is distinct from KH₂PO₄ in that it crystallizes at room temperature in a monoclinic phase unknown for its isotopomer, therefore the question as to whether it would support the corresponding high temperature phases remained open until our report here of the transformation of monoclinic KD₂PO₄ to an isomorphous triclinic high temperature phase: space group P with a=7.475(1) Å, b=7.440(1) Å, c=7.184(1) Å, α=88.53(1) Å, β=86.81(1)°, γ=88.09(1)°, V=398.58 Å³. This is the first known high temperature phase of DKDP, a material coveted at room temperature for its optical properties.     

Experimental studies on the Kβ/Kα intensity ratio of Zn at different thickness and pressure

Kβ/Kα intensity ratios of Zn were measured at a photon excitation energy of using a high-resolution Si(Li) detector for several thickness at different pressure. Present results were compared with theoretical data and other experimental values. The results were in good agreement theoretical values based on Hartree-Fock theory.     

Germanium detector array — GERDA

GERDA will be a new experiment at the Laboratori Nazionali del Gran Sasso (LNGS) to study neutrinoless double beta decay of ⁷⁶Ge at background levels <10⁻³ cts/(keV kg y) at , two orders of magnitude lower than in the previous experiments. Bare Ge-diodes, enriched to 86% in ⁷⁶Ge, are operated in liquid argon complemented by a water shield to reduce the external backgrounds. Intrinsic backgrounds will be suppressed by the pulse shape analysis and segmented electrodes. In GERDAs first phase, the detector array will consist of the existing and refurbished detectors of the previous Heidelberg-Moscow and IGEX experiments. After one year of measurement, the setup should allow us to scrutinize the claimed observation of 0νββ decay in ⁷⁶Ge. In its second phase, GERDA will use an additional set of new enriched ⁷⁶Ge crystals, as segmented or point contact detectors. After 100 kg y the sensitivity will be ; this corresponds to an effective Majorana mass range from 0.1 eV to 0.2 eV.