Thermodynamical Limit for Correlated Gaussian Random Energy Models

 Let {E _Σ (N)} _ΣΣN be a family of |Σ _N |=2 ^N centered unit Gaussian random variables defined by the covariance matrix C _N of elements c _N (Σ,τ):=Av(E _Σ (N)E _τ (N)) and the corresponding random Hamiltonian. Then the quenched thermodynamical limit exists if, for every decomposition N=N ₁ +N ₂ , and all pairs (Σ,τ)Σ _N ×Σ _N :

Rotational and Translational Mobility of Nitroxide Spin Probes in Ionic Liquids and Molecular Solvents

Rotational and translational movements of 1-oxyl-2,2,6,6-tetramethyl-4-oxypiperidine (TEMPOL) spin probe in the room temperature ionic liquid (RTIL) 1-octyl-3-methylimidazolium tetrafluoroborate (omimBF₄) and in two molecular solvents, 1-propanol and isopropyl benzene (cumene), have been studied by X-band electron paramagnetic resonance (EPR) spectroscopy. Rotational correlation times τ _c of spin probes and the intermolecular spin exchange rate constants k _e were measured from EPR spectra at different temperatures and TEMPOL concentrations, and compared with the published data. The τ _c values were calculated both by known equations and from the EPR spectra simulation. Rotation movements of TEMPOL in omimBF₄ cannot be described by the model of the isotropic Brownian diffusion, which is valid for conventional solvents. The correct modeling of EPR spectra in RTIL can be achieved with the assumption of different rotational mobility of the spin probe around different molecular axes. The rotational, D _rot, and translational, D _tr, diffusion coefficients were calculated from τ _c and k _e values. The Debye–Stokes–Einstein law is valid in all three solvents while the dependence of D _tr on T/η is not linear in Stokes–Einstein coordinates. The effective activation energy E _rot^a of the rotational movements in omimBF₄ is noticeably higher than the corresponding values for conventional solvents, while the effective activation energies E _tr^a of the translational movements are comparable in all solvents studied.     

Universal crossover of liquid dynamics in supercritical region

We demonstrate that all liquids in supercritical region may exist in two qualitatively different states: solid-like and gas-like. Solid-like to gas-like crossover corresponds to the condition τ ≈ τ₀, where τ is liquid relaxation time and τ₀ is the minimum period of transverse waves. This condition corresponds to the loss of shear stiffness of a liquid at all frequencies and defines a new narrow crossover zone on the phase diagram. We show that the intersection of this zone corresponds to the disappearance of high-frequency sound, qualitative changes of diffusion and viscous flow, increase in particle thermal speed to half of the speed of sound and reduction of the specific heat at constant volume to 2k _B per particle. The new crossover is universal: it separates two liquid states at arbitrarily high pressure and temperature, and even exists in systems where liquid-gas transition and the critical point are absent overall.     

Chemical exchange of hydroxyl protons in quercetin measured by pulsed field gradient NMR

The diffusion behavior of hydroxyl protons (OH) in quercetin in 100% DMSO-d₆ (deuterium dimethylsulfoxide) and a 90% DMSO-d₆ solution containing 10% H₂O was investigated with 600 MHz ¹H pulsed field gradient (PFG) nuclear magnetic resonance (NMR). Only resonances of the 5-hydroxyl protons (OH5) were well resolved in NMR spectra of quercetin for all solutions under study. This phenomenon is explained by the intramolecular hydrogen bonding between OH5 protons and the 4-carbonyl oxygen (CO4). During diffusion experiments, the OH5 protons showed a biexponential diffusion decay, indicating an exchange process with water. As water content in the solvents increased, the lifetime (τ _q) of the OH5 protons decreased from 96.7±10.0 ms in 100% DMSO-d₆ to 14.3±1.4 ms in the 90% DMSO-d₆ solution containing 10% H₂O, indicating an increase in the exchange rate (k _q = l/τ _q) of the OH5 protons. This study demonstrates that the diffusion approach with PFG-NMR is much faster and easier for estimating the short lifetime or fast exchange rate of hydroxyl protons in quercetin.     

Average diffusion-to-the-wall times for laser-tagged molecules in a long cylinder

An approximate closed-form expression is derived for the average wall-reaching rate k_W or time τ_W=k_W ^-1 of laser-tagged molecules diluted in an inert carrier gas migrating to the wall of a long cylinder where they are removed with sticking coefficient η_W. The exact equation for the sticky wall problem requires a trial-and-error solution of a transcendental relation with Bessel–functions. With the aid of the Fermi–Amaldi albedo theory, an explicit “compromise” relation is derived which approximates the exact diffusion curve of k_W versus η_W rather well. The result is applied to obtain curves of k_W versus η_W at different gas mix pressures for UF₆ diluted in N₂. Received: 5 June 2000 / Revised version: 31 January 2001 / Published online: 27 April 2001     

Nonadiabatic corrections to the velocity of a Brownian motor with a complex potential profile

A number of laws have been established that govern the motion of a Brownian particle in a periodic potential profile for the adiabatically fast (with the time τ₀) and adiabatically slow variations in its shape. The average velocity of a particle has been calculated including a nonadiabatic contribution depending on τ₀ and the characteristic times of the system, which are determined by the characteristic features of the potential profile. It has been shown that the nonadiabatic correction to the velocity is proportional to τ₀² for a smooth potential profile and to τ₀ for a hopping movement in a potential containing barriers and wells, and this correction limits the large values of the rectification factor of motion for a high-performance motor operation mode.     

Separation of cross-relaxation and exchange in two-site spin systems without resolved couplings

Variable temperature two-dimensional nuclear Overhauser enhancement experiment (2-D NOESY) is used to extract the rate constants and cross-relaxation rates that contribute to the same cross-peaks in NOESY spectra. Rate constants (k _AB) and cross-relaxation rates (R _AB) for two-site spin systems are related to the ratio between the cross-peak and diagonal peak integrals (F) by the expression:R _AB -k _AB = (1/2τ _m)ln[(1 -F)/(1 +F)], where τ_m is the mixing time. As a model, we investigated the exchange processes in a system of dimer calix[4]arenes of C_4v symmetrical configuration with guest inclusion (benzene or benzene-d₆), where the measurement of exchange processes is hindered by the presence of strong nuclear Overhauser enhancement between protons in adjacent aromatic rings in the cone conformation of the calix[4]arene.     

Anisotropic impurity scattering in palladium silver alloys

Measurements have been made of the Hall coefficientR of some alloys of silver in palladium over the temperature range 1°K to 120°K. The alloys contain between ∼1 and ∼10 at.-% silver. Values ofR were also obtained at room temperature and these were in good agreement with earlier published work. The values ofR are negative in all the alloys, and |R| increases both on reducing the temperature and increasing the silver concentration,c. Below ∼10°K, |R| becomes independent of temperature but shows a linear dependence onc, increasing by a factor of 2.5 over the concentration range measured. This increase is too great to be accounted for in terms of band structure changes alone, so we have examined the effects of anisotropic impurity scattering. To a first approximation it can be shown thatR is proportional to an anisotropy parameterA, defined asA=〈τ ²(k)〉/〈τ(k)〉², whereτ(k) represents the relaxation time of an electron in a statek, and 〈〉 is an average over the Fermi surface. In palladium we assume that the majority of the current is carried by the s-electrons. In the presence of silver impurities these electrons can be scattered into s-states or d-states with relaxation times given byτ _ss α1/c(1−c) andτ _sd α1/c ²(1−c) respectively. FollowingPlate we have assumed thatτ _ss is isotropic and thatτ _sd is anisotropic, leading to an overall anisotropic relaxation time for impurity scattering. We then find the parameterA increases approximately linearly with silver content, in accordance with our experimental results.     

Trajectory attractor of a reaction-diffusion system with a series of zero diffusion coefficients

We study a reaction-diffusion system of N equations with k nonzero and N − k zero diffusion coefficients. More exactly, the first k equations of the system contain the terms a _i Δu _i − f _j (u, v), i = 1, …, k, with the diffusion coefficient a _i > 0. The right-hand sides of the other N − k equations contain only nonlinear interaction functions −h _j (u, v), j = k + 1, …, N, with zero diffusion. Here u = (u ₁, …, u _k ) and v = (υ _k+1, …, υ _N ) are unknown concentration vectors. Under appropriate assumptions on the interaction functions f(·) and h(·), we construct the trajectory attractor of this reaction-diffusion system. We also find the trajectory attractors , δ = (δ ₁, …, δ _k ), for the analogous reaction-diffusion systems having the terms δ _j Δυ _j − h _j (u, v), j = k + 1, …, N, with small diffusion coefficients δ _j ⩾ 0 in the last N − k equations. We prove that the trajectory attractors converge to (in an appropriate topology) as δ → 0+. Dedicated to the memory of Vladimir Borovikov Partially supported by the Russian Foundation for Basic Research (projects nos. 08-01-00784 and 07-01-00500).     

Magnetic structure of Ce<Subscript>2</Subscript>Fe<Subscript>17 − <Emphasis Type="Italic">x</Emphasis></Subscript>Mn<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> intermetallic compounds

The magnetic structure of intermetallic compounds Ce₂Fe_{17 − x} Mn _x (0 ≤ x ≤ 3) was studied using neutron diffraction. The neutron diffraction patterns measured at 4.2 K contain satellites indicating a modulated structure with the wave vector k = [0, 0, τ]. As the concentration x increases, the value of τ increases, while the average magnetic moment of Fe/Mn atoms decreases. A change in the magnitudes of the average magnetic moment and wave vector k is explained by competition between exchange interactions at distances of nearest neighbor transition element atoms.     

Photoelectrical characteristics of as-grown highresistance GaAs single crystals

The electrophysical and photoelectrical properties of high-resistance GaAs produced by single crystal growth are studied and analyzed. The electron (τ _n ) and hole (τ _p ) lifetimes are estimated. The charge-carrier lifetimes are compared in as-grown and diffusion high-resistance GaAs. The conclusion is made that in high-resistance GaAs produced by chromium diffusion, the charge-carrier recombination mechanism qualitatively differs from that in as-grown GaAs. The charge-carrier recombination in diffusion GaAs is determined by the occurrence of recombination barriers due to chromium diffusion.     

Defect entropies and enthalpies in BaF<Subscript>2</Subscript>

Various experimental techniques have revealed that the predominant intrinsic point defects in BaF₂ are anion Frenkel defects. Their formation, enthalpy and entropy, as well as the corresponding parameters for the fluorine vacancy and fluorine interstitial motion have been determined. In addition, low temperature dielectric relaxation measurements in BaF₂doped with uranium leads to the parameters τ₀, E in the Arrhenius relation τ = τ₀ exp(E/k _B T) for the relaxation time τ. For the relaxation peak associated with a single tetravalent uranium, the migration entropy deduced from the pre-exponential factor τ₀ is smaller than the anion Frenkel defect formation entropy by almost two orders of magnitude. We show that, despite their great variation, the defect entropies and enthalpies are interconnected through a model based on anharmonic properties of the bulk material which have been recently studied by employing density-functional theory and density-functional perturbation theory.     

An approximate expression for the galvanomagnetic tensor

Using the iterative solution to the Boltzmann equation for electrons in d.c. electric and magnetic fields, an expression for the resistivity tensor can be obtained in the form of an infinite series. This series can be approximated by retaining only the first two terms. In the cases where relaxation times exist — in the sense that the collision term in the Boltzmann equation can be written asg(k)/τ(k), whereτ(k) is the relaxation time, andf (k) = f _E(ɛ k) + [∂f _E(εk)/∂ε]·g(k) the distribution function for electrons with wavevectork — this approximation is exact. For polyvalent metals in the one-OPW approximation, the complete galvanomagnetic tensor can be obtained using this approximation and the result differs from that obtained by using a time of relaxation given by an expression suggested byZiman. A calculation for a simple model Fermi surface, with screened Coulomb scattering, is carried out and the results compared with those of the relaxation time approximation.     

Constructing Entanglement Witnesses for States in?Infinite-Dimensional Bipartite Quantum Systems

In this paper, two approaches of constructing entanglement witnesses for finite- or infinite-dimensional bipartite quantum systems are presented. Let H _A and H _B be complex Hilbert spaces and {E _k } and {F _k } be sequences of self-adjoint Hilbert-Schmidt operators on H _A and H _B , respectively, such that Tr(E^f_kE_l)=Tr(F^f_kF_l)=d_kl\mathrm{Tr}(E^{\dag}_{k}E_{l})=\mathrm{Tr}(F^{\dag}_{k}F_{l})=\delta_{kl}. Then W=I−∑ _k E _k ⊗F _k is an entanglement witness on H _A ⊗H _B if W\not 3 0W\not\geq 0. If ρ is an entangled state and τ ₀ is the nearest separable state to ρ under the Hilbert-Schmidt norm, then W=c ₀ I+τ ₀−ρ with c ₀=Tr[τ ₀(ρ−τ ₀)] is an entanglement witness.     

Zeros of Airy Function and Relaxation Process

One-dimensional system of Brownian motions called Dyson’s model is the particle system with long-range repulsive forces acting between any pair of particles, where the strength of force is β/2 times the inverse of particle distance. When β=2, it is realized as the Brownian motions in one dimension conditioned never to collide with each other. For any initial configuration, it is proved that Dyson’s model with β=2 and N particles, $\mbox {\boldmath $\mbox {\boldmath , is determinantal in the sense that any multitime correlation function is given by a determinant with a continuous kernel. The Airy function (z){\rm Ai}(z) is an entire function with zeros all located on the negative part of the real axis ℝ. We consider Dyson’s model with β=2 starting from the first N zeros of Ai(z){\rm Ai}(z) , 0>a ₁>⋅⋅⋅>a _N , N≥2. In order to properly control the effect of such initial confinement of particles in the negative region of ℝ, we put the drift term to each Brownian motion, which increases in time as a parabolic function: Y _j (t)=X _j (t)+t ²/4+{d ₁+∑ _ℓ=1 ^N (1/a _ℓ )}t,1≤j≤N, where d₁=Ai￠(0)/Ai(0)d_{1}={\rm Ai}'(0)/{\rm Ai}(0) . We show that, as the N→∞ limit of $\mbox {\boldmath $\mbox {\boldmath , we obtain an infinite particle system, which is the relaxation process from the configuration, in which every zero of (z){\rm Ai}(z) on the negative ℝ is occupied by one particle, to the stationary state m_Ai\mu_{{\rm Ai}} . The stationary state m_Ai\mu_{{\rm Ai}} is the determinantal point process with the Airy kernel, which is spatially inhomogeneous on ℝ and in which the Tracy-Widom distribution describes the rightmost particle position.     

Basic physics of semiconductor hydrogen sensors

The most probable physical models of hydrogen sensors based on thin stannic oxide films, MOS-structures, and tunnel MOS-diodes are discussed. The emphasis is on the mechanisms of formation of sensor response to hydrogen. The analytical equations describing the dependence of the response on the hydrogen concentration nH₂ are derived for all types of sensors. The relations describing the dependences of the SnO ₂-sensor conductivity and response on the absolute humidity of a gas mixture are given. It is shown that the relaxation time τ_rel of the response of SnO ₂-and MOS-structure sensors is determined by the relaxation time τ_a of hydrogen atom adsorption on the SnO ₂ and SiO ₂ surfaces, respectively. For the MOS-diodes, τ_rel = τ_a at nH₂ and τ_rel = τ_d at nH₂≥7.5·10³, where τ_d is the relaxation time of hydrogen atom diffusion through an SiO ₂ layer. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 84–98, April, 2008.     

Realistic searches on stretched exponential networks

We consider navigation or search schemes on networks which have a degree distribution of the form P(k) ∝ exp(−k ^γ). In addition, the linking probability is taken to be dependent on social distances and is governed by a parameter λ. The searches are realistic in the sense that not all search chains can be completed. An estimate of μ = ρ/s _d, where ρ is the success rate and s _d the dynamic path length, shows that for a network of N nodes, μ ∝ N ^−δ in general. Dynamic small world effect, i.e., δ ≃ 0 is shown to exist in a restricted region of the λ−γ plane.      

D-dimensional massless particle with extended gauge invariance

We propose the model ofD-dimensional massless particle whose Lagrangian is given by theN-th extrinsic curvature of world-line. The system hasN+1 gauge degrees of freedom constitutingW-like algebra; the classical trajectories of the model are space-like curves which obey the conditionsk _N+a=k_N−a, k_2N =0,a=1, ...,N−1,N≤[(D−2)/2], while the firstN curvaturesk _i remain arbitrary. We show that the model admits consistent formulation on the anti-DeSitter space. The solutions of the system are the massless irreducible representations of Poincaré group withN nonzero helicities, which are equal to each other. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.     

Fluctuating Electric Field Gradients at 111Cd in Ice

¹¹¹Cd–PAC measurements have been made using the high specific activity of ¹¹¹In in the methanol–water mixtures of various concentrations at the room temperature. These experiments revealed that the perturbation factors 〈A ₂ G ₂〉 (integrated over two mean lives τ_N) do not follow the dependence of the macroscopic viscosity η. The observed dynamic character of the PAC spectra in ice is explained by the mobility of orientational and ionic defects. The activation energy for the diffusion process was determined to be E _a =0.35(1) eV. This revised version was published online in September 2006 with corrections to the Cover Date.