The Variational Principle for a Class of Asymptotically Abelian C*-Algebras

Let (A,α) be a C^*-dynamical system. We introduce the notion of pressure P _α(H) of the automorphism α at a self-adjoint operator H∈A. Then we consider the class of AF-systems satisfying the following condition: there exists a dense α-invariant *-subalgebra ? of A such that for all pairs a,b∈? the C^*-algebra they generate is finite dimensional, and there is p=p(a,b)∈ℕ such that [α ^j (a),b]= 0 for |j|≥p. For systems in this class we prove the variational principle, i.e. show that P _α(H) is the supremum of the quantities h _φ(α) −φ(H), where h _φ(α) is the Connes–Narnhofer–Thirring dynamical entropy of α with respect to the α-invariant state φ. If H∈A, and P _α(H) is finite, we show that any state on which the supremum is attained is a KMS-state with respect to a one-parameter automorphism group naturally associated with H. In particular, Voiculescu's topological entropy is equal to the supremum of h _φ(α), and any state of finite maximal entropy is a trace. Received: 19 April 2000 / Accepted: 14 June 2000     

Bound states and critical behavior of the Yukawa potential

We investigate the bound states of the Yukawa potential V (r)=−λexp(−αr)/r, using different algorithms: solving the Schr?dinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical α = α_C, above which no bound state exists. We study the relation between α_C and λ for various angular momentum quantum number l, and find in atomic units, α_C(l) = λ[A ₁ exp(−l/B ₁) + A ₂ exp(−l/B ₂)], with A ₁ = 1.020(18), B ₁ = 0.443(14), A ₂ = 0.170(17), and B ₂ = 2.490(180).     

Time Quasi-Periodic Unbounded Perturbations¶of Schrödinger Operators and KAM Methods

We eliminate by KAM methods the time dependence in a class of linear differential equations in ℓ² subject to an unbounded, quasi-periodic forcing. This entails the pure-point nature of the Floquet spectrum of the operator H ₀+εP(ωt) for ε small. Here H ₀ is the one-dimensional Schr?dinger operator p ²+V, V(x)∼|x|^α, α <2 for |x|→∞, the time quasi-periodic perturbation P may grow as |x|^β, β <(α−2)/2, and the frequency vector ω is non resonant. The proof extends to infinite dimensional spaces the result valid for quasiperiodically forced linear differential equations and is based on Kuksin's estimate of solutions of homological equations with non-constant coefficients. Received: 3 October 2000 / Accepted: 20 December 2000     

Three-particle recombination coefficient of a weakly nonideal ultracold plasma in a high magnetic field

An expression for the recombination coefficient α _B in a weakly nonideal ultracold plasma in a high magnetic field has been proposed. According to this expression, α _B ∼ T _e ^−1.5 B ⁻², where T _e is the temperature of electrons and B is the strength of the magnetic field. Comparison of calculated values with experimental data including the results of the recent experiments on recombination in antihydrogen confirms the theoretical dependence.     

2p3/2?13x?1?3x?13d?1 X-ray satellites spectra in the Lα1 region of 4d transition elements

The X-ray satellite spectra arising due to 2p _3/2 ⁻¹3x ⁻¹−3x ⁻¹3d ⁻¹ (x ≡ s, p, d) transition array, in elements with Z = 40 to 48, have been calculated, using available Hartree-Fock-Slater (HFS) data on 1s ⁻¹−2p ⁻¹ 3x ⁻ and 2p _3/2 ⁻¹−3x ⁻¹,3x ⁻¹ Auger transition energies. The relative intensities of all the possible transitions have been estimated by considering cross — sections for the Auger transitions simultaneous to a hole creation and then distributing statistically the total cross sections for initial two hole states 2p _3/2 ⁻¹−3x ⁻¹ amongst various allowed transitions from these initial states to 3x ⁻¹ 3d ⁻¹ final states by Coster-Kronig (CK) and shake off processes. In both these processes initial single hole creation is the prime phenomenon. Each transition has been assumed to give rise to a Gaussian line and the overall spectrum has been computed as the sum of these Gaussian curves. The calculated spectra have been compared with the measured satellite energies in Lα₁ spectra. Their intense peaks have been identified as the observed satellite lines. The peaks in the theoretical satellite spectra were identified as the experimentally reported satellites α₃, α₄ and α₅, which lie on the high-energy side of the Lα₁ dipole line.     

On the Energy Growth of Some Periodically Driven Quantum Systems with Shrinking Gaps in the Spectrum

We consider quantum Hamiltonians of the form H(t)=H+V(t) where the spectrum of H is semibounded and discrete, and the eigenvalues behave as E _n ∼n ^α , with 0<α<1. In particular, the gaps between successive eigenvalues decay as n ^α−1. V(t) is supposed to be periodic, bounded, continuously differentiable in the strong sense and such that the matrix entries with respect to the spectral decomposition of H obey the estimate ‖V(t) _m,n ‖≤ε|m−n|^−p max {m,n}^−2γ for m≠n, where ε>0, p≥1 and γ=(1−α)/2. We show that the energy diffusion exponent can be arbitrarily small provided p is sufficiently large and ε is small enough. More precisely, for any initial condition Ψ∈Dom(H ^1/2), the diffusion of energy is bounded from above as 〈H〉 _Ψ (t)=O(t ^σ ), where . As an application we consider the Hamiltonian H(t)=|p| ^α +ε v(θ,t) on L ²(S ¹,dθ) which was discussed earlier in the literature by Howland.     

Probing the field-induced variation of the chemical potential in Bi2Sr2CaCu2Oy via magneto-thermopower measurements

Approximating the shape of the magneto-thermoelectric power (TEP) ΔS(T,H) measured in Bi₂Sr₂CaCu₂O_y by an asymmetric linear triangle of the form ΔS(T,H)≃S _p (H)±B ^±(H)(T _c −T) with positive B ⁻(H) and B ⁺(H) defined below and above T _c , we observe that B ⁺(H) ≃2B ⁻(H). To account for this asymmetry, we explicitly introduce the field-dependent chemical potential μ(H) of holes into the Ginzburg-Landau theory and calculate both an average ΔS _av(T,H) and fluctuation contribution ΔS _fl(T,H) to the total magneto-TEP ΔS(T,H). As a result, we find a rather simple relationship between the field-induced variation of the chemical potential in this material and the above-mentioned magneto-TEP data around T _c , viz. Δ μ(H)∝S _p (H). Zh. éksp. Teor. Fiz. 116, 257–262 (July 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

e + e − pair production in ultrarelativistic heavy-ion collisions at intermediate impact parameters

Using the semiclassical Green’s function in the Coulomb field, we analyze the probabilities of single and multiple e ⁺ e ⁻ pair production at a fixed impact parameter b between colliding ultrarelativistic heavy nuclei. We perform calculations in the Born approximation with respect to the parameter Z _Bα and exactly in Z _Aα, where Z _A and Z _B are the charge numbers of the corresponding nuclei. We also obtain the approximate formulas for the probabilities valid for Z _Aα, Z _Bα ≲ 1. The text was submitted by the authors in English.     

Spin-spin interaction of Ni2+ ions in ZnSiF6·6H2O

The angular dependences of the electron spin resonance spectrum of 1% Ni²⁺ ions in a ZnSiF₆·6H₂O matrix are investigated experimentally at 36 GHz and 4.2 K. Besides the main spectrum of the isolated ion, we observed a spectrum due to interacting pairs of Ni²⁺ ions, located in the first (nn) and second (2n) coordination spheres and coupled by, besides the magnetic dipole-dipole interaction, isotropic exchange: J _nn = (−197±1)×10⁻⁴, J _2nα = (−5±1)×10⁻⁴, and J _2nβ = (3±2)×10⁻⁴ cm⁻¹. Lines due to other isolated Ni²⁺ ions, which have a different initial splitting D, are also present in the spectrum with intensity comparable to the pair spectrum. Low-symmetry distortions of the crystal field are observed, caused by a pair of impurity ions located close to one another. It is shown that the previously proposed interpretation is incorrect. Fiz. Tverd. Tela (St. Petersburg) 41, 1602–1608 (September 1999)     

On bound state computations in three- and four-electron atomic systems

A variational approach is developed for bound state calculations in three- and four-electron atomic systems. This approach can be applied to determine, in principle, an arbitrary bound state in three- and four-electron ions and atoms. Our variational wave functions are constructed from four- and five-body Gaussoids that respectively depend on six (r ₁₂, r ₁₃, r ₁₄, r ₂₃, r ₂₄, r ₃₄) and ten (r ₁₂, r ₁₃, r ₁₄, r ₁₅, r ₂₃, r ₂₄, r ₂₅, r ₃₄, r ₃₅ and r ₄₅) relative coordinates. The approach allows operating with the more than one electron spin functions. In particular, the trial wave functions for the ¹ S states in four-electron atomic systems include the two independent spin functions χ₁ = αβαβ + βαβα − βααβ − αββα and χ₂ = 2ααββ + 2ββαα − βααβ − αββα − βαβα − αβαβ. We also discuss the construction of variational wave functions for the excited 2³ S states in four- electron atomic systems.     

The synthesis of boron-containing nanoparticles inert at room temperature

Boron-containing (C₂B₄H₂) _n nanoparticles with size 6.7, 7.8, and 10.8 nm inert at room temperature were synthesized. The synthesis was performed by the pyrolysis of gaseous carborane C₂B₄H₆ at 1200–1280 K and the initial carborane pressure (5–25) × 10⁻³ MPa. An analytic dependence relating the size of nanoparticles to the temperature and initial carborane pressure was obtained.     

ESR of V4+ in α-RbTiOPO4 single crystals

We have recorded and investigated the ESR spectrum of vanadium-doped α-RbTiOPO₄ single crystals in the temperature interval 77–300 K. Two types of structurally distinct centers, V1 and V2, with a 4:1 ratio of the peak intensities were observed. The angular dependences of the resonance magnetic fields are described by a spin Hamiltonian corresponding to axial symmetry with the parameters g _∥1=1.9305, g _⊥1=1.9565, A _∥1=−168.2×10⁻⁴cm⁻¹, and A _⊥1=−54.3×10⁻⁴cm⁻¹ for V1 centers and g _∥2=1.9340, g _⊥2=1.9523, A _∥2=−169.0×10⁻⁴cm⁻¹, and A _⊥2=−55.2×10⁻⁴cm⁻¹ for V2 centers. A model of a paramagnetic center is proposed: The vanadium ions replace titanium ions in two structurally distinct positions Ti1 and Ti2 (V1 and V2 centers, respectively). The possibility that a VO²⁺ ion forms when α-RbTiOPO₄ crystals and crystals of the KTP group (KTiOPO₄, NaTiOPO₄, α-and β-LiTiOPO₄), studied earlier, are doped with vanadium is discussed. Fiz. Tverd. Tela (St. Petersburg) 40, 534–536 (March 1998)     

EPR of trivalent iron ions in a LiCaAlF6 crystal

The orientational dependences of the EPR spectra of Fe³⁺-doped LiCaAlF₆ single crystals (space group P31c, Z=2), grown at the Laboratory of Magnetic Radio Spectroscopy at Kazan’ State University, have been investigated in detail. The spectrum is described by a trigonal spin Hamiltonian with the following parameters: B ₂₀=40.072×10⁻⁴ cm⁻¹, B ₄₀=−5.799×10⁻⁴ cm⁻¹, B ₄₃=−4.281×10⁻⁴ cm⁻¹, A _s=24.33±1, A _p=6.13±1, g _∥=g _⊥=2.00217±0.0003. A theoretical calculation of the hyperfine structure parameters shows that they are described quite well when allowance is made for the overlapping of the wave functions of the paramagnetic center and the ligands (F⁻). Fiz. Tverd. Tela (St. Petersburg) 39, 488–490 (March 1997)     

A Conjecture for the Superintegrable Chiral Potts Model

We adapt our previous results for the “partition function” of the superintegrable chiral Potts model with open boundaries to obtain the corresponding matrix elements of e^{−α H} , where H is the associated Hamiltonian. The spontaneous magnetization ℳ _r can be expressed in terms of particular matrix elements of e^{−α H} S ₁ ^r e^{−β H} , where S ₁ is a diagonal matrix. We present a conjecture for these matrix elements as an m by m determinant, where m is proportional to the width of the lattice. The author has previously derived the spontaneous magnetization of the chiral Potts model by analytic means, but hopes that this work will facilitate a more algebraic derivation, similar to that of Yang for the Ising model.     

Doppler spectroscopy of a beam in the channel of a H− ion source

It is shown that high-accuracy contact-free measurements of the divergence and emittance of an accelerated H⁻ ion beam at the exit from the source can in principle be performed by passive Doppler spectroscopy of a beam of excited hydrogen atoms produced by neutralization of the ions with excitation on the residual gas in the source channel. The intensity of the H_α-line radiation detected by the Doppler system is calculated, taking into account the principal processes leading to the excitation and deexcitation of the 3s, 3p, and 3d levels of the hydrogen atoms in the beam, for residual gas densities of the order of 10⁻⁴–10⁻⁵ Torr in the source channel. The computed H_α-line intensity was confirmed experimentally, making it possible to perform photoelectronic detection of the spectral contour of the line in the current mode rather than the photon-counting mode. Zh. Tekh. Fiz. 68, 15–18 (June 1998)     

Emission of axions by a hydrogen-like atom in an ultrastrong magnetic field

The resonance effect of emission of axions by a hydrogen-like atom in an ultrastrong magnetic field B ≫ B ₀ = m ²/e = 4.41 × 10¹³ Gs, which is induced by polarization of electron-positron vacuum, is considered. The emission probability and the radiation intensity are on the order of (B/B ₀) × 10⁻¹² of electromagnetic radiation characteristics, which exceeds the conventional ratio by many orders of magnitude. It is shown that, at the temperature of early Universe ≲(Zα)² m, the contribution from the resonance mechanism prevails. However, the relation between the concentrations of relic photons and axions cannot explain the origin of cold dark matter. The axion energy density in “our epoch” is 10⁻⁴(B/B ₀) eV/cm³.     

Construction of the Incipient Infinite Cluster for Spread-out Oriented Percolation Above 4 + 1 Dimensions

 We construct the incipient infinite cluster measure (IIC) for sufficiently spread-out oriented percolation on ℤ ^d × ℤ₊, for d +1 > 4+1. We consider two different constructions. For the first construction, we define ℙ ⁿ (E) by taking the probability of the intersection of an event E with the event that the origin is connected to (x,n)  ℤ ^d × ℤ₊, summing this probability over x  ℤ ^d , and normalising the sum to get a probability measure. We let n → ∞ and prove existence of a limiting measure ℙ_∞, the IIC. For the second construction, we condition the connected cluster of the origin in critical oriented percolation to survive to time n, and let n → ∞. Under the assumption that the critical survival probability is asymptotic to a multiple of n ⁻¹, we prove existence of a limiting measure ℚ_∞, with ℚ_∞ = ℙ_∞. In addition, we study the asymptotic behaviour of the size of the level set of the cluster of the origin, and the dimension of the cluster of the origin, under ℙ_∞. Our methods involve minor extensions of the lace expansion methods used in a previous paper to relate critical oriented percolation to super-Brownian motion, for d+1 > 4+1. Received: 13 December 2001 / Accepted: 11 July 2002 Published online: 29 October 2002 RID="*" ID="*" Present address: Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. E-mail: rhofstad@win.tue.nl     

Nuclear Spin-Lattice Relaxation of 82BrFe

The field dependence of the nuclear spin-lattice relaxation (SLR) of cold implanted ⁸²Br (T ≤ 25 mK) in α-Fe single crystals was investigated with nuclear magnetic resonance of oriented nuclei (NMR/ON) at low temperatures as experimental technique. The SLR at the lattice sites with the hyperfine fields found by earlier NMR/ON experiments was measured as a function of the applied external magnetic field B _ext parallel to the three principle axes [100], [110] and [111] of the iron single crystal. The data were evaluated with the full relaxation formalism in the single impurity limit and for comparison also with the often employed model of a single exponential function with an effective relaxation time T ₁′. With a phenomenological model the high field values of the relaxation rates r _{∞, [100]′} = 6.6(2) · 10⁻¹⁵ T²sK⁻¹, r _{∞, [110]} = 5.4(2) · 10⁻¹⁵ T²sK⁻¹ and r _{∞, [111]} = 5.2(1) · 10⁻¹⁵ T²sK⁻¹ were obtained.     

Influence of heme periphery upon electronic structúre and Mössbauer spectra parameters of hemoglobin

Quantum-chemical analysis of electronic structure peculiarities and mossbauer spectra parameters was performed for penta-coordinated complex of ferro-protoporphyrin with imidazole (Fe(+2)PPIm). Peripheral substitutes (−CH₃, −C₂H₃, −C₂H₄COOH) introduced in the porphyrin macrocycle simulated real chemical structure of protoporphyrin (PP) in heme group of Hb. Calculations displayed that doubly occupied molecular orbitals (MO) of the peripheral substitutes (−CH=CH₂ and −CH₂−CH₂−COOH) always appeared near the occupat ion border. The orientation of vinyl fragment have the essential influence upon Fe₅ dorbital populations and quadrupole splitting_AE_Q for⁵B₁ and⁵B₂ terms. The values of isomer shift were insensitive to that modification of fragment orientation.