Dirac Operators Coupled to the Quantized Radiation Field: Essential Self-adjointness à la Chernoff

We study the Dirac operator D ₀ in an external potential V, coupled to a quantized radiation field with energy H _f and vector potential A. Our result is a Chernoff-type theorem, i.e., we prove, for the operator D ₀+α · A+V +λ H _f with λ ∈{0, 1}, that the essential self-adjointness is not affected by the behavior of V at ∞.      

Multiphoton ionization of molecules under the conditions of strong field-induced perturbation of Rydberg states

Multiphonon ionization of the H₂ molecule under the action of a weak (probe) field, which provides the initial population of the low-lying (working) level, and intense monochromatic linearly polarized radiation is studied. The multiphoton ionization process occurs under the conditions of strong field perturbation of two intermediate Rydberg series, np0(¹Σ _u ⁺ and np2(¹Π_u), of the optical R(0)branch which have different ionization potentials. The series are occupied simultaneously as a result of single-photon absorption by an excited H ₂ ^* molecule in the working state 4s σH′¹Σ _g ⁺ (v=0). As a result of the irregularity in the arrangement of the intermediate levels from a large group of states that are combined in the multiphoton ionization process a sharp and irregular change occurs in the dependence of the shifts and widths Γ_n of the levels on the intensity f of the strong field in a transition from one level to another. It is shown that for field intensities f such that the level widths remain much less than the splitting between the levels (Γ_n≪/n ³) the stabilizing effect (i.e., the field-induced narrowing of the levels as f→∞) in the form Γ_n ∝ 1/f ² (as happens in atoms with a structureless core) is not observed in molecular systems. Zh. éksp. Teor. Fiz. 115, 1987–2000 (June 1999)     

掺Gd3+钼酸盐AMoO4 (A=Ca,Sr, Ba,Pb)自旋哈密顿参量的理论计算

采用基于单电子晶体场机制的对角化能量矩阵方法, 计算了Gd³⁺在钼酸盐AMoO₄ (A=Ca, Sr, Ba, Pb)晶体中的自旋哈密顿参量(g因子g_//, g_⊥和零场分裂b₂⁰, b₄⁰, b₄⁴, b₆⁰, b₆⁴). 矩阵中的晶体场参量采用重叠模型计算. 计算结果显示, 应用三个合理的可调参量[即重叠模型中的内禀参量A₂ (R₀), A₄ (R₀)和A₆ (R₀)], 计算的七个自旋哈密顿参量与实验结果符合甚好, 表明该方法可用于计算或解释Gd³⁺在晶体中的自旋哈密顿参量. 关键词： AMoO₄ (A=Ca,Sr,Ba,Pb):Gd³⁺晶体')" href="#">AMoO₄ (A=Ca,Sr,Ba,Pb):Gd³⁺晶体 自旋哈密顿参量 晶体场理论 对角化能量矩阵     

Expectation values of unbounded observables

For an unbounded quantum mechanical observableA, the expectation value A _f and the mean square deviation _f A cannot be denned for all (pure) statesf by A _f = (f,Af) and ( _f A)² = (f,A ² f)-(f,Af)², respectively. More general definitions are given here, which are also valid for state mixtures (density matrices). A general uncertainty relation for unbounded observables is derived.     

Effect of an edge field on the acceptance of a quadrupole mass filter operating at the bottom vertex of the stability rectangle

A quadrupole mass filter (QMF) can operate with a large acceptance and high transmission at the bottom vertex S (a=2.5210, q=2.8153) of the stability quadrilateral. The combined acceptance at a level of 50% transmission and a resolving power of 100 equals 2.0×10⁻³ r ₀ ⁴ f ², which is comparable to the acceptance (5.1×10⁻³ r ₀ ⁴ f ²) of the standard operating regime of a QMF in the first stability region under the same computational conditions and optimal on-axis ion velocity. The acceptance is approximately three times higher in the presence of edge fields than in their absence. The optimal on-axis ion energy equals 1.15r ₀ f, where r ₀ is the radius of the field (the radius of the inscribed circle between the vertices of the electrodes) and f is the working frequency. In the gas-analysis regime a sensitivity of 10⁻⁵ A/Pa is achieved on a mass filter with rod length and rod diameter of 15 cm and 8 mm, respectively, frequency f=1 MHz, and field radius r ₀=0.35 cm. Zh. Tekh. Fiz. 67, 121–124 (October 1997)     

Conservation of Energy,Entropy Identity,and Local Stability for the Spatially Homogeneous Boltzmann Equation

For nonsoft potential collision kernels with angular cutoff, we prove that under the initial condition f ₀(v)(1+|v|²+|logf ₀(v)|)L ¹(R ³), the classical formal entropy identity holds for all nonnegative solutions of the spatially homogeneous Boltzmann equation in the class L ([0, ); L ¹ ₂(R ³))C ¹([0, ); L ¹(R ³)) [where L ¹ _s (R ³)={ff(v)(1+|v|²) ^s/2L ¹(R ³)}], and in this class, the nonincrease of energy always implies the conservation of energy and therefore the solutions obtained all conserve energy. Moreover, for hard potentials and the hard-sphere model, a local stability result for conservative solutions (i.e., satisfying the conservation of mass, momentum, and energy) is obtained. As an application of the local stability, a sufficient and necessary condition on the initial data f ₀ such that the conservative solutions f belong to L ¹ _loc([0, ); L ¹ ₂₊ (R ³)) is also given.     

Construction of Fredholm representations and a modification of the Higson-Roe corona

The Fredholm representation theory is well adapted to the construction of homotopy invariants of non-simply-connected manifolds by means of the generalized Hirzebruch formula [σ(M)] = 〈L(M)ch _A f*ξ, [M]〉 ∈ K _A ⁰(pt) ⊗ Q, where A = C*[π] is the C*-algebra of the group π, π = π ₁(M). The bundle ξ ∈ K _A ⁰(Bπ) is the canonical A-bundle generated by the natural representation π → A. Recently, the first author constructed a natural family of Fredholm representations that lead to a symmetric vector bundle on the completion of the fundamental group with a modification of the Higson-Roe corona, provided that the completion is a closed manifold.     

Gravitation and electromagnetism

Through an examination of the Bohm-Aharonov experiment, we shall propose a new theory of gravitation and electromagnetism. The fundamental assumption of our theory is that the motion of a particle in a combination of gravitational and electromagnetic fields is determined from a variational principle of the form f _A ^B d = 0. The form of the physical time is determined from an examination of the Maxwell-Einstein action function. The field and motion equations are formally identical to those of Maxwell-Einstein theory. The theory predicts that even in a field-free region of space, electromagnetic potentials can alter the phase of a wave function and the lifetime of a charged particle. The phase alteration has been observed in the Bohm-Aharonov experiment. There is an indication that the lifetime alteration has shown up in a recent CERN storage ring experiment. Experimental tests are proposed.     

Spherical harmonics and cartesian tensor scalar product expansions of the distribution function

On the basis of the expansion of the distribution function in a sum of the spherical harmonics, the distribution functionf(v, r, t) is expanded in a series of scalar products of two Cartesian tensors term by term, i.e. The tensors and ^(l) (l=2, 3) are constructed in dependence on the spherical harmonic expansion coefficients (the tensors and ^(l) (l=0, 1) have been constructed by Jancel and Kahan [3]). On the basis of the knowledge of the analytic form off ₂ andf ₃ the equations forf ₁ f ₂ andf ₃ for the case of the Boltzmann's equation are determined.Technická 2, Praha 6, Czechoslovakia.     

A Particle in a Magnetic Field of an Infinite Rectilinear Current

We consider the Schrödinger operator H=(i+A)² in the space L ₂(R ³) with a magnetic potential A created by an infinite rectilinear current. We show that the operator H is absolutely continuous, its spectrum has infinite multiplicity and coincides with the positive half-axis. Then we find the large-time behavior of solutions exp(–i H t)f of the time dependent Schrödinger equation. Our main observation is that a quantum particle has always a preferable (depending on its charge) direction of propagation along the current. Similar result is true in classical mechanics.     

Instability of the lowest triplet state of benzene under environmental perturbations : zero-field splitting and radiative properties of the spin components

Coupling is considered between the lower ³ B _1u and ³ E _1u states of benzene under the combined influence of substituents and the crystal field. A model is derived in which the value of the E.S.R. parameter E, the orientation of the zero-field axes relative to the molecular frame and the radiative properties of the upper two spin components of the lowest triplet state are interpreted in terms of an electronic wavefunction.

With the model the reduced intensity of the 0-0 band relative to the 8₁ ⁰ band in the phosphorescence spectra of a number of benzene-like systems is explained. Further the radiative properties of the zero-field spin components of toluene in a benzene host are interpreted; in this system the angle between the in-plane zero-field axes and the molecular axes appears to be 74° (±6°).     

Flexible-to-semiflexible chain crossover on the pressure-area isotherm of a lipid bilayer

We find theoretically that competition between ∼K _f q ⁴ and ∼Qq ² terms in the Fourier-transformed conformational energy of a single-lipid chain, in combination with interchain entropic repulsion in the hydrophobic part of the lipid (bi)layer, may cause a crossover on the bilayer pressure-area isotherm P(A)∼(A−A ₀)^−α. The crossover manifests itself in the transition from α = 5/3 to α = 3. Our microscopic model represents a single-lipid molecule as a worm-like chain with a finite irreducible cross-section area A ₀, a flexural rigidity K _f , and a stretching modulus Q in a parabolic potential with the self-consistent curvature B(A) formed by entropic interactions between hydrocarbon chains in the lipid layer. The crossover area A* obeys the relation Q/√K _f B(A*) ≈ 2. We predict a peculiar possibility of deducing the effective elastic moduli K _f and Q of an individual hydrocarbon chain from the analysis of the isotherm with such a crossover. Also calculated is the crossover-related behavior of the area compressibility modulus K _A , the equilibrium area per lipid A _t , and the chain order parameter S(θ). The text was submitted by the authors in English.     

Measurement of the f0(1270) polarization in the J/ψ → f0γ decay

The polarization of the f⁰(1270) and ?⁰(770) produced in the J/ψ decays into f⁰γ and ?⁰π⁰ are measured in e⁺e^? collisions at 3.1 GeV. A fit to the f⁰ production and decay angular distributions yields the values A₁/A₀ = 0.6 ± 0.3 and A₂/A₀ = 0.3 _?1.6^+0.6, where A_λ are the f⁰ helicity amplitudes. These results are in good agreement with the values predicted from a QCD two-gluon-exchange model. In addition an upper limit of 2.3 × 10^?4 is obtained for the J/ψ → f′⁰(1514) γ decay branching ratio which implies Γ(J/ψ → f′γ)/Γ(J/ψ → f⁰γ) ? 0.12 ± 0.05.     

Originalarbeiten / Travaux originaux / Original Papers

An account is given of a variational calculation to estimate the amplitudes of resonance factorsɛ in a recent theory to describe the enhancement of crystalline field potentials by conduction electrons in heavy rare earth metals. It is demonstrated that the values ofɛ obtained by minimising the energy of interaction between conduction electrons and rare earth ions are consistent with those previously used to form a comparison with experiment. These latter values were obtained by maximising theA ₂ ⁰ crystal field coefficient with respect toɛ. Consistency is exhibited in both the sign and order of magnitude of the resonance amplitudes and renders the theory parameterless. The values ofɛ show an approximate linear dependence with the number of electrons in the incompletef shell of the rare earth ions.     

The Dynamics of Intramolecular Excited State Relaxation of <Emphasis Type="Italic">N</Emphasis>-Anthryl Substituted Pyridinium Cations

N-(1-Anthryl)-2,4,6-trimethyl-pyridinium (I), N-(2-anthryl)-2,4,6-trimethyl-pyridinium (II) and 10-(1-anthryl)-1,2,3,4,5,6,7,8-octahydro-acridinium cations (III) with anomalously high fluorescence Stokes shift have been investigated. Fluorescence kinetics analysis at various temperatures showed that in the range 293–77 K, the radiative deactivation rate constants (k_f) increase by 5.5 to 30 times. The low-temperature time-resolved emission spectra of I–III were found to be consistent with the model: A A^* B^* where A^* is the local excited twisted form and B^* is the relaxed more planar, bent conformer of the molecule. The rate constants of the excited relaxed state formation (k₁) and back reaction (k_–1) of compounds studied were estimated.     

Zero-field splitting of <Superscript>4</Superscript><Emphasis Type="Italic">T</Emphasis><Subscript>2</Subscript> term for 3d<Superscript>3</Superscript> ions in tetragonal symmetry

By taking into account slight interactions, i.e. spin-spin, spin-other-orbit and orbit-orbit interactions, in addition to spin-orbit interaction, the zero-field splitting of ⁴ T ₂ state for 3d³ ions at tetragonal symmetry has been studied. The convergence of the approximation perturbation formula of ⁴ T ₂ state for 3d³ ions at tetragonal symmetry has been investigated, and the contributions to zero-field splitting arising from magnetic interaction and tetragonal crystal field are discussed. It is found that there exists combined mechanism between magnetic interactions and tetragonal crystal field.      

Extended triplet set C343 of DNA sequences and its application to the p53 gene

Recently, much research has indicated that more and more cancers pose a threat to human life. Cancers are caused by oncogenes. Many human oncogenes have been found and most of them are located on chromosomes. The discovery of the oncogene plays a significant role in the treatment of cancer. The p53 tumor suppressor gene has received much attention because it frequently mutates or deletes in tumor cells of most people. Thus, the study of oncogenes is significant. In order to establish the Galois field (GF(7)), the indefinite gene is introduced as D and oncogene is introduced as O, and P. Taking the polynomial coefficients a₀, a₁, a₂ ∈ GF(7) and the bijective function f:GF(7) → {D,A,C,O,G,T,P}, where f(0) = D, f(1) = A, f(2) = C, f(3) = O, f(4) = G, f(5) = T, and f(6) = P, the bijective φ may be written as φ(a₀ + a₁x + a₂x²). Based on the algebraic structure, we can not only analyse the DNA sequence of oncogenes, but also predict possible new cancers.     

New Investigations of the AΔ-XΠ Band System in the CH Radical and a New Reduction of the Vibration-Rotation Spectrum of CH from the ATMOS Spectra

Seven bands of the A²Δ-X²Π system of the CH radical have been photographed in emission from a Geissler tube using conventional spectroscopic techniques. Under high resolution and using Th lines as standards, as well as an interferometric comparator equipped with a photoelectric scanning device, the 0-0, 1-1, 2-2, 0-1, and 1-2 bands have been rephotographed and the 3-3 and 2-3 bands, with a total number of 144 lines, have been recorded for the first time. In the previously reported (J. Mol. Spectrosc.134, 305, 1989; 147, 16, 1991) evaluation of the ATMOS spectrum of CH for determining the molecular parameters we found total interparameter correlations between some of them, due to the absence of high-J lines of the P and Q branches. With the help of the precise constants obtained from our 0-0 band measurements (12 branches with J_max = 24.5, f = 181, σ = 0.0025 cm⁻¹) of the A²Δ-X²Π transition, we have been able to remove the correlations and obtain more accurate molecular parameters for the X²Π ground state. These constants have subsequently been used to derive new exact molecular parameters for the A²Δ , ν = 1, 2, and 3 levels of CH. The Λ-doubling constants in the A²Δ state were obtained for the first time. The complex vibrational analysis has been carried out to determine the equilibrium molecular constants. Also, RKR potentials and r-centroids have been calculated for both the combining states, as well as Franck-Condon factors for the A-X system.     

Numerical study of Fermi-Pasta-Ulam recurrence for water waves over finite depth

Highly accurate direct numerical simulations have been performed for two-dimensional free-surface potential flows of an ideal incompressible fluid over a constant depth h, in the gravity field g. In each numerical experiment, at t = 0 the free surface profile was in the form y = A ₀cos(2πx/L), and the velocity field v = 0. The computations demonstrate the phenomenon of Fermi-Pasta-Ulam (FPU) recurrence takes place in such systems for moderate initial wave amplitudes A ₀ ≲ 0.12h and spatial periods at least L ≲ 120h. The time of recurrence T _FPU is well fitted by the formula T _FPU(g/h)^1/2 ≈ 0.16(L/h)²(h/A ₀)^1/2.