Inequivalent Quantization in the Field of a Ferromagnetic Wire

We argue that it is possible to bind neutral atom (NA) to the ferromagnetic wire (FW) by inequivalent quantization of the Hamiltonian. We follow the well known von Neumann’s method of self-adjoint extensions (SAE) to get this inequivalent quantization, which is characterized by a parameter Σ∈ℝ(mod2π). There exists a single bound state for the coupling constant η ²∈[0,1). Although this bound state should not occur due to the existence of classical scale symmetry in the problem. But since quantization procedure breaks this classical symmetry, bound state comes out as a scale in the problem leading to scaling anomaly. We also discuss the strong coupling region η ²<0, which supports bound state making the problem re-normalizable.     

The fundamental-electroweak scale hierarchy in the standard model

The multiple-point principle, according to which several vacuum states with the same energy density exist, is put forward as a fine-tuning mechanism predicting the ratio between the fundamental and electroweak scales in the Standard Model (SM). It is shown that this ratio is exponentially huge: ∼e ⁴⁰. Using renormalization group equations for the SM, we obtain the effective potential in the two-loop approximation and investigate the existence of its postulated second minimum at the fundamental scale. The investigation of the evolution of the top-quark Yukawa coupling constant in the two-loop approximation shows that, with initial values of the top-quark Yukawa coupling in the interval h(M _t )=0.95±0.03 (here, M _t is the top-quark pole mass), a second minimum of the SM effective potential can exist in the region ϕ_min2≈10¹⁶−10²² GeV. A prediction is made of the existence of a new bound state of six top quarks and six antitop quarks, formed owing to Higgs boson exchanges between pairs of quarks-antiquarks. This bound state is supposed to condense in a new phase of the SM vacuum. This gives rise to the possibility of having a phase transition between vacua with and without such a condensate. The existence of three vacuum states (new, electroweak, and fundamental) solves the hierarchy problem in the SM. The text was submitted by the authors in English.     

Improved condition for the absence of bound states and converging analytic bounds to critical screening parameter

Converging lower bound to the critical screening parameterD _c associated with the ground state of a two-particle system interacting through a cut-off Coulomb potential is obtained analytically using an improved condition for the absence of bound states. The predicted numerical result for the lower bound is found to be within 10⁻³% of the exact result. On the other hand, a multi-parameter variational approach yields a tight upper bound, within 0.54% of the exact result. It is shown that the critical screening parameter for the exciteds-states can also be determined in an approximate way. We obtainD _c ^ms ≈ [0.764435n ⁻²+0.617737n ⁻³]⁻¹ wheren is the principal quantum number. The predictedD _c for various quantum states (n=1 to 8) are in good agreement with the values obtained numerically by Singh and Varshni.     

On the dimensionality of superconductivity in cuprate superconductors

The question of the dimensionality of superconductivity is considered within the framework of a model of superconductivity via asymmetric, delocalized “crystalline” π orbitals (analogous to the corresponding molecular orbitals) extending along chains of covalently bonded copper and oxygen ions. It is shown that superconductivity is preceded by a separation of the bonds in the CuO₂ layer into covalent and ionic bonds with ordering of the covalent bonds into chains. Such an ordering facilitates the formation of a crystalline π orbital lowering the crystal energy by the resonance energy of the π bond and is therefore favored. The superconducting current is created by non-dissipative motion of π-electron pairs along the asymmetric, “crystalline” π orbitals extending along chains of covalently bonded copper and oxygen ions, in the presence of an ionic bond between neighboring chains extending through the easily polarizable O²⁻ ions. This ionic bond correlates the motion of the electron pairs along all the π orbitals and stabilizes the superconducting state. Only in this sense is the apparent “onedimensionality” of superconductivity in cuprate superconductors to be understood. Zh. Tekh. Fiz. 68, 82–84 (November 1998)     

Resonances and the Weinberg-Tomozawa 56-baryon-35-meson interaction

Vector meson degrees of freedom are incorporated into the Weinberg-Tomozawa (WT) meson-baryon chiral Lagrangian by using a scheme which relies on spin-flavor SU(6) symmetry. The corresponding Bethe-Salpeter approximation successfully reproduces previous SU(3)-flavor WT results for the lowest-lying s-wave negative-parity baryon resonances, and it also provides some information on the dynamics of the heavier ones. Moreover, it also predicts the existence of an isoscalar spin-parity ^- K^*N bound state (strangeness +1) with a mass around 1.7-1.8GeV, unstable through K^* decay. Neglecting d-wave KN decays, this state turns out to be quite narrow ( Γ≤15MeV) and it might provide clear signals in reactions like γp→ˉ⁰ pK ⁺ π ^- by looking at the three-body pK ⁺ π ^- invariant mass.     

The generalized dynamical equation and the vacuum polarization effect in hydrogenlike atoms

Based on the generalized dynamical equation, vacuum polarization effects are studied within the scope of the bound state theory in quantum electrodynamics. We find a vacuum-polarization correction to the Lamb shift for the 1S state of the hydrogen atom on the order of (α/π)²(Zα)⁴ that is not considered in the standard theory of bound states in quantum electrodynamics.     

1H NMR relaxation investigation of herbicides interacting with photosystem II preparations fromSpinacia oleracea L.

The interaction of three common herbicides, paraquat, acifluorfen and alachlor, with spinach chloroplast photosystem II (PS II) was investigated by measuring¹H nuclear magnetic resonance spin-lattice relaxation rates, transient nuclear Overhauser effect (NOE) and NOE spectroscopy (NOESY) spectra. Binding to PS II was detected by (i) the enhancement of single-selective relaxation rates and (ii) the decrease in the optimal mixing time providing maximal cross-peak intensity in NOESY spectra. Titration of relaxation enhancements was used to calculate the dissociation constants (K _d) from the bound state for paraquat (K _d = 292 ± 71 μM⁻¹) and acifluorfen (K _d = 311 ± 58 μM⁻¹). A similarK _d was apparent for alachlor. Double-selective relaxation rates allowed the isolation of dipolar relaxation terms between selected proton pairs wherefrom dynamic features of the bound state were evaluated. In all cases the motional correlation time of bound herbicide (τ_c = 0.1−0.4 ns at 300 K) was found two orders of magnitude slower than in the free-solution state. In the case of alachlor the E and Z isomers were observed to bind differently to PS II and a change in conformation could be hypothesized.     

Symmetry and boundness of four-particle coulomb systems

The problem of boundness of a ⁺ b ⁺ c ⁻ d ⁻ four-particle Coulomb systems (quadrions) is studied versus the masses of the particles involved. Inequalities that make it possible to deduce that, if some reference quadrions form a bound state, the same is true for a large number of quadrions formed by particles having various masses were derived. A compendium of calculations for energies of reference systems that possess various symmetries [positronium molecules (e ⁺ e ⁺ e ⁻ e ⁻) and quadrions of the a ⁺ b ⁺ b ⁻ b ⁻, a ⁺ b ⁺ a ⁻ b ⁻, and a ⁺ a ⁺ b ⁻ c ⁻ types] is given, and groups of bound asymmetric quadrions corresponding to them are determined. An inequality for kinetic energies of particles that makes it possible to find out, by using asymmetric reference systems, whether specific quadrions are bound is obtained. It is shown that the boundness of many quadrions is ensured by the boundness of respective three-particle systems. The entire body of the present results permits proving that, of the total number of 406 quadrions containing electrons, muons, pions, kaons, protons, deuterons, and tritons and their antiparticles, 227 quadrions are bound.     

Constant-cutoff approach to meson-hyperon couplings

The kaon coupling constants at hyperon-nucleon vertices and the pion coupling constants at hyperon-hyperon vertices are calculated in the framework of the constant-cutoff approach to the CHK bound-state model of hyperons, where the postive-parity hyperons such as Λ, Σ, and ∑^*=∑(1385) are theP-wave bound states of an antikaon and theSU(2) Skyrme soliton, while Λ^* is theS-wave bound state. Meson coupling constants are defined as matrix elements of the meson-source terms between two single-baryon states following the method developed for resolving the Yukawa coupling problem in theSU(2) Skyrme soliton model. The magnitudes of the meson coupling constants are found to be close to those obtained using the complete Skyrme model and the phenomenological values.     

Cluster models of light nuclei and the method of hyperspherical harmonics: Successes and challenges

Hyperspherical-harmonics method to investigate the lightest nuclei having three-cluster structure is discussed together with recent experiments. Properties of bound states and methods to explore three-body continuum are presented. The challenges created by large neutron excess and halo phenomena are highlighted. Astrophysical aspects of the ⁷Li + n → ⁸Li + γ reaction and the solar-boron-neutrinos problem are analyzed. Three-cluster structure of highly excited states in ⁸Be is shown to be responsible for extreme isospin mixing. Progress in studies of ⁶He- and ¹¹Li-induced inclusive and exclusive nuclear reactions is demonstrated, providing information on the nature of continuum structures of Borromean nuclei. The text was submitted by the authors in English.     

Partial-wave Scattering and Statistical Mechanics via the l-wave Non-local Separable Potential of Rank-two

The equilibrium statistical mechanics relations are shown to be related to T-matrix, which describes the scattering processes taking place in the thermodynamic system consisting of free particles and independent correlated pairs, interacting via the separable non-local potential of rank two in the ℓth partial wave. Thermodynamic properties are related to the correlated states, when making a pole expansion of the analytically continued momentum matrix element of R _ℓ (z), the difference between the resolvents of the interacting and free Hamiltonians. It is shown that local potentials equivalent to the nonlocal ones have an attractive part which is responsible for a bound state and negative values of some thermodynamic properties.     

Hartree-Fock variational bounds for ground state energy of chargeless fermions with finite magnetic moment in the presence of a hard core potential: A stable ferromagnetic state

We use different determinantal Hartree-Fock (HF) wave functions to calculate true variational upper bounds for the ground state energy of N spin-half fermions in volume V ₀, with mass m, electric charge zero, and magnetic moment μ, interacting through magnetic dipole-dipole interaction. We find that at high densities when the average interparticle distance r ₀ becomes small compared to the magnetic length r _m ≡ 2mμ²/ħ², a ferromagnetic state with spheroidal occupation function n _↑(), involving quadrupolar deformation, gives a lower upper bound compared to the variational energy for the uniform paramagnetic state or for the state with dipolar deformation. This system is unstable towards infinite density collapse, but we show explicitly that a suitable short-range repulsive (hard core) interaction of strength U ₀ and range a can stop this collapse. The existence of a stable equilibrium high density ferromagnetic state with spheroidal occupation function is possible as long as the ratio of coupling constants Γ_cm ≡ (U ₀ a ³/μ²) is not very small compared to 1.      

D-branes inpp-wave background

We show the existence of classical solutions ofD-branes as well as a system ofD3-branes oriented at an arbitrary angle with respect to each other, in a six-dimensionalpp-wave background obtained fromAdS ₃ × S³ ×R ⁴ , withR — R andNS — NS 3-from flux. The world volume coordinate of D5-brane lies along the six-dimensional pp-wave directions, whereas thepp-wave direction is transverse to the system of D3-branes. We also present moreD-brane bound state solutions by applyingT-duality symmetries. The system ofD3-branes oriented at an arbitrary angle is shown to preserve 1/16 supersymmetries. Finally a brief discussion of the open string construction is presented for both the cases.     

Analytic Perturbation Theory for Bound States in the Transfer Matrix Spectrum of Weakly Correlated Lattice Ferromagnetic Spin Systems

We consider general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region (β≪1). Each model is characterized by a single site apriori spin distribution taken to be even. We also take the parameter α=〈s ⁴〉−3〈s ²〉²>0, i.e. in the region which we call Gaussian subjugation, where 〈s ^k 〉 denotes the kth moment of the apriori distribution. Associated with the model is a lattice quantum field theory known to contain a particle of asymptotic mass −lnβ and a bound state below the two-particle threshold. We develop a β analytic perturbation theory for the binding energy of this bound state. As a key ingredient in obtaining our result we show that the Fourier transform of the two-point function is a meromorphic function, with a simple pole, in a suitable complex spectral parameter and the coefficients of its Laurent expansion are analytic in β.     

Spectrum of the H− Ion in the s-Wave Model

 The H⁻ ion in the s-wave model has one bound state and a Rydberg series of resonances, one associated with each inelastic threshold of the electron hydrogen system. We calculate the energy of the bound state and the energies of the resonances as well as their total widths up to N = 9 and partial widths up to N = 7. Received July 5, 1999; revised February 18, 2000; accepted for publication February 22, 2000     

Femtoscopic correlations and final state resonance formation

The correlation femtoscopy formalism including resonance formation due to the final state interaction and its applicability conditions are discussed. The example calculations of π⁺Ξ⁻ and K ⁺ K ⁻ correlation functions are done with the account of Ξ*(1530) and ϕ(1020) resonances, respectively. It is shown that in these calculations the usual form of the smoothness approximation should be substituted by a more general one. A strong sensitivity of resonance formation in the final state to the position-momentum correlations at particle freeze-out is demonstrated.     

Separation of different wave components in the Bethe–Salpeter wave function

The scalar products of polarization tensor and unit vectors are presented explicitly in spherical coordinate system expanded in terms of spherical harmonic functions. By applying the obtained formulae, different wave components in the Salpeter wave function can be shown explicitly, and the results are consistent with the results obtained by L–S coupling analysis. The cancelation formula is given, by which the terms with pure L = J + 1 wave components in the Salpeter wave function for the bound state with h_P=(-1)^J\eta_{\rm P}=(-1)^J can be obtained by separating the L = J − 1 wave components from mixing terms. This separation provides the basis for studying higher-order contributions from the coupling of L = J − 1 and J + 1 wave states, and for solving the Salpeter equation exactly without approximation.     

Influence of vertex coulomb effects on peripheral partial amplitudes for the consecutive transfer of two protons in A(X,Y)B peripheral nuclear reactions induced by light loosely bound (exotic) nuclei at low energies

The amplitude for the consecutive transfer of two protons in A(X, Y)B peripheral nuclear reactions induced by loosely bound light (exotic) nuclei and described by a nonrelativistic square Feynman diagram in which the first transferred proton is loosely bound while the second one in tightly bound is considered. It is shown that the inclusion of three-ray Coulomb vertex effects in the square diagram leads to the appearance of an additional “Coulomb” singularity in the variable cos θ (here, θ is the c.m. scattering angle), this singularity being closer to the physical domain, −1 ≤ cos θ ≤ 1, than the well-known “triangle” singularities corresponding to the amplitude of the square diagram in which the internal line is contracted. The asymptotic behavior of the partial-wave amplitudes for l ≫ 1 that are generated by the aforementioned singularities is found explicitly. A comparative analysis of the resulting partial-wave amplitudes for l ≫ 1 is performed for specific peripheral nuclear reactions induced by ⁸B and ¹²N ions at various energies.     

C M ? C N D -computable state

The notions of D-computable state and D-concurrence are generalized to the C ^M ⊗ C ^N system. A class of D-computable state on C ^M ⊗ C ^N is given and the calculating method of the lower bound of D-concurrence is provided. The obvious expression of the lower bound of D-concurrence for the state mixed by two D-pure states is derived. Supported by the National Natural Science Foundation of China (Grant No. 60433050) and the Key Project of the Science Foundation of Xuzhou Normal University (Grant No. 06XLA05)