On the chromo-electric permittivity and Debye screening in hot QCD

We study the response functions (chromo-electric susceptibilities) for an interacting quark-gluon plasma. The interaction effects have been encoded in the effective fugacities for quasi-partons which are extracted self-consistently from the two equations of state for hot QCD. The first one is the fully perturbative O(g ⁵) EOS and the second one, which is O(g ⁶ln(1/g)) , incorporates some non-perturbative effects. We find that the response function shows large deviations from the ideal behavior. We further determine the temperature dependence of the Debye mass by fixing the effective coupling constant Q² which appears in the transport equation. We show that our formalism naturally yields the leading-order HTL expression for the Debye mass if we employ the ideal EOS. Employing the Debye mass, we estimate the dissociation temperatures for various charmonium and bottomonium bound states. These results are consistent with the current theoretical studies.     

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.     

Resonances in A=6 Nuclei: Use of Supersymmetric Quantum Mechanics

We propose a novel theoretical technique for the calculation of resonances at low excitation energies in weakly bound systems. Starting from an effective potential, supersymmetric quantum mechanics can be successfully used to generate families of isospectral potentials having desirable and adjustable properties. For resonance states, for which there is no bound ground state of the same spin-parity, one can construct an isospectral potential with a bound state in the continuum (BIC). The potential looks quite different but is strictly isospectral with the original one. The quasi-bound state in the original shallow potential will be effectively trapped in the deep well of the isospectral family facilitating an easier and more accurate calculation of the resonance energy. Application to ⁶He, ⁶Be, and ⁶Li systems yields quite accurate results. The beauty of our technique: We get both the bound ground state and the resonances by a single technique and using the same potential.     

Algebraic entropy,symmetries and linearization of quad equations consistent on the cube

We discuss the non–autonomous nonlinear partial difference equations belonging to Boll classi?cation of quad graph equations consistent around the cube. We show how starting from the compatible equations on a cell we can construct the lattice equations, its Bäcklund transformations and Lax pairs. By carrying out the algebraic entropy calculations we show that the H⁴ trapezoidal and the H⁶ families are linearizable and in a few examples we show how we can effectively linearize them.     

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.     

Bound States in Coulomb Systems ‐ Old Problems and New Solutions

We analyze the quantum statistical treatment of bound states in Hydrogen considered as a system of electrons and protons. Within this physical picture we calculate analytically isotherms of pressure for Hydrogen in a broad density region and compare to some results from the chemical picture. Our study is restricted to the range of intermediate temperatures 10⁴K < T < 10⁵K and not too high densities n < 10²⁴ protons per cm³, the formation of molecules is neglected. First we resume in detail the two transitions along isotherms: (i) formation of bound states occurring by increasing the density from low to moderate values, (ii) the destruction of bound states in the high density region, modelled here by Pauli‐Fock effects. Avoiding chemical models we will show, why bound states according to a discrete part of the spectra occur only in a valley in the T‐p plane. First we study virial expansions in the canonical ensemble and then in the grand canonical ensemble. We show that in fugacity representations the population of bound states saturates at higher density and that a combination of both representations provides quickly converging equations of state. In the case of degenerate systems we calculated first the density‐dependent energy levels, and find the pressure in Hartree‐Fock‐Wigner approximation showing the prominent role of Pauli blocking and Fock effects in the selfenergy (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dependence of the Three-Nucleon Binding Energy on Some Different Effects

The bound state of three-nucleon system is studied as a three-body problem which is solved following the different approaches of the Faddeev formalism as well as the unitary pole approximation. The three-body problem is reduced to a set of coupled integral equations by using separable approximations. Numerical calculations are carried out for the resulting integral equations and the separable expansion. In the present work, we calculate the ground-state binding energy of the bound three-nucleon system ³H. The main interest of the present work is to investigate the sensitivity of the three-nucleon binding energy to different effects. For this reason, we study the dependence of this energy on different forms of local and separable nucleon-nucleon potentials, the effective range of the nucleon-nucleon interaction, and on the percent of the D state in the deuteron wave function. Also we test the sensitivity of the three-nucleon binding energy to the considered number of terms from the separable expansion.     

The ADHM Construction and Non-local Symmetries of the Self-dual Yang–Mills Equations

We construct the most general reducible connection that satisfies the self-dual Yang–Mills equations on a simply-connected, open subset of flat \mathbbR⁴{\mathbb{R}^4}. We show how all such connections lie in the orbit of the flat connection on \mathbbR⁴{\mathbb{R}^4} under the action of non-local symmetries of the self-dual Yang–Mills equations. Such connections fit naturally inside a larger class of solutions to the self-dual Yang–Mills equations that are analogous to harmonic maps of finite type.     

Scattering properties of the ultracold 133Cs2 triplet state

The elastic scattering properties of ultracold 133Cs2 triplet state are investigated in detail.We construct a potential curve of the 133Cs2 triplet state,based on the latest ab initio molecular potential data and show how the scattering parameters are obtained by using three methods:the Numerov method,the semiclassical method and the variable phase method,where the scattering lengths of the 133Cs2 triplet state,i.e.301.79a0,300.67a0 and 310.81a0 are obtained respectively,with a0 being the Bohr radius.We also calculate the effective range and the number of bound states for the 133Cs2 triplet state.Our results are in agreement with the recent experimental data and the theoretical calculations.This confirms that the results of the scattering properties of the ultracold 133Cs2 triplet state,calculated by using these three methods,are reliable.     

Bound states of heavy quarks on the light plane

We investigate in detail the light plane formulation of bound state equations and of the interactions of bound states. This formalism is particularly well suited to discuss bound states of heavy quarks since these states can be well approximated as two particle states but yet there are significant relativistic corrections to the conventional nonrelativistic approach. Applications are made to electromagnetic decays of charmonium (ψ→e ⁺ e ^?, η _c →γγ, ψ′→η _c γ, etc.).     

Analytic continuation of the effective-range expansion as a method for determining the features of bound states: Application to the 6Li nucleus

The scattering function (effective-range function) for the two-channel elastic scattering of charged particles is used to analyze dα scattering at low energies. In order to construct this function, use is made of various sets of phase shifts and mixing parameter, both those that were obtained by solving Faddeev equations in the three-body (n, p, α) model and those that were deduced from available phaseshift analyses. By means of an analytic continuation of the scattering function to the point of the pole corresponding to the bound state of the ⁶Li nucleus, the values of the vertex constants and asymptotic normalization coefficients are found for the process ⁶Li → α + d. Possible means for refining these results are discussed.     

Asymmetric Diffusion and the Energy Gap Above¶the 111 Ground State of the Quantum XXZ Model

We consider the anisotropic three dimensional XXZ Heisenberg ferromagnet in a cylinder with axis along the 111 direction and boundary conditions that induce ground states describing an interface orthogonal to the cylinder axis. Let L be the linear size of the basis of the cylinder. Because of the breaking of the continuous symmetry around the axis, the Goldstone theorem implies that the spectral gap above such ground states must tend to zero as L→∞. In [3] it was proved that, by perturbing in a sub-cylinder with basis of linear size R≪L the interface ground state, it is possible to construct excited states whose energy gap shrinks as R ^-2. Here we prove that, uniformly in the height of the cylinder and in the location of the interface, the energy gap above the interface ground state is bounded from above and below by const.L ^-2. We prove the result by first mapping the problem into an asymmetric simple exclusion process on ℤ³ and then by adapting to the latter the recursive analysis to estimate from below the spectral gap of the associated Markov generator developed in [7]. Along the way we improve some bounds on the equivalence of ensembles already discussed in [3] and we establish an upper bound on the density of states close to the bottom of the spectrum. Received: 9 August 2001 / Accepted: 29 October 2001     

Search for the H-Dibaryon with a Large-Acceptance Hyperon Spectrometer

Recent Lattice QCD calculations predict a weekly bound H-dibaryon or a resonant state near the ΛΛ threshold although definite results should be waited for with physical quark masses. We propose to search for the H-dibaryon in ΛΛ production from (K ^?, K ⁺) reactions off nuclei and also for the weakly bound H-dibaryon by its weak decays to answer the long-standing question about the existence of the H-dibaryon. For this experiment, we plan to construct a large-acceptance hyperon spectrometer with a time projection chamber to detect Λ particles with a good momentum resolution. This spectrometer will also enhance the capability of hadron physics at J-PARC.     

EMC and polarized EMC effects in nuclei

We determine nuclear structure functions and quark distributions for ⁷Li, ¹¹B, ¹⁵N and ²⁷Al. For the nucleon bound state we solve the covariant quark–diquark equations in a confining Nambu–Jona-Lasinio model, which yields excellent results for the free nucleon structure functions. The nucleus is described using a relativistic shell model, including mean scalar and vector fields that couple to the quarks in the nucleon. The nuclear structure functions are then obtained as a convolution of the structure function of the bound nucleon with the light-cone nucleon distributions. We find that we are readily able to reproduce the EMC effect in finite nuclei and confirm earlier nuclear matter studies that found a large polarized EMC effect.     

On Slant Magnetic Curves in S-manifolds

We consider slant normal magnetic curves in (2n + 1)-dimensional S-manifolds. We prove that γ is a slant normal magnetic curve in an S-manifold (M^2m+s, φ, ξ^α, η^α, g) if and only if it belongs to a list of slant φ-curves satisfying some special curvature equations. This list consists of some specific geodesics, slant circles, Legendre and slant helices of order 3. We construct slant normal magnetic curves in ?2^n+s(–3s) and give the parametric equations of these curves.     

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.     

Three-body formalism for deuteron stripping reactions

A three-body formalism for deuteron stripping reactions has been developed. The equations of Altet al (1967) (AGS) for the three particle system (target A, n, p) are reduced to a set of coupled one-dimensional integral equations with the use of (i) angular momentum basis for representation and (ii) separable approximation for the two bodyt-matrices (which delineate the interactions between the particle pairs). The on-shell solutions of this set of integral equations are then related to the cross sections of the rearrangement processes. The inputs in this calculation, viz., the separable interactions between the particle pairs in the respective channels are simply constructed from the respective two body bound state in accordance with the bound state approximation (BSA) conforming to the ‘unitarity’ requirement. Using this formalism preliminary calculations for the (d, p) and (d, n) reaction cross sections on¹⁶O have been carried out and they seem to have considerable semblance with the observed cross sections.     

Hot QCD equations of state and RHIC

We show how hot QCD equations of states can be adapted to make definite predictions for quarkgluon plasma at RHIC.We consider equations of state up to O(g⁵) and O[g⁶(ln(1/g)+δ)]. Our method involves the extraction of equilibrium distribution functions for gluons and quarks from these equations of state by capturing the interaction effects entirely in the effective chemical potentials. We further utilize these distribution functions to study the screening length in hot QCD and dissociation phenomenon of heavy quarkonia states by combining this understanding with the semi-classical transport theory.     

Spectral Analysis of Weakly Coupled Stochastic Lattice Ginzburg–Landau Models

We consider the relaxation to equilibrium of solutions , t>0, , of stochastic dynamical Langevin equations with white noise and weakly coupled Ginzburg–Landau interactions. Using a Feynman–Kac formula, which relates stochastic expectations to correlation functions of a spatially non-local imaginary time quantum field theory, we obtain results on the joint spectrum of H, , where H is the self-adjoint, positive, generator of the semi-group associated with the dynamics, and P ^j , j= 1, …, d are the self-adjoint generators of the group of lattice spatial translations. We show that the low-lying energy-momentum spectrum consists of an isolated one-particle dispersion curve and, for the mass spectrum (energy-momentum at zero-momentum), besides this isolated one-particle mass, we show, using a Bethe–Salpeter equation, the existence of an isolated two-particle bound state if the coefficient of the quartic term in the polynomial of the Ginzburg–Landau interaction is negative and d= 1, 2; otherwise, there is no two-particle bound state. Asymptotic values for the masses are obtained. Received: 27 September 2000 / Accepted: 16 January 2001     

Sensitivity of the three-body calculations to different effects

The bound state of few-body systems in light nuclei is studied as a three-body problem. The three-body problem is solved following the different approaches of the Faddeev formalism as well as the unitary pole approximation. Separable approximations are introduced to reduce the three-body problem to a set of coupled integral equations. Numerical calculations are carried out for the resulting integral equations and the separable expansion. In the present work, we calculate the ground-state binding energy of the bound three-nucleon system³H. The main interest of the present work is to investigate the sensitivity of the three-body binding energy to different effects in the problem. For this reason, we study the dependence of the three-body binding energy of different forms of local and separable two-body potentials, on the effective range of the two-body potentials, and on the percent of theD state in the deuteron wave function. Also, we test the sensitivity of the three-body binding energy to the considered number of terms from the separable expansion.