Is the energy density of the ground state of the sine-Gordon model unbounded from below for beta^2 > 8 pi ?

We discuss Coleman's theorem concerning the energy density of the ground state of the sine-Gordon model proved in Phys. Rev. D 11, 2088 (1975). According to this theorem the energy density of the ground state of the sine-Gordon model should be unbounded from below for coupling constants beta^2 > 8 pi. The consequence of this theorem would be the non-existence of the quantum ground state of the sine-Gordon model for beta^2 > 8 pi. We show that the energy density of the ground state in the sine-Gordon model is bounded from below even for beta^2 > 8 pi. This result is discussed in relation to Coleman's theorem (Comm. Math. Phys. 31, 259 (1973)), particle mass spectra and soliton-soliton scattering in the sine-Gordon model.Comment: 22 pages, Latex, no figures, revised according to the version accepted for publication in Journal of Physics

Singular values of fractional integral operators: A unification of theorems of Hille, Tamarkin, and Chang

AbstractWe obtain upper bounds on the singular values of fractional integral operators of the form Lα · = ∝0x(x − y)x − 1Γ(α) · dy under the constraint α > 0. These bounds are employed to extend various results obtained over the last half century on the rate of decrease of eigenvalues and singular values of much more general integral operators. Apart from one relatively difficult theorem of Hardy and Littlewood (Math. Z., 27 (1928), 565–606) the devices used are quite simple. They involve no complex variable arguments

Remarks on the Gribov Problem in Direct Maximal Center Gauge

We review the equivalence of maximal center gauge fixing to the problem of finding the best fit, to a given lattice gauge field, by a thin vortex configuration. This fit is necessarily worst at the location of P-plaquettes. We then compare the fits achieved in Gribov copies generated by (i) over-relaxation; (ii) over-relaxation after Landau gauge preconditioning; and (iii) simulated annealing. Simulated annealing yields the best fit if all links on the lattice are included, but the situation changes if we consider only the lattice volume exterior to P-plaquettes. In this exterior region, the fit is best for Gribov copies generated by over-relaxation, and worst for Gribov copies generated after Landau gauge preconditioning. The two fitting criteria (including or not including the P-plaquettes) yield string tensions differing by -34% to +20% respectively, relative to the full string tension. Our usual procedure (``quenched minimization'') seems to be a compromise between these criteria, and yields string tensions at an intermediate value close to the full string tension.Comment: 14 pages, 6 figure

On the D-wave state component of the deuteron in the Nambu-Jona-Lasinio model of light nuclei

The D-wave state component of the neutron-proton bound state in the deuteron is calculated in the Nambu-Jona-Lasinio model of light nuclei - the relativistically covariant quantum field theoretic approach to the description of low-energy nuclear forces. The theoretical value of the fraction of the D-wave state relative to the S-wave state is equal to eta_d = 0.0238. This agrees well with the phenomenological value eta_d = 0.0256(4) quoted by Kamionkowski and Bahcall (ApJ. 420, 884 (1994)).Comment: 7 pages, latex, no figure

First-principles GW calculations for DNA and RNA nucleobases

On the basis of first-principles GW calculations, we study the quasiparticle properties of the guanine, adenine, cytosine, thymine, and uracil DNA and RNA nucleobases. Beyond standard G0W0 calculations, starting from Kohn-Sham eigenstates obtained with (semi)local functionals, a simple self-consistency on the eigenvalues allows to obtain vertical ionization energies and electron affinities within an average 0.11 eV and 0.18 eV error respectively as compared to state-of-the-art coupled-cluster and multi-configurational perturbative quantum chemistry approaches. Further, GW calculations predict the correct \pi -character of the highest occupied state, thanks to several level crossings between density functional and GW calculations. Our study is based on a recent gaussian-basis implementation of GW with explicit treatment of dynamical screening through contour deformation techniques.Comment: 5 pages, 3 figure

On the theory of equivalent operators and application to the numerical solution of uniformly elliptic partial differential equations

AbstractThis work is motivated by the preconditioned iterative solution of linear systems that arise from the discretization of uniformly elliptic partial differential equations. Iterative methods with bounds independent of the discretization are possible only if the preconditioning strategy is based upon equivalent operators. The operators A, B: W → V are said to be V norm equivalent if ∥Au∥v∥Bu∥v is bounded above and below by positive constants for u ϵ D, where D is “sufficiently dense.” If A is V norm equivalent to B, then for certain discretization strategies one can use B to construct a preconditioned iterative scheme for the approximate solution of the problem Au = F. The iteration will require an amount of work that is at most a constant times the work required to approximately solve the problem Bû = \̂tf to reduce the V norm of the error by a fixed factor. This paper develops the theory of equivalent operators on Hubert spaces. Then, the theory is applied to uniformly elliptic operators. Both the strong and weak forms are considered. Finally, finite element and finite difference discretizations are examined

From Solar Proton Burning to Pionic Deuterium through the Nambu-Jona-Lasinio model of light nuclei

Within the Nambu-Jona-Lasinio model of light nuclei (the NNJL model), describing strong low-energy nuclear interactions, we compute the width of the energy level of the ground state of pionic deuterium. The theoretical value fits well the experimental data. Using the cross sections for the reactions nu_e + d -> p + p + e^- and nu_e + d -> p + n + nu_e, computed in the NNJL model, and the experimental values of the events of these reactions, detected by the SNO Collaboration, we compute the boron neutrino fluxes. The theoretical values agree well with the experimental data and the theoretical predictions within the Standard Solar Model by Bahcall. We argue the applicability of the constraints on the astrophysical factor for the solar proton burning, imposed by helioseismology, to the width of the energy level of the ground state of pionic deuterium. We show that the experimental data on the width satisfy these constraints. This testifies an indirect measurement of the recommended value of the astrophysical factor for the solar proton burning in terrestrial laboratories in terms of the width of the energy level of the ground state of pionic deuterium.Comment: 10 pages, no figures, Late

Partial least squares, conjugate gradient and the fisher discriminant

The theory of multivariate regression has been extensively studied and is commonly used in many diverse scientific areas. A wide variety of techniques are currently available for solving the problem of multivariate calibration. The volume of literature on this subject is so extensive that understanding which technique to apply can often be very confusing. A common class of techniques for solving linear systems, and consequently applications of linear systems to multivariate analysis, are iterative methods. While common linear system solvers typically involve the factorization of the coefficient matrix A in solving the system Ax = b, this method can be impractical if A is large and sparse. Iterative methods such as Gauss-Seidel, SOR, Chebyshev semi-iterative, and related methods also often depend upon parameters that require calibration and which are sometimes hard to choose properly. An iterative method which surmounts many of these difficulties is the method of conjugate gradient. Algorithms of this type find solutions iteratively, by optimally calculating the next approximation from the residuals