Electromagnetic superconductivity of vacuum induced by strong magnetic field: Numerical evidence in lattice gauge theory

Using numerical simulations of quenched SU(2)$\mathit{SU}(2)$ gauge theory we demonstrate that an external magnetic field leads to spontaneous generation of quark condensates with quantum numbers of electrically charged ρ   mesons if the strength of the magnetic field exceeds the critical value e_Bc=0.927(77) GeV²$e{B}_c=0.927(77){\text{GeV}}^2$ or _Bc=(1.56±0.13)⋅10¹⁶ Tesla$B_c=(1.56\pm 0.13)\cdot {10}^{16}\text{Tesla}$. The condensation of the charged ρ mesons in strong magnetic field is a key feature of the magnetic-field-induced electromagnetic superconductivity of the vacuum.     

Very-high-order weno schemes

We study weno(2r − 1) reconstruction [D.S. Balsara, C.W. Shu, Monotonicity prserving weno schemes with increasingly high-order of accuracy, J. Comput. Phys. 160 (2000) 405–452], with the mapping (wenom) procedure of the nonlinear weights [A.K. Henrick, T.D. Aslam, J.M. Powers, Mapped weighted-essentially-non-oscillatory schemes: achieving optimal order near critical points, J. Comput. Phys. 207 (2005) 542–567], which we extend up to weno17 (r=9)$(r=9)$. We find by numerical experiment that these procedures are essentially nonoscillatory without any stringent cfl limitation (cfl∈[0.8,1])$(\text{<small-caps>cfl</small-caps>}\in [0.8\text{,}1])$, for scalar hyperbolic problems (both linear and scalar conservation laws), provided that the exponent p_β$p_{\beta }$ in the definition of the Jiang–Shu [G.S. Jiang, C.W. Shu, Efficient implementation of weighted eno schemes, J. Comput. Phys. 126 (1996) 202–228] nonlinear weights be taken as p_β=r$p_{\beta }=r$, as originally proposed by Liu et al. [X.D. Liu, S. Osher, T. Chan, Weighted essentially nonoscillatory schemes, J. Comput. Phys. 115 (1994) 200–212], instead of p_β=2$p_{\beta }=2$ (this is valid both for weno and wenom reconstructions), although the optimal value of the exponent is probably p_β(r)∈[2,r]$p_{\beta }(r)\in [2\text{,}r]$. Then, we apply the family of very-high-order wenom_pβ=r${\text{<small-caps>wenom</small-caps>}}_{p_{\beta }=r}$ reconstructions to the Euler equations of gasdynamics, by combining local characteristic decomposition [A. Harten, B. Engquist, S. Osher, S.R. Chakravarthy, Uniformly high-order accurate essentially nonoscillatory schemes iii, J. Comput. Phys. 71 (1987) 231–303], with recursive-order-reduction (ror) aiming at aleviating the problems induced by the nonlinear interactions of characteristic fields within the stencil. The proposed ror algorithm, which generalizes the algorithm of Titarev and Toro [V.A. Titarev, E.F. Toro, Finite-volume weno schemes for 3-D conservation laws, J. Comput. Phys. 201 (2004) 238–260], is free of adjustable parameters, and the corresponding rorwenom_pβ=r${\text{<small-caps>rorwenom</small-caps>}}_{p_{\beta }=r}$ schemes are essentially nonoscillatory, as Δx→0$\mathrm{\Delta }x\to 0$, up to r=9$r=9$, for all of the test-cases studied. Finally, the unsplit linewise 2-D extension of the schemes is evaluated for several test-cases.     

The black-box fast multipole method

A new O(N)$O(N)$ fast multipole formulation is proposed for non-oscillatory kernels. This algorithm is applicable to kernels K(x,y)$K(x\text{,}y)$ which are only known numerically, that is their numerical value can be obtained for any (x,y)$(x\text{,}y)$. This is quite different from many fast multipole methods which depend on analytical expansions of the far-field behavior of K  , for |x-y|$|x-y|$ large. Other “black-box” or “kernel-independent” fast multipole methods have been devised. Our approach has the advantage of requiring a small pre-computation time even for very large systems, and uses the minimal number of coefficients to represent the far-field, for a given L²$L^2$ tolerance error in the approximation. This technique can be very useful for problems where the kernel is known analytically but is quite complicated, or for kernels which are defined purely numerically.     

On DBI Textures with generalized Hopf fibration

In this Letter we show numerical existence of O(4)$O(4)$ Dirac–Born–Infeld (DBI) Textures living in (N+1)$(N+1)$ dimensional spacetime. These defects are characterized by S^N→S³$S^N\to S^3$ mapping, generalizing the well-known Hopf fibration into _πN(S³)${\pi }_N(S^3)$, for all N>3$N>3$. The nonlinear nature of DBI kinetic term provides stability against size perturbation and thus renders the defects having natural scale.     

Fluctuation–dissipation inequality for quadratic open systems

For open systems derived from quadratic total Hamiltonians, we derive a dynamic fluctuation–dissipation (FD) inequality valid for any total initial state and without regard to the sign of the dissipation. With the added constraint that this state be factorized with the reservoir in thermal equilibrium, an uncertainty relation arises naturally from the FD inequality that can be stronger than the usual uncertainty principle in the form 〈q²〉〈p²〉??²/4$〈q^2〉〈p^2〉?{?}^2/4$. We discuss some of the properties of the uncertainty relation relevant to decoherence.     

Dynamical properties of a dissipative discontinuous map: A scaling investigation

The effects of dissipation on the scaling properties of nonlinear discontinuous maps are investigated by analyzing the behavior of the average squared action 〈I²〉$〈I^2〉$ as a function of the n-th iteration of the map as well as the parameters K and γ  , controlling nonlinearity and dissipation, respectively. We concentrate our efforts to study the case where the nonlinearity is large; i.e., K?1$K?1$. In this regime and for large initial action _I0?K$I_0?K$, we prove that dissipation produces an exponential decay for the average action 〈I〉$〈I〉$. Also, for _I0≅0$I_0\cong 0$, we describe the behavior of 〈I²〉$〈I^2〉$ using a scaling function and analytically obtain critical exponents which are used to overlap different curves of 〈I²〉$〈I^2〉$ onto a universal plot. We complete our study with the analysis of the scaling properties of the deviation around the average action ω.     

Discrete gauge symmetries in discrete MSSM-like orientifolds

Motivated by the necessity of discrete _ZN${\mathbb{Z}}_N$ symmetries in the MSSM to insure baryon stability, we study the origin of discrete gauge symmetries from open string sector U(1)$U(1)$?s in orientifolds based on rational conformal field theory. By means of an explicit construction, we find an integral basis for the couplings of axions and U(1)$U(1)$ factors for all simple current MIPFs and orientifolds of all 168 Gepner models, a total of 32 990 distinct cases. We discuss how the presence of discrete symmetries surviving as a subgroup of broken U(1)$U(1)$?s can be derived using this basis. We apply this procedure to models with MSSM chiral spectrum, concretely to all known U(3)×U(2)×U(1)×U(1)$U(3)\times U(2)\times U(1)\times U(1)$ and U(3)×Sp(2)×U(1)×U(1)$U(3)\times \mathit{Sp}(2)\times U(1)\times U(1)$ configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5)$\mathit{SU}(5)$ GUT models. We find examples of models with _Z2${\mathbb{Z}}_2$ (R-parity) and _Z3${\mathbb{Z}}_3$ symmetries that forbid certain B and/or L violating MSSM couplings. Their presence is however relatively rare, at the level of a few percent of all cases.     

Isomer-tagged differential-plunger measurements in proton-unbound Ho

The lifetime of an excited state above a weakly populated isomer in the proton-unbound odd–odd nucleus ¹⁴⁴Ho has been measured using the recoil distance Doppler shift method. This measurement represents the first differential-plunger lifetime measurement to utilize recoil-isomer tagging. The first excited Iπ=(¹⁰⁺)$I^{\pi }=({10}^{+})$ state above the two-quasiparticle πh_11/2⊗νh_11/2(⁸⁺)$\pi h_{11/2}\otimes \nu h_{11/2}(8^{+})$ isomer was determined to have a lifetime of τ=6(1) ps$\tau =6(1)\text{ps}$. Potential energy surface calculations, based on the configuration-constrained blocking method, predict the isomeric state to have γ  -soft triaxial-nuclear shape with |γ|≈24°$|\gamma |\approx 24\text{°}$. The lifetime of the (¹⁰⁺)$({10}^{+})$ state can be understood from these calculations if there is a degree of rotational alignment in this band, with the K value being lower than the bandhead spin. However, the validity of the K quantum number with large predicted triaxiality and gamma softness requires further theoretical study.     

The constraint on FCNC coupling of the top quark with a gluon from ep-collisions

Using the constraint on the single top production cross-section obtained at the HERA collider, σ(ep→etX)$\sigma (ep\to etX)$, we evaluate an upper limit on coupling constant of the anomalous top quark interaction with a gluon via flavor-changing neutral current: |κ_tgq/Λ|?0.4 TeV⁻¹$|{\kappa }_{tgq}/\Lambda |?0.4{\text{TeV}}^{\mathrm{-1}}$, BR(t→gq)<13%$\mathrm{BR}(t\to gq)<13\mathrm{\%}$.     

A new time–space domain high-order finite-difference method for the acoustic wave equation

A new unified methodology was proposed in Finkelstein and Kastner (2007) [39] to derive spatial finite-difference (FD) coefficients in the joint time–space domain to reduce numerical dispersion. The key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies. We develop this new time–space domain FD method further for 1D, 2D and 3D acoustic wave modeling using a plane wave theory and the Taylor series expansion. New spatial FD coefficients are frequency independent though they lead to a frequency dependent numerical solution. We prove that the modeling accuracy is 2nd-order when the conventional (2M)$(2M)$th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the acoustic wave equation. However, under the same discretization, the new 1D method can reach (2M)$(2M)$th-order accuracy and is always stable. The 2D method can reach (2M)$(2M)$th-order accuracy along eight directions and has better stability. Similarly, the 3D method can reach (2M)$(2M)$th-order accuracy along 48 directions and also has better stability than the conventional FD method. The advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models. In addition, we study the influence of the FD stencil length on numerical modeling for 1D inhomogeneous media, and derive an optimal FD stencil length required to balance the accuracy and efficiency of modeling. A new time–space domain high-order staggered-grid FD method for the 1D acoustic wave equation with variable densities is also developed, which has similar advantages demonstrated by dispersion analysis, stability analysis and modeling experiments. The methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering.     

Vacuum phase transition at nonzero baryon density

It is argued that the dominant contribution to the interaction of quark–gluon plasma at moderate T?Tc$T?T_c$ is given by the nonperturbative vacuum field correlators. Basing on that nonperturbative equation of state of quark–gluon plasma is computed and in the lowest approximation expressed in terms of absolute values of Polyakov lines for quarks and gluons Lfund(T),Ladj(T)=(Lfund)^9/4$L_{\mathrm{fund}}(T),L_{\mathrm{adj}}(T)={(L_{\mathrm{fund}})}^{9/4}$ known from lattice and analytic calculations. Phase transition at any μ   is described as a transition due to vanishing of one of correlators, DE(x)$D^E(x)$, which implies the change of gluonic condensate ΔG₂$\mathrm{\Delta }{G}_2$. Resulting transition temperature Tc(μ)$T_c(\mu )$ is calculated in terms of ΔG₂$\mathrm{\Delta }{G}_2$ and Lfund(Tc)$L_{\mathrm{fund}}(T_c)$. The phase curve Tc(μ)$T_c(\mu )$ is in a good agreement with lattice data. In particular Tc(0)=0.27$T_c(0)=0.27$; 0.19; 0.17 GeV$0.17\text{ GeV}$ for nf=0,2,3$n_f=0,2,3$ and fixed ΔG₂=0.0035 GeV⁴$\mathrm{\Delta }{G}_2=0.0035{\text{ GeV}}^4$.     

Tensor decomposition in electronic structure calculations on 3D Cartesian grids

In this paper, we investigate a novel approach based on the combination of Tucker-type and canonical tensor decomposition techniques for the efficient numerical approximation of functions and operators in electronic structure calculations. In particular, we study applicability of tensor approximations for the numerical solution of Hartree–Fock and Kohn–Sham equations on 3D Cartesian grids. We show that the orthogonal Tucker-type tensor approximation of electron density and Hartree potential of simple molecules leads to low tensor rank representations. This enables an efficient tensor-product convolution scheme for the computation of the Hartree potential using a collocation-type approximation via piecewise constant basis functions on a uniform n×n×n$n\times n\times n$ grid. Combined with the Richardson extrapolation, our approach exhibits O(h³)$O(h^3)$ convergence in the grid-size h=O(n^-1)$h=O(n^{-1})$. Moreover, this requires O(3rn+r³)$O(3\mathit{rn}+r^3)$ storage, where r   denotes the Tucker rank of the electron density with r=O(logn)$r=O(\log n)$, almost uniformly in n  . For example, calculations of the Coulomb matrix and the Hartree–Fock energy for the CH₄${\text{CH}}_4$ molecule, with a pseudopotential on the C atom, achieved accuracies of the order of 10^-6${10}^{-6}$ hartree with a grid-size n of several hundreds. Since the tensor-product convolution in 3D is performed via 1D convolution transforms, our scheme markedly outperforms the 3D-FFT in both the computing time and storage requirements.     

Three ways to solve the Poisson equation on a sphere with Gaussian forcing

Motivated by the needs of vortex methods, we describe three different exact or approximate solutions to the Poisson equation on the surface of a sphere when the forcing is a Gaussian of the three-dimensional distance, ∇²ψ=exp(-2?²(1-cos(θ))-C^Gauss(?)${\nabla }^2\psi =\exp (-2{?}^2(1-\cos (\theta ))-C^{\mathit{Gauss}}(?)$. (More precisely, the forcing is a Gaussian minus the “Gauss constraint constant”, C^Gauss$C^{\mathit{Gauss}}$; this subtraction is necessary because ψ$\psi$ is bounded, for any type of forcing, only if the integral of the forcing over the sphere is zero [Y. Kimura, H. Okamoto, Vortex on a sphere, J. Phys. Soc. Jpn. 56 (1987) 4203–4206; D.G. Dritschel, Contour dynamics/surgery on the sphere, J. Comput. Phys. 79 (1988) 477–483]. The Legendre polynomial series is simple and yields the exact value of the Gauss constraint constant, but converges slowly for large ?$?$. The analytic solution involves nothing more exotic than the exponential integral, but all four terms are singular at one or the other pole, cancelling in pairs so that ψ$\psi$ is everywhere nice. The method of matched asymptotic expansions yields simpler, uniformly valid approximations as series of inverse even powers of ?$?$ that converge very rapidly for the large values of ?  (?>40)$(?>40)$ appropriate for geophysical vortex computations. The series converges to a nonzero O(exp(-4?²))$O(\exp (-4{?}^2))$ error everywhere except at the south pole where it diverges linearly with order instead of the usual factorial order.     

Supersymmetric grand unification with light color-triplet

We construct a natural model of the supersymmetric SU(6)$\mathit{SU}(6)$ unification, in which the symmetry breaking, down to the standard model gauge group, results in the number of pseudo-Nambu–Goldstone superfields with interesting properties. Namely, besides the Higgs doublet–antidoublet pair which is responsible for the electroweak phase transition, the Nambu–Goldstone sector consists of multiplets in the anti- and fundamental representations of SU(5)$\mathit{SU}(5)$. While being strictly massless in the supersymmetric limit, they acquire the weak scale masses as a result of its breaking. The color-triplet components of this light sector could, in principle, mediate an unacceptably fast proton decay; however, because of the natural TeV/_MGUT$\text{TeV}/M_{\mathrm{GUT}}$ suppression of the Yukawa couplings to the light quarks and leptons, their existence is compatible with the experimental bound on proton lifetime. This suppression is made further interesting, since it results in the lifetime, of the lightest of the above-mentioned colored particles from 1 s to 1 day$1\text{day}$, long enough for it to appear stable in the detector. Furthermore, we argue that the accommodation of the color-triplet pseudo-Nambu–Goldstones, without fine-tuning or contradicting observations, implies SU(6)$\mathit{SU}(6)$ unification.