Random ballistic growth and diffusion in symmetric spaces

Sequential ballistic deposition (BD) with next-nearest-neighbor (NNN) interactions in a N  -column box is viewed as a time-ordered product of (N×N)$(N\times N)$-matrices consisting of a single _sl2${\mathit{sl}}_2$-block which has a random position along the diagonal. We relate the uniform BD growth with the diffusion in the symmetric space _HN=SL(N,R)/SO(N)$H_N=\mathit{SL}(N,R)/\mathit{SO}(N)$. In particular, the distribution of the maximal height of a growing heap is connected with the distribution of the maximal distance for the diffusion process in _HN$H_N$. The coordinates of _HN$H_N$ are interpreted as the coordinates of particles of the one-dimensional Toda chain. The group-theoretic structure of the system and links to some random matrix models are also discussed.     

Dynamical SUSY breaking in heterotic M-theory

It is shown that four-dimensional N=1$N=1$ supersymmetric QCD with massive flavors in the fundamental representation of the gauge group can be realized in the hidden sector of E₈×E₈$E_8\times E_8$ heterotic string vacua. The number of flavors can be chosen to lie in the range of validity of the free-magnetic dual, using which one can demonstrate the existence of long-lived meta-stable non-supersymmetric vacua. This is shown explicitly for the gauge group Spin(10)$\mathit{Spin}(10)$, but the methods are applicable to Spin(Nc)$\mathit{Spin}(N_c)$, SU(Nc)$\mathit{SU}(N_c)$ and Sp(Nc)$\mathit{Sp}(N_c)$ for a wide range of color index Nc$N_c$. Hidden sectors of this type can potentially be used as a mechanism to break supersymmetry within the context of heterotic M-theory.     

Self-duality of the compactified Ruijsenaars–Schneider system from quasi-Hamiltonian reduction

The Delzant theorem of symplectic topology is used to derive the completely integrable compactified Ruijsenaars–Schneider _IIIb${\mathrm{III}}_{\mathrm{b}}$ system from a quasi-Hamiltonian reduction of the internally fused double SU(n)×SU(n)$\mathit{SU}(n)\times \mathit{SU}(n)$. In particular, the reduced spectral functions depending respectively on the first and second SU(n)$\mathit{SU}(n)$ factor of the double engender two toric moment maps on the _IIIb${\mathrm{III}}_{\mathrm{b}}$ phase space CP(n−1)$\mathbb{C}P(n-1)$ that play the roles of action-variables and particle-positions. A suitable central extension of the SL(2,Z)$\mathit{SL}(2,\mathbb{Z})$ mapping class group of the torus with one boundary component is shown to act on the quasi-Hamiltonian double by automorphisms and, upon reduction, the standard generator S   of the mapping class group is proved to descend to the Ruijsenaars self-duality symplectomorphism that exchanges the toric moment maps. We give also two new presentations of this duality map: one as the composition of two Delzant symplectomorphisms and the other as the composition of three Dehn twist symplectomorphisms realized by Goldman twist flows. Through the well-known relation between quasi-Hamiltonian manifolds and moduli spaces, our results rigorously establish the validity of the interpretation [going back to Gorsky and Nekrasov] of the _IIIb${\mathrm{III}}_{\mathrm{b}}$ system in terms of flat SU(n)$\mathit{SU}(n)$ connections on the one-holed torus.     

Fixed point resolution in extensions of permutation orbifolds

We determine the simple currents and fixed points of the orbifold theory CFT⊗CFT/Z₂$\mathit{CFT}\otimes \mathit{CFT}/{\mathbb{Z}}_2$, given the simple currents and fixed point of the original CFT  . We see in detail how this works for the SUk₍₂₎$\mathit{SU}{(2)}_k$ WZW model, focusing on the field content (i.e. h  -spectrum of the primary fields) of the theory. We also look at the fixed point resolution of the simple current extended orbifold theory and determine the SJ$S^J$ matrices associated to each simple current for SU₂₍₂₎$\mathit{SU}{(2)}_2$ and for the B_1(n)$B{(n)}_1$ and D_1(n)$D{(n)}_1$ series.     

Fluxmetric and magnetometric demagnetizing factors for cylinders

Fluxmetric and magnetometric demagnetizing factors, _Nf$N_{\mathrm{f}}$ and _Nm$N_{\mathrm{m}}$, for cylinders along the axial direction are numerically calculated as functions of material susceptibility χ$\chi$ and the ratio γ$\gamma$ of length to diameter. The results have an accuracy better than 0.1% with respect to min(_Nf,m,1-_Nf,m)$\min (N_{\mathrm{f},\mathrm{m}},1-N_{\mathrm{f},\mathrm{m}})$ and are tabulated in the range of 0.01?γ?500$0.01?\gamma ?500$ and -1?χ<∞$-1?\chi <\infty$. _Nm$N_{\mathrm{m}}$ along the radial direction is evaluated with a lower accuracy from _Nm$N_{\mathrm{m}}$ along the axis and tabulated in the range of 0.01?γ?1$0.01?\gamma ?1$ and -1?χ<∞$-1?\chi <\infty$. Some previous results are discussed and several applications are explained based on the new results.     

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.     

Semiempirical fine-tuning for Hartree–Fock ionization potentials of atomic ions with non-integral atomic number

Amovilli and March (2006) [8] used diffusion quantum Monte Carlo techniques to calculate the non-relativistic ionization potential I(Z)$I(Z)$ in He-like atomic ions for the range of (fractional) nuclear charges Z   lying between the known critical value _Zc=0.911$Z_{\mathrm{c}}=0.911$ at which I(Z)$I(Z)$ tends to zero and Z=2$Z=2$. They showed that it is possible to fit I(Z)$I(Z)$ to a simple quadratic expression. Following that idea, we present here a semiempirical fine-tuning of Hartree–Fock ionization potentials for the isoelectronic series of He, Be, Ne, Mg and Ar-like atomic ions that leads to excellent estimations of _Zc$Z_{\mathrm{c}}$ for these series. The empirical information involved is experimental ionization and electron affinity data. It is clearly demonstrated that Hartree–Fock theory provides an excellent starting point for determining I(Z)$I(Z)$ for these series.     

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$\mathrm{\Delta }{G}_2=0.0035{\text{ GeV}}^4$.     

Lorentz covariant nucleon self-energy decomposition of the nuclear symmetry energy

Using the Hugenholtz–Van Hove theorem, we derive analytical expressions for the nuclear symmetry energy _Esym(ρ)$E_{\mathrm{sym}}(\rho )$ and its density slope L(ρ)$L(\rho )$ in terms of the Lorentz covariant nucleon self-energies in isospin asymmetric nuclear matter. These general expressions are useful for determining the density dependence of the symmetry energy and understanding the Lorentz structure and the microscopic origin of the symmetry energy in relativistic covariant formulism. As an example, we analyze the Lorentz covariant nucleon self-energy decomposition of _Esym(ρ)$E_{\mathrm{sym}}(\rho )$ and L(ρ)$L(\rho )$ and derive the corresponding analytical expressions within the nonlinear σ–ω–ρ–δ relativistic mean field model.     

On hydrogen transport in the first wall material of fusion devices in the presence of a broadband distribution of traps over the trapping energy

The dynamics of hydrogen dissolved in a sample with continuous distribution of traps over trapping energy φ(ε)∝exp(−αε)$\phi (\epsilon )\propto \exp (-\alpha \epsilon )$ (ε=E/T$\epsilon =E/T$ is the ratio of trapping energy E to the sample's temperature T  ) is considered. Assuming that the hydrogen density is smaller than the trap density and the most of hydrogen is trapped, we found that the dynamics of hydrogen transport can be described by either sub-diffusion or non-linear diffusion equations. Analysis of the outgassing of the sample homogeneously loaded with hydrogen gives, in the most important cases, both power-law, _ΓH∝t^−p${\Gamma }_{\mathrm{H}}\propto t^{-p}$ (p≥1/2$p\ge 1/2$) and exponential, ln(_ΓH)∝−t^α$\ln ({\Gamma }_{\mathrm{H}})\propto -t^{\alpha }$, time dependencies of the outgassing flux, _ΓH(t)${\Gamma }_{\mathrm{H}}(t)$.     

Gauge field strength tensor from the overlap Dirac operator

We derive the classical continuum limit of the operator trsσ_μνDov(x,x)${\mathrm{tr}}_s{\sigma }_{\mu \nu }{D}^{\mathrm{ov}}(x,x)$ with Dov$D^{\mathrm{ov}}$ being the overlap Dirac operator and show that it corresponds to the gauge field strength tensor F_μν(x)$F_{\mu \nu }(x)$.