Zero Modes for the Magnetic Pauli Operator in Even-Dimensional Euclidean Space

We study the ground state of the Pauli Hamiltonian with a magnetic field in ${\mathbb{R}^{2d}}$ , d > 1. We consider the case where a scalar potential W is present and the magnetic field B is given by ${B=2i\partial\bar{\partial} W}$ . The main result is that there are no zero modes if the magnetic field decays faster than quadratically at infinity. If the magnetic field decays quadratically then zero modes may appear, and we give a lower bound for the number of them. The results in this paper partly correct a mistake in a paper from 1993.     

Comments on |V ub /V cb | and |V ub | from non-leptonic B decays within the perturbative QCD approach

The Color String Percolation Model (CSPM) is used to determine the equation of state (EOS) of the Quark–Gluon Plasma (QGP) produced in central Au–Au collisions at $\sqrt{s_{\mathit{NN}}} = 200$  A GeV using STAR data at RHIC. When the initial density of interacting colored strings exceeds the 2D percolation threshold a cluster is formed, which defines the onset of color deconfinement. These interactions also produce fluctuations in the string tension which transforms the Schwinger particle (gluon) production mechanism into a maximum entropy thermal distribution analogous to QCD Hawking–Unruh radiation. The single string tension is determined by identifying the known value of the universal hadron limiting temperature T _c =167.7±2.6 MeV with the CSPM temperature at the critical percolation threshold parameter ξ _c =1.2. At midrapidity the initial Bjorken energy density and the initial temperature determine the number of degrees of freedom consistent with the formation of a ～2+1 flavor QGP. An analytic expression for the equation of state, the sound velocity $C_{s}^{2}(\xi)$ is obtained in CSPM. The CSPM $C_{s}^{2}(\xi)$ and the bulk thermodynamic values energy density ε/T ⁴ and entropy density s/T ³ are in excellent agreement in the phase transition region with recent lattice QCD simulations (LQCD) by the HotQCD Collaboration.     

Extremely large bandwidth and ultralow-dispersion slow light in photonic crystal waveguides with magnetically controllability

A line-defect waveguide within a two-dimensional magnetic-fluid-based photonic crystal with 45^o-rotated square lattice is presented to have excellent slow light properties. The bandwidth centered at $ \lambda_{0} $  = 1,550 nm of our designed W1 waveguide is around 66 nm, which is very large than that of the conventional W1 waveguide as well as the corresponding optimized structures based on photonic crystal with triangular lattice. The obtained group velocity dispersion $ \beta_{2} $ within the bandwidth is ultralow and varies from ?1,191 $ a/(2\pi c^{2} ) $ to 855 $ a/(2\pi c^{2} ) $ (a and c are the period of the lattice and the light speed in vacuum, respectively). Simultaneously, the normalized delay-bandwidth product is relatively large and almost invariant with magnetic field strength. It is indicated that using magnetic fluid as one of the constitutive materials of the photonic crystal structures can enable the magnetically fine tunability of the slow light in online mode. The concept and results of this work may give a guideline for studying and realizing tunable slow light based on the external-stimulus-responsive materials.     

On hvLif -like solutions in gauged Supergravity

We perform a thorough investigation of Lifshitz-like metrics with hyperscaling violation (hvLif) in four-dimensional theories of gravity coupled to an arbitrary number of scalars and vector fields, obtaining new solutions, electric, magnetic, and dyonic, that include the known ones as particular cases. After establishing some general results on the properties of purely hvLif solutions, we apply the previous formalism to the case of ${\mathcal {N}}=2,~d=4$ supergravity in the presence of Fayet–Iliopoulos terms, obtaining particular solutions to the $t^3$ -model, and explicitly embedding some of them in Type-IIB string theory.     

Mössbauer study of magnetism in FeII − III (oxy-)hydroxycarbonate green rusts; ferrimagnetism of FeII − III hydroxycarbonate

Fe^II???III hydroxycarbonate Fe $^{\rm II}_{4}$ Fe $^{\rm III}_{2}$ (OH)₁₂CO₃, green rust GR(CO $_{3}^{2-})$ , reveals a ferrimagnetic behaviour. Moments that lie within two-dimensional cation layers are parallel for same species and antiparallel between Fe^II and Fe^III. Respective ordering temperatures are 5.2 and 7 K. A sextet with distribution from 350 to 580 kOe for Fe^III and an octet reflecting a mixture of states with field of 130 kOe and quadrupole splitting of ?3.0 mm s^???1 for Fe^II are observed at 1.4 K. Ferric oxyhydroxycarbonate Fe $^{\rm III}_{6}$ O₁₂H₈CO₃ is ferromagnetic and displays at 4 K a sextet with field between 400 and 500 kOe (maximum at 480 kOe) and transition at 80 K. GR(CO $_{3}^{2-})$ deprotonation gives magnetic domains with compositions at x?=?1/3, 2/3 and 1 due to long range order.     

Coset Constructions of Logarithmic (1, p) Models

One of the best understood families of logarithmic onformal field theories consists of the (1, p) models (p =  2, 3, . . .) of central charge c _{1, p} =1 ? 6(p ? 1)²/p. This family includes the theories corresponding to the singlet algebras ${\mathcal{M}(p)}$ and the triplet algebras ${\mathcal{W}(p)}$ , as well as the ubiquitous symplectic fermions theory. In this work, these algebras are realised through a coset construction. The ${W^{(2)}_n}$ algebra of level k was introduced by Feigin and Semikhatov as a (conjectured) quantum hamiltonian reduction of ${\widehat{\mathfrak{sl}}(n)_k}$ , generalising the Bershadsky–Polyakov algebra ${W^{(2)}_3}$ . Inspired by work of Adamovi? for p = 3, vertex algebras ${\mathcal{B}_p}$ are constructed as subalgebras of the kernel of certain screening charges acting on a rank 2 lattice vertex algebra of indefinite signature. It is shown that for p≤5, the algebra ${\mathcal{B}_p}$ is a quotient of ${W^{(2)}_{p-1}}$ at level ?(p ? 1)²/p and that the known part of the operator product algebra of the latter algebra is consistent with this holding for p> 5 as well. The triplet algebra ${\mathcal{W}(p)}$ is then realised as a coset inside the full kernel of the screening operator, while the singlet algebra ${\mathcal{M}(p)}$ is similarly realised inside ${\mathcal{B}_p}$ . As an application, and to illustrate these results, the coset character decompositions are explicitly worked out for p =  2 and 3.     

The N = 16 Spherical Shell Closure in 24O

The unbound excited states of the most neutron-rich dripline oxygen isotope, ²⁴O, have been investigated by using the ²⁴O(p,p′)²⁴O^* reaction at the beam energy of 62 MeV/nucleon in inverse kinematics. The first and second unbound excited states of ²⁴O have been observed at ${E_{\rm x}= 4.63_{-0.14}^{+0.30}}$  MeV and ${E_{\rm x}= 5.13_{-0.24}^{+0.19}}$  MeV (preliminary) along with the evidence for another higher lying state at around 7.3 MeV. The quadrupole deformation parameter ${\beta_{2^+}}$ was deduced to be ${0.15_{-0.03}^{+0.08}}$ (preliminary) for the first time. The systematics of the ${\beta_{2^+}}$ and the ${E_{\rm x}(2_1^+)}$ in the Z = 8 isotopes shows the N = 16 spherical shell closure in ²⁴O.     

Electroweak radiative corrections to $$W^+W^-\gamma $$ production at the ILC

We consider holographic superconductors in a rotating black string spacetime. In view of the mandatory introduction of the \(A_\varphi \) component of the vector potential we are left with three equations to be solved. Their solutions show that the rotation parameter \(a\) influences the critical temperature \(T_\mathrm{c}\) and the conductivity \(\sigma \) in a simple but non-trivial way.     

Bianchi type-II String Cosmological Model with Magnetic Field in Scale-Covariant Theory of Gravitation

The spatially homogeneous and totally anisotropic Bianchi type-II cosmological solutions of massive strings have been investigated in the presence of the magnetic field in the framework of scale-covariant theory of gravitation formulated by Canuto et al. (Phys. Rev. Lett. 39, 429, 1977). With the help of special law of variation for Hubble^’s parameter proposed by Berman (Nuovo Cimento 74, 182, 1983) string cosmological model is obtained in this theory. We use the power law relation between scalar field ? and scale factor R to find the solutions. Some physical and kinematical properties of the model are also discussed.     

Formation and crystallization kinetics of Nd–Fe–B-based bulk amorphous alloy

In order to improve the glass-forming ability (GFA) of Nd–Fe–B ternary alloys to obtain fully amorphous bulk Nd–Fe–B-based alloy, the effects of Mo and Y doping on GFA of the alloys were investigated. It was found that the substitution of Mo for Fe and Y for Nd enhanced the GFA of the Nd–Y–Fe–Mo–B alloys. It was also revealed that the GFA of the samples was optimized by 4 at.% Mo doping and increased with the Y content. The fully amorphous structures were all formed in the Nd $_{6-{x}}$ Y $_{{x}}$ Fe $_{68}$ Mo $_{4}$ B $_{22}$ (x $=$ 1–5) alloy rods with 1.5 mm-diameter. After subsequent crystallization, the devitrified Nd $_{3}$ Y $_{3}$ Fe $_{68}$ Mo $_{4}$ B $_{22}$ alloy rod exhibited a uniform distribution of grains with a coercivity of 364.1 kA/m. The crystallization behavior of Nd $_{3}$ Y $_{3}$ Fe $_{68}$ Mo $_{4}$ B $_{22}$ BMG was investigated in isothermal situation. The Avrami exponent n determined by JAM plot is lower than 2.5, implying that the crystallization is mainly governed by a growth of particles with decreasing nucleation rate.     

On the Second Mixed Moment of the Characteristic Polynomials of 1D Band Matrices

We consider the asymptotic behavior of the second mixed moment of the characteristic polynomials of 1D Gaussian band matrices, i.e., of the Hermitian N × N matrices H _N with independent Gaussian entries such that 〈H _ij H _lk 〉 = δ _ik δ _jl J _ij , where ${J=(-W^2\triangle+1)^{-1}}$ . Assuming that ${W^2=N^{1+\theta}}$ , ${0 < \theta \leq 1}$ , we show that the moment’s asymptotic behavior (as ${N\to\infty}$ ) in the bulk of the spectrum coincides with that for the Gaussian Unitary Ensemble.     

On Gravitational Effects in the Schrödinger Equation

The Schrödinger  equation for a particle of rest mass $m$ and electrical charge $ne$ interacting with a four-vector potential $A_i$ can be derived as the non-relativistic limit of the Klein–Gordon  equation $\left( \Box '+m^2\right) \varPsi =0$ for the wave function $\varPsi $ , where $\Box '=\eta ^{jk}\partial '_j\partial '_k$ and $\partial '_j=\partial _j -\mathrm {i}n e A_j$ , or equivalently from the one-dimensional  action $S_1=-\int m ds +\int neA_i dx^i$ for the corresponding point particle in the semi-classical approximation $\varPsi \sim \exp {(\mathrm {i}S_1)}$ , both methods yielding the equation $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2m}\eta ^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + m + n e\phi \right) \varPsi $ in Minkowski  space–time  , where $\alpha ,\beta =1,2,3$ and $\phi =-A_0$ . We show that these two methods generally yield equations  that differ in a curved background  space–time   $g_{ij}$ , although they coincide when $g_{0\alpha }=0$ if $m$ is replaced by the effective mass $\mathcal{M}\equiv \sqrt{m^2-\xi R}$ in both the Klein–Gordon  action $S$ and $S_1$ , allowing for non-minimal coupling to the gravitational  field, where $R$ is the Ricci scalar and $\xi $ is a constant. In this case $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2\mathcal{M}'} g^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + \mathcal{M}\phi ^{(\mathrm g)} + n e\phi \right) \varPsi $ , where $\phi ^{(\mathrm g)} =\sqrt{g_{00}}$ and $\mathcal{M}'=\mathcal{M}/\phi ^{(\mathrm g)} $ , the correctness of the gravitational  contribution to the potential having been verified to linear order $m\phi ^{(\mathrm g)} $ in the thermal-neutron beam interferometry experiment due to Colella et al. Setting $n=2$ and regarding $\varPsi $ as the quasi-particle wave function, or order parameter, we obtain the generalization of the fundamental macroscopic Ginzburg-Landau equation of superconductivity to curved space–time. Conservation of probability and electrical current requires both electromagnetic gauge and space–time  coordinate conditions to be imposed, which exemplifies the gravito-electromagnetic analogy, particularly in the stationary case, when div ${{\varvec{A}}}=\hbox {div}{{\varvec{A}}}^{(\mathrm g)}=0$ , where ${{\varvec{A}}}^{\alpha }=-A^{\alpha }$ and ${{\varvec{A}}}^{(\mathrm g)\alpha }=-\phi ^{(\mathrm g)}g^{0\alpha }$ . The quantum-cosmological Schrödinger  (Wheeler–DeWitt) equation is also discussed in the $\mathcal{D}$ -dimensional  mini-superspace idealization, with particular regard to the vacuum potential $\mathcal V$ and the characteristics of the ground state, assuming a gravitational  Lagrangian   $L_\mathcal{D}$ which contains higher-derivative  terms up to order $\mathcal{R}^4$ . For the heterotic superstring theory  , $L_\mathcal{D}$ consists of an infinite series in $\alpha '\mathcal{R}$ , where $\alpha '$ is the Regge slope parameter, and in the perturbative approximation $\alpha '|\mathcal{R}| \ll 1$ , $\mathcal V$ is positive semi-definite for $\mathcal{D} \ge 4$ . The maximally symmetric ground state satisfying the field equations is Minkowski  space for $3\le {\mathcal {D}}\le 7$ and anti-de Sitter  space for $8 \le \mathcal {D} \le 10$ .     

The Lie–Rinehart Universal Poisson Algebra of Classical and Quantum Mechanics

The Lie–Rinehart algebra of a (connected) manifold ${\mathcal {M}}$ , defined by the Lie structure of the vector fields, their action and their module structure over ${C^\infty({\mathcal {M}})}$ , is a common, diffeomorphism invariant, algebra for both classical and quantum mechanics. Its (noncommutative) Poisson universal enveloping algebra ${\Lambda_{R}({\mathcal {M}})}$ , with the Lie–Rinehart product identified with the symmetric product, contains a central variable (a central sequence for non-compact ${{\mathcal {M}}}$ ) ${Z}$ which relates the commutators to the Lie products. Classical and quantum mechanics are its only factorial realizations, corresponding to Z  =  i z, z  =  0 and ${z = \hbar}$ , respectively; canonical quantization uniquely follows from such a general geometrical structure. For ${z =\hbar \neq 0}$ , the regular factorial Hilbert space representations of ${\Lambda_{R}({\mathcal{M}})}$ describe quantum mechanics on ${{\mathcal {M}}}$ . For z  =  0, if Diff( ${{\mathcal {M}}}$ ) is unitarily implemented, they are unitarily equivalent, up to multiplicity, to the representation defined by classical mechanics on ${{\mathcal {M}}}$ .     

Liouville-Type Theorems for the Forced Euler Equations and the Navier–Stokes Equations

In this paper we study the Liouville-type properties for solutions to the steady incompressible Euler equations with forces in ${\mathbb {R}^N}$ . If we assume “single signedness condition” on the force, then we can show that a ${C^1 (\mathbb {R}^N)}$ solution (v, p) with ${|v|^2+ |p| \in L^{\frac{q}{2}}(\mathbb {R}^N),\,q \in (\frac{3N}{N-1}, \infty)}$ is trivial, v = 0. For the solution of the steady Navier–Stokes equations, satisfying ${v(x) \to 0}$ as ${|x| \to \infty}$ , the condition ${\int_{\mathbb {R}^3} |\Delta v|^{\frac{6}{5}} dx < \infty}$ , which is stronger than the important D-condition, ${\int_{\mathbb {R}^3} |\nabla v|^2 dx < \infty}$ , but both having the same scaling property, implies that v = 0. In the appendix we reprove Theorem 1.1 (Chae, Commun Math Phys 273:203–215, 2007), using the self-similar Euler equations directly.     

FRW in Cosmological Self-creation Theory

We use the Brans-Dicke theory from the framework of General Relativity (Einstein frame), but now the total energy momentum tensor fulfills the following condition $[\frac{1}{\phi}T^{\mu \nu M}+T^{\mu \nu}(\phi)]_{;\nu}=0$ . We take as a first model the flat FRW metric and with the law of variation for Hubble’s parameter proposal by Berman and Gomide (Nuovo Cimento B 74: 182, 1983), we find solutions to the Einstein field equations by the cases: inflation (γ=?1), radiation ( $\gamma=\frac{1}{3}$ ), stiff matter (γ=1). For the Inflation case the scalar field grows fast and depends strongly of the constant M _γ=?1 that appears in the solution, for the Radiation case, the scalar stop its expansion and then decrease perhaps due to the presence of the first particles. In the Stiff Matter case, the scalar field is decreasing so for a large time, ?→0. In the same line of classical solutions, we find an exact solution to the Einstein field equations for the stiff matter (γ=1) and flat universe, using the Hamilton-Jacobi scheme.     

Global Existence for the Critical Dissipative Surface Quasi-Geostrophic Equation

In this article, we study the critical dissipative surface quasi-geostrophic equation (SQG) in ${\mathbb{R}^2}$ R 2 . Motivated by the study of the homogeneous statistical solutions of this equation, we show that for any large initial data θ ₀ liying in the space ${\Lambda^{s} (\dot{H}^{s}_{uloc}(\mathbb{R}^2)) \cap L^\infty(\mathbb{R}^2)}$ Λ s ( H ˙ u l o c s ( R 2 ) ) ∩ L ∞ ( R 2 ) the critical (SQG) has a global weak solution in time for 1/2 <  s <  1. Our proof is based on an energy inequality verified by the equation ${(SQG)_{R,\epsilon}}$ ( S Q G ) R , ? which is nothing but the (SQG) equation with truncated and regularized initial data. By classical compactness arguments, we show that we are able to pass to the limit ( ${R \rightarrow \infty}$ R → ∞ , ${\epsilon \rightarrow 0}$ ? → 0 ) in ${(SQG)_{R,\epsilon}}$ ( S Q G ) R , ? and that the limit solution has the desired regularity.     

Analytic Binding Energies for Two-Baryon Bound States in 2 + 1 Strongly Coupled Lattice QCD With Two-Flavors

We consider a lattice SU(3) QCD model in 2 + 1 dimensions, with two flavors and 2 × 2 spin matrices. An imaginary time functional integral formulation with Wilson’s action is used in the strong coupling regime, i.e. small hopping parameter ${0 < \kappa \ll 1}$ , and much smaller plaquette coupling ${\beta, 0 < \beta \ll \kappa}$ . In this regime, it is known that the low-lying energy-momentum spectrum contains isolated dispersion curves identified with baryons and mesons with asymptotic masses ${m\approx-3\ln\kappa}$ and ${m_m\approx-2\ln\kappa}$ , respectively. We prove the existence of two (labelled by ±) two-baryon bound states for each of the total isospin sectors I = 0,1 and we obtain, in each case, the exact binding energies ${\epsilon_{I\,\pm} }$ (of order ${\kappa^2}$ ) which extend to jointly analytic function in ${\kappa}$ and β. We also prove that these points are the only mass spectrum up to slightly above the bound state masses. Precisely, we show, for ${\alpha_0=\frac 14, \alpha_1=\frac 1{12}, \alpha_2=\frac12, \alpha_3=\frac 34}$ and small ${\delta >0 }$ , that the bound state masses ${2m-\epsilon_{I\,\pm}}$ are the only points in the mass spectrum in ${(0,2m-\epsilon_{I\,\pm}+\delta \alpha_I\kappa^2)}$ , for I = 0,1, and in ${(0,2m-(1+\delta)\alpha_I\kappa^2)}$ , for I = 2,3. These results are exact and validate our previous results obtained in a ladder approximation. The method employs suitable two- and four-point correlations with spectral representations and a lattice Bethe-Salpeter equation. For I = 0,1, a quark, antiquark space-range one potential of order ${\kappa^2}$ is found to be the dominant contribution to the two-baryon interaction and the interaction of the individual quark isospins of one baryon with those of the other is described by permanents. A novel spectral free decomposition (but spectral representation motivated, for real κ and β) of the two-point correlation, after performing a complex extension, is a key ingredient in showing the joint analyticity of the binding energy.     

Semiclassical strings in supergravity PFT

In this paper, we introduce the bulk viscosity in the formalism of modified gravity theory in which the gravitational action contains a general function \(f(R,T)\) , where \(R\) and \(T\) denote the curvature scalar and the trace of the energy–momentum tensor, respectively, within the framework of a flat Friedmann–Robertson–Walker model. As an equation of state for a prefect fluid, we take \(p=(\gamma -1)\rho \) , where \(0 \le \gamma \le 2\) and a viscous term as a bulk viscosity due to the isotropic model, of the form \(\zeta =\zeta _{0}+\zeta _{1}H\) , where \(\zeta _{0}\) and \(\zeta _{1}\) are constants, and \(H\) is the Hubble parameter. The exact non-singular solutions to the corresponding field equations are obtained with non-viscous and viscous fluids, respectively, by assuming a simplest particular model of the form of \(f(R,T) = R+2f(T)\) , where \(f(T)=\alpha T\) ( \(\alpha \) is a constant). A big-rip singularity is also observed for \(\gamma <0\) at a finite value of cosmic time under certain constraints. We study all possible scenarios with the possible positive and negative ranges of \(\alpha \) to analyze the expansion history of the universe. It is observed that the universe accelerates or exhibits a transition from a decelerated phase to an accelerated phase under certain constraints of \(\zeta _0\) and \(\zeta _1\) . We compare the viscous models with the non-viscous one through the graph plotted between the scale factor and cosmic time and find that the bulk viscosity plays a major role in the expansion of the universe. A similar graph is plotted for the deceleration parameter with non-viscous and viscous fluids and we find a transition from decelerated to accelerated phase with some form of bulk viscosity.