Variation of fundamental constants in space and time: Theory and observations

Review of recent works devoted to the temporal and spatialvariation of the fundamental constants and dependence of the fundamentalconstants on the gravitational potential (violation of local position invariance) is presented. We discuss the variation of the fine structure constant α=e²/ħc, strong interaction andfundamental masses (Higgs vacuum), e.g. the electron-to-proton mass ratioμ=m_e/M_p or X_e=m_e/Λ_QCD and X_q=m_q/Λ_QCD.We also present new results from Big Bang nucleosynthesisand Oklo natural nuclear reactor data and propose new measurements of enhanced effects in atoms, nuclei and molecules, both in quasar and laboratory spectra.     

New analysis of the Douglas-Herzberg system (A1Π- X1Σ+) in the CH+ ion radical

Three bands of the A¹Π- X¹Σ⁺ system in the ¹²CH⁺ ion radical have been rephotographed under high resolution as an emission spectra using a Geissler-type discharge tube. The conventional technique of spectroscopy has been implemented. Using the Th lines as a standards, as well as an interferometric comparator equipped with a photoelectric scanning device, the 0-0 , 0-1 and 2-1 bands have been reanalyzed. By means of much longer bands (J_max = 17 in the Q(J) branch of the 0-0 band; J_max = 16 in the R(J) branch of the 0-1 band; J_max = 14 in the P(J) and Q(J) branches of the 2-1 band), than have been observed so far, as well as the merged calculations, using another five bands given by Carrington et al. [A. Carrington, D.A. Ramsay, Phys. Scripta 25, 272 (1982)] additionally, more accurate molecular constants for the X¹Σ⁺ state, the improved reduced band system origin T_e = 24118.726 (14) cm^-1 as well as for the first time the equilibrium molecular constants with their one standard deviation for the A¹Π state in the CH⁺ molecule have been computed: ω_e'=1864.402(22), ω_ex_e'=115.832(14), ω_ey_e'= 2.6301(24), B_e'=11.88677(72), α_e'= 0.9163(18), γ_e'= -2.29(12)×10^-2, ε_e'= 4.95(20)×10^-3, D_e'=1.92960(31)×10^-3, β_e'= 1.0733(50)×10^-4, δ_e'= -1.312(16)×10^-5, , α_qe'= -3.14(16)×10^-3, and q_De'= -2.20(14)×10^-5 cm^-1. Only in our research the addition to the zero-point energy Y'₀₀=-1.9430 cm^-1 and cm^-1 have been calculated. The equilibrium bond lengths of r'_e=1.235053(37) ? and ? for the A¹Π and X¹Σ⁺ states, respectively have been computed. Full quantum-mechanics characteristic of the A-X bands system in the ¹²CH⁺ molecule, i.e. RKR turning points, the Franck-Condon factors and r-centroids have been obtained. Dissociation energies D_e^{X1 Σ+}=(38470± 3503) cm^-1 and D_e^{A1 Π}= (14415 ±3509) cm^-1 for the molecule under consideration have been estimated.     

Oscillations of the magnetoresistance in an inclined magnetic field for MIS structures on (100) silicon with a high electron density

At electron densities N _S>6×10⁻² cm⁻²² a second series of oscillations, which are tentatively attributed to population of the second energy subband, is observed in addition to the main series of Shubnikov-de Haas oscillations. A change in phase of the oscillations of the second series is observed at some angle of inclination α_e of the field. The measured value of α_e is used to calculate the ratio of the cyclotron mass to the effective g factor. The maximum possible cyclotron mass is also determined as m _H< 0.32m _e. On this basis it is concluded that the second series of oscillations is due to electrons which have an in-plane effective mass m*≈0.2m _e and which belong to the same valleys of the Fermi surface as in the case of the main oscillations. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 2, 136–140 (25 January 1998)     

Distribution of Particles Which Produces a “Smart” Material

If A _q(β, α, k) is the scattering amplitude, corresponding to a potential , where D⊂ℝ³ is a bounded domain, and is the incident plane wave, then we call the radiation pattern the function , where the unit vector α, the incident direction, is fixed, β is the unit vector in the direction of the scattered wave, and k>0, the wavenumber, is fixed. It is shown that any function , where S ² is the unit sphere in ℝ³, can be approximated with any desired accuracy by a radiation pattern: , where ∊ >0 is an arbitrary small fixed number. The potential q, corresponding to A(β), depends on f and ∊, and can be calculated analytically. There is a one-to-one correspondence between the above potential and the density of the number of small acoustically soft particles D _m⊂ D, 1≤ m≤ M, distributed in an a priori given bounded domain D⊂ℝ³. The geometrical shape of a small particle D _m is arbitrary, the boundary S _m of D _m is Lipschitz uniformly with respect to m. The wave number k and the direction α of the incident upon D plane wave are fixed. It is shown that a suitable distribution of the above particles in D can produce the scattering amplitude , at a fixed k>0, arbitrarily close in the norm of L ²(S ²× S ²) to an arbitrary given scattering amplitude f(α ', α), corresponding to a real-valued potential q∊ L ²(D), i.e., corresponding to an arbitrary refraction coefficient in D. MSC: 35J05, 35J10, 70F10, 74J25, 81U40, 81V05, 35R30. PACS: 03.04.Kf.     

Phase transition and electrical properties of (K<Subscript>0.5</Subscript>Na<Subscript>0.5</Subscript>)(Nb<Subscript>1-x</Subscript>Ta<Subscript>x</Subscript>)O<Subscript>3</Subscript> lead-free piezoelectric ceramics

(K_0.5Na_0.5)(Nb_1-xTa_x)O₃ lead-free piezoelectric ceramics have been prepared by an ordinary sintering technique. The results of X-ray diffraction reveal that Ta⁵⁺ diffuses into the K_0.5Na_0.5NbO₃ lattices to form a solid solution with an orthorhombic perovskite structure. Because of the high melting temperature of KTaO₃, the (K_0.5Na_0.5)(Nb_1-xTa_x)O₃ ceramics can be sintered at higher temperatures. The partial substitution of Ta⁵⁺ for the B-site ion Nb⁵⁺ decreases both paraelectric/cubic–ferroelectric/tetragonal and ferroelectric/tetragonal–ferroelectric/orthorhombic phase transition temperatures, T_C and T_O-T. It also induces a relaxor phase transition and weakens the ferroelectricity of the ceramics. The ceramics become ‘softened’, leading to improvements in d₃₃, k_p, k_t and ε_r and a decease in E_c, Q_m and N_p. The ceramics with x=0.075–0.15 become optimum, having d₃₃=127–151 pC/N, k_p=0.43–0.44, k_t=0.43–0.44, ε_r=541–712, tanδ=1.75–2.48% and T_C=378–329 °C. PACS 77.65.-j; 77.84.Dy; 77.84.-s     

Critical Behavior for Maximal Flows on the Cubic Lattice

Let F ₀ and F _m be the top and bottom faces of the box [0, k]×[0, l]×[0, m] in Z ³. To each edge e in the box, we assign an i.i.d. nonnegative random variable t(e) representing the flow capacity of e. Denote by Φ _k, l, m the maximal flow from F ₀ to F _m in the box. Let p _c denote the critical value for bond percolation on Z ³. It is known that Φ _k, l, m is asymptotically proportional to the area of F ₀ as m, k, l→∞, when the probability that t(e)>0 exceeds p _c , but is of lower order if the probability is strictly less than p _c . Here we consider the critical case where the probability that t(e)>0 is exactly equal to p _c , and prove that $$\mathop {{\text{lim}}}\limits_{k,l,m \to \infty } \frac{1}{{kl}}\Phi _{k,l,m} = 0{\text{ a}}{\text{.s and in }}L_1 $$ The limiting behavior of related to surfaces on Z ³ are also considered in this paper.     

Damping of zero sound in Luttinger liquids

We calculate the damping γ_q of collective density oscillations (zero sound) in a one-dimensional Fermi gas with dimensionless forward scattering interaction F and quadratic energy dispersion k² / 2 m at zero temperature. Using standard many-body perturbation theory, we obtain γ_q from the expansion of the inverse irreducible polarization to first order in the effective screened (RPA) interaction. For wave-vectors | q| /k_F ≪F (where k_F = m v_F is the Fermi wave-vector) we find to leading order γ_q ∝| q |³ /(v_F m²). On the other hand, for F ≪| q| /k_F most of the spectral weight is carried by the particle-hole continuum, which is distributed over a frequency interval of the order of q²/m. We also show that zero sound damping leads to a finite maximum proportional to |k - k_F | ^{-2 + 2 η} of the charge peak in the single-particle spectral function, where η is the anomalous dimension. Our prediction agrees with photoemission data for the blue bronze K_0.3MoO₃. We comment on other recent calculations of γ_q.     

Kinematical separation of α-n final-state interaction at 50 MeV incident energy

A kinematically complete experiment has been performed to study the α-n final-state interaction (FSI) in the α + d ↦α + p + n break-up reaction at 50 MeV incident energy for the alpha-particles. For this, we have chosen four pairs of correlation angles for the outgoing alpha and protons. These are ( θ_α = 18^°, θ_p = 42^°), ( θ_α = 20^°, θ_p = 45^°), ( θ_α = 22^°, θ_p = 42^°) and ( θ_α = 22^°, θ_p = 47^°), selected kinematically where the allowed phase spaces are in favor of the α-n final-state interaction. Our experimental data show strong α-n FSI in all the selected configurations. Also, the FSI is found to be stronger at the lower alpha-particle energy when two FSI peaks appear in the same configuration. Received: 17 June 2002 / Accepted: 3 October 2002 / Published online: 4 February 2003 RID="a" ID="a"e-mail: dey_s2001@yahoo.com; Present address: 445 Waupelani Drive, Apt. F3, State College, PA 16801, USA. Communicated by M. Gar?on     

A Conjecture for the Superintegrable Chiral Potts Model

We adapt our previous results for the “partition function” of the superintegrable chiral Potts model with open boundaries to obtain the corresponding matrix elements of e^{−α H} , where H is the associated Hamiltonian. The spontaneous magnetization ℳ _r can be expressed in terms of particular matrix elements of e^{−α H} S ₁ ^r e^{−β H} , where S ₁ is a diagonal matrix. We present a conjecture for these matrix elements as an m by m determinant, where m is proportional to the width of the lattice. The author has previously derived the spontaneous magnetization of the chiral Potts model by analytic means, but hopes that this work will facilitate a more algebraic derivation, similar to that of Yang for the Ising model.     

Improvement of perturbation theory in QCD for e + e − →hadrons and the problem of α s freezing

A method of improving perturbation theory in QCD is developed which can be applied to any polarization operator. The case of the polarization operator Π(q ²), corresponding to the process e ⁺ e ⁻→ hadrons, is considered in detail. By the use of the analytical properties of Π(q ²) and a perturbation expansion of Π(q ²) for q ²<0, the function ImΠ(q ²) at q ²>0 is defined in such a way that the infrared pole is eliminated. The convergence of the perturbation series for R(q ²)=σ(e ⁺ e ⁻ →hadrons)/(e ⁺ e ⁻→μ ⁺ μ ⁻) is improved. After substitution of R(q ²) into the dispersion relation an improved Adler function D(q ²) is obtained, having no infrared pole and a frozen α _s (q ²). Good agreement with experiment is achieved. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 3, 167–170 (10 August 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

von Neumann entropy signatures of a transition in one-dimensional electron systems with long-range correlated disorder

We study the von Neumann entropy and related quantities in one-dimensional electron systems with on-site long-range correlated potentials. The potentials are characterized by a power-law power spectrum S(k) μ\propto 1/k ^α, where α is the correlation exponent. We find that the first-order derivative of spectrum-averaged von Neumann entropy is maximal at a certain correlation exponent α _m for a finite system, and has perfect finite-size scaling behaviors around α _m . It indicates that the first-order derivative of the spectrum-averaged von Neumann entropy has singular behavior, and α _m can be used as a signature for transition points. For the infinite system, the threshold value α _c = 1.465 is obtained by extrapolating α _m .     

Isothermal depolarization currents in triglycine sulphate

5 s; the polarizing field was varied from 10 V/cm to 10 kV/cm, and the temperature between -190 °C and 25 °C. The results confirm that the depolarization current in TGS follows the formula I_d∼[(ω_pt)ⁿ+(ω_pt)^m]^-1, where n<1 and m>1. The values of the parameters n and m depend on both the electric field strength and the polarization time as well as on the temperature of the experiment. The loss peak frequency ω_p exhibits activation character: ω_p∼exp(-E/k_BT) with E=0.34 eV at temperatures directly below room temperature and E=0.013 eV in the range of liquid nitrogen temperatures. Received: 1 April 1997/Accepted: 7 April 1997     

Next-to-next-leading order correction to 3-jet rate and event-shape distribution

The hadronic events from the e ⁺ e ⁻ annihilation data at the centre-of-mass energies ranging from 60 to 197 GeV were studied. The AMY and OPAL Collaborations offered a unique opportunity to test QCD by measuring the energy dependence of different observables. The coupling constant, α _s, was measured by two different methods: first by employing the three-jet observables. Combining all the data, the value of as at next-to-next leading order (NNLO) was determined to be 0.117 ± 0.004(hard) ± 0.006(theo). Secondly, from the event-shape distributions, the strong coupling constant, α _s, was extracted at NNLO and it’s evaluation was tested with the energy scale. The results were consistent with the running of α _s, expected from QCD predictions. Averaging over different observables, α _s was determined to be 0.115 ± 0.007(hard) ± 0.003(theo).     

Connectivity of growing networks with link constraints

We propose a growing network model with link constraint, in which new nodes are continuously introduced into the system and immediately connected to preexisting nodes, and any arbitrary node cannot receive new links when it reaches a maximum number of links k_m. The connectivity of the network model is then investigated by means of the rate equation approach. For the connection kernel A(k)=k^γ, the degree distribution n_k takes a power law if γ≥1 and decays stretched exponentially if 0≤γ< 1. We also consider a network system with the connection kernel A(k)=k^α(k_m-k)^β. It is found that n_k approaches a power law in the α> 1 case and has a stretched exponential decay in the 0≤α< 1 case, while it can take a power law with exponential truncation in the special α=β=1 case. Moreover, n_k may have a U-type structure if α> β.     

Instantons on the Quantum 4-pheres S4q

We introduce noncommutative algebras A _q of quantum 4-spheres S ⁴ _q , with q∈ℝ, defined via a suspension of the quantum group SU _q (2), and a quantum instanton bundle described by a selfadjoint idempotent e∈ Mat₄(A _q ), e ²=e=e ^*. Contrary to what happens for the classical case or for the noncommutative instanton constructed in [8], the first Chern–Connes class ch ₁(e) does not vanish thus signaling a dimension drop. The second Chern–Connes class ch ₂(e) does not vanish as well and the couple (ch ₁(e), ch ₂(e) defines a cycle in the (b,B) bicomplex of cyclic homology. Received: 12 December 2000 / Accepted: 10 March 2001     

Neutrino radiation by an electon in quantizing nuclear and strong magnetic fields

The probability and intensity of neutrino radiation of a hydrogen-like atom in the strong magnetic field B >> Z ²α² B ₀, α = e ² = 1/137, B ₀ = m ²/e = 4.41⋅10¹³ G are determined. The temperature dependence of the intensity of an atom ensemble is analyzed.     

The 2+-2+ transition of 879 keV in160Dy investigated by electron-gamma directional correlation

e-γ directional correlation measurements of 2⁺(879 keV)2⁺(87 keV)0⁺ cascade in¹⁶⁰Dy have been made and the magnitude of electric monopole to quadrapole mixing ratio for 879 keV transition was found to beq _k =?0.03(10) for λ=0 (λ-according to Hager-Saltzer definition).     

B→K*ℓ+ℓ- decay in soft-collinear effective theory

We study the rare B decay B→K^*ℓ⁺ℓ^- using soft-collinear effective theory (SCET). At leading power in 1/m_b, a factorization formula is obtained valid to all orders in α_s. For phenomenological application, we calculate the decay amplitude including order α_s corrections, and resum the logarithms by evolving the matching coefficients from the hard scale down to the scale . The branching ratio for B→K^*ℓ⁺ℓ^- is uncertain due to the imprecise knowledge of the soft form factors ζ_⊥(q²) and ζ_∥(q²). Constraining the soft form factor ζ_⊥(q²=0) from data on B→K^*γ yields ζ_⊥(q²=0)=0.32±0.02. Using this input, together with the light-cone sum rules to determine the q²-dependence of ζ_⊥(q²) and the other soft form factor ζ_∥(q²), we estimate the partially integrated branching ratio in the range 1 GeV²≤q²≤7 GeV² to be (2.92^+0.67 _-0.61)×10^-7. We discuss how to reduce the form factor related uncertainty by combining data on B→ρ(→ππ)ℓν_ℓ and B→K^*(→Kπ)ℓ⁺ℓ^-. The forward-backward asymmetry is less sensitive to the input parameters. In particular, for the zero-point of the forward-backward asymmetry in the standard model, we get q₀ ²=(4.07^+0.16 _-0.13) GeV². The scale dependence of q₀ ² is discussed in detail. PACS 13.25.Hw, 12.39.St, 12.38.Bx     

Lattice Dislocations in a 1-Dimensional Model

The spectral properties of the Schr?dinger operator T(t)=−d ²/dx ²+q(x,t) in L ²(ℝ) are studied, where the potential q is defined by q=p(x+t), x>0, and q=p(x), x<0; p is a 1-periodic potential and t∈ℝ is the dislocation parameter. For each t the absolutely continuous spectrum σ _ac (T(t))=σ _ac (T(0)) consists of intervals, which are separated by the gaps γ _n (T(t))=γ _n (T(0))=(α _n ⁻,α _n ⁺), n≥1. We prove: in each gap γ _n ≠?, n≥ 1 there exist two unique “states” (an eigenvalue and a resonance) λ _n ^±(t) of the dislocation operator, such that λ _n ^±(0)=α _n ^± and the point λ _n ^±(t) runs clockwise around the gap γ _n changing the energy sheet whenever it hits α _n ^±, making n/2 complete revolutions in unit time. On the first sheet λ _n ^±(t) is an eigenvalue and on the second sheet λ _n ^±(t) is a resonance. In general, these motions are not monotonic. There exists a unique state λ₀(t) in the basic gap γ₀(T(t))=γ₀(T(0))=(−∞ ,α₀ ⁺). The asymptotics of λ _n ^±(t) as n→∞ is determined. Received: 5 April 1999 / Accepted: 3 March 2000     

Propagator of the Lattice Domain Wall Fermion and the Staggered Fermion

We calculate the propagator of the domain wall fermion (DWF) of the RBC/UKQCD collaboration with 2 + 1 dynamical flavors of 16³ × 32 × 16 lattice in Coulomb gauge, by applying the conjugate gradient method. We find that the fluctuation of the propagator is small when the momenta are taken along the diagonal of the 4-dimensional lattice. Restricting momenta in this momentum region, which is called the cylinder cut, we compare the mass function and the running coupling of the quark-gluon coupling α _s,g1(q) with those of the staggered fermion of the MILC collaboration in Landau gauge. In the case of DWF, the ambiguity of the phase of the wave function is adjusted such that the overlap of the solution of the conjugate gradient method and the plane wave at the source becomes real. The quark-gluon coupling α _s,g1(q) of the DWF in the region q > 1.3 GeV agrees with ghost-gluon coupling α _s (q) that we measured by using the configuration of the MILC collaboration, i.e., enhancement by a factor (1 + c/q ²) with c ≃ 2.8 GeV² on the pQCD result. In the case of staggered fermion, in contrast to the ghost-gluon coupling α _s (q) in Landau gauge which showed infrared suppression, the quark-gluon coupling α _s,g1(q) in the infrared region increases monotonically as q→ 0. Above 2 GeV, the quark-gluon coupling α _s,g1(q) of staggered fermion calculated by naive crossing becomes smaller than that of DWF, probably due to the complex phase of the propagator which is not connected with the low energy physics of the fermion taste. An erratum to this article can be found at