The big bang as a result of the first-order phase transition driven by a change of the scalar curvature in an expanding early Universe: The “hyperinflation” scenario

We suggest that the Big Bang could be a result of the first-order phase transition driven by a change in the scalar curvature of the 4D spacetime in an expanding cold Universe filled with a nonlinear scalar field φ and neutral matter with an equation of state p = νε (where p and ε are the pressure and energy density of the matter, respectively). We consider the Lagrangian of a scalar field with nonlinearity φ⁴ in a curved spacetime that, along with the term–ξR|φ|² quadratic in φ (where ξ is the interaction constant between the scalar and gravitational fields and R is the scalar curvature), contains the term ξRφ₀(φ + φ⁺) linear in φ, where φ₀ is the vacuum mean of the scalar field amplitude. As a consequence, the condition for the existence of extrema of the scalar-field potential energy is reduced to an equation cubic in φ. Provided that ν > 1/3, the scalar curvature R = [κ(3ν–1)ε–4Λ] (where κ and Λ are Einstein’s gravitational and cosmological constants, respectively) decreases with decreasing ε as the Universe expands, and a first-order phase transition in variable “external field” parameter proportional to R occurs at some critical value R _c < 0. Under certain conditions, the critical radius of the early Universe at the point of the first-order phase transition can reach an arbitrary large value, so that this scenario of unrestricted “inflation” of the Universe may be called “hyperinflation.” After the passage through the phase-transition point, the scalar-field potential energy should be rapidly released, which must lead to strong heating of the Universe, playing the role of the Big Bang.     

Atomic tunneling states with dissipation in glasses: temperature-dependent two-level systems

By taking account of the influence of dissipation on atomic tunneling states in glasses, we introduce a density of states of two-level systems which is non-linearly temperature dependent. Based on this model, we can explain the “excess T³” anomaly in the specific heat and the “plateau” in the thermal conductivity of glasses.     

Analysis of micropatch surface structure from thermionic compensation

The translation of a log A_R versus φ_R display of Richardson data into a sequence of Gaussian distributions of true work function φ reveals dynamic aspects of micropatch structure for the thermionic emitter. A processing procedure which adds emission sites without modifying the topography of the gross patch structure associates with a set of Gaussians centered on a common area-averaged work function φ. This is typified by Mo-on-W and Mo-on-Re. Micropatches which build up at surface defects into clusters of the absorbate have a sequence of Gaussian distributions with shifting φ. Thorium-on-tungsten is in this latter class.     

Particle diffraction by a thin rigid crystal lattice: A formal approach

The diffraction process of a particle by a thin rigid crystal is considered. An integral equation is derived for the particle wave function φ which is quite suitable to obtain physical and mathematical properties. A class of potentials is presented for which the integral equation can be solved by means of the Fredholm theory. The convergence of the Born series for φ is studied, as well as the existence and convergence properties of the transmission and reflection amplitudes T^±. Results are given about φ and T^±: (i) at high energies, (ii) at those special energies such that new diffracted beams appear, and (iii) at glancing incidence on the crystal. Analyticity properties of T^± as functions of the energy are derived and analytic representations for them are presented. The diffraction process when the particle is being simultaneously accelerated by a uniform electric field is also considered. Finally, the generalization to the case of an imperfect thin crystal is treated.     

Adsorption of lead on low-index planes of tungsten

Using probe-hole field emission microscopy the effect of adsorbed lead on the work function of the 100 and 110 planes of tungsten hasbeen studied and compared with the findings of Bauer et al. who studied the same system using LEED/Auger techniques. The effect of lead on the average work function $\text{}\text{?}$gf and that of (211) is also reported. Sub-monolayer lead increases φ(211) and this is ascribed to formation of a lead-tungsten dipole, the lead being negatively charged, with dipole moment 0.035 × 10^?30 C-m and polarizability 2.0 ų. On (110) lead reduces φ and behaves as a dipole with positively charged lead of moment 0.15 × 10^?30 C-m and polarizability 2.5 ų. φ(100) is also observed to decrease at low coverages equilibrated at low temperatures. This contrasts with Bauer's findings but is considered to result from failure of the Fowler—Nordheim model. With increasing lead coverage on all planes φ(hkl) tends to a constant value φ_sat. By comparison with Bauer et al. we can identify φ_sat on (110) as a compressed monolayer of lead. Likewise φ_sat produced by low temperature (～450 K) spreading on (100) is also associated with a compressed (1 × 1) structure. The lower value of φ(100) produced at higher temperatures (～850 K) is identified with the microfacetted surface observed by Bauer et al. Lead is observed to be absent from (110) when mean adatom densities as high as 8 × 10¹⁴ atoms cm^?2 are thermally equilibrated, and this is shown to result from the relatively low binding energy of lead on (110). The general agreement between the present findings and those of Bauer lends confidence to the belief that both techniques can detect the same behaviour despite the very large (10¹⁰) difference in the size of the area examined.     

The energy tensor of matter in the projectve theory of relativity

In the projective theory of relativity the 5-dimensional field equation \(_{\mu \nu } \) and the resulting equation of motion Tμυ_;μ = 0 are investigated. There Tμυ stands for the 5-dimensional tensor of macroscopic matter. The 4-dimensional field equations and equation of motion obtained by projection are a generalization of Einstein's theory of general relativity and Maxwell's electrodynamics, involving a scalar field φ.They contain a single constant φ₀.The weak field approximation is investigated for the case of an ideal fluid and leads to Newton's mechanics, including Newton's gravitational law, and to Maxwell's electrodynamics. For the constant φ₀ one obtains the approximate value φ₀c⁴/γ_N with Newton's gravitational constant γ_N.For homogeneous and isotropic cosmological models consisting of matter only the general solution for the radius K of curvature is given. This solution is independent of the equation of state of matter For a pure dust universe the general solution for the scalar field φ is given. For a closed universe a power law φ ?K^?1 is valid which leads to Mach's principle. The calculation of the age of a closed universe yields over 7×10⁹y,if one uses mean values of the present cosmological data.     

Gravitating global monopoles in extra dimensions and the braneworld concept

Multidimensional configurations with a Minkowski external spacetime and a spherically symmetric global monopole in extra dimensions are discussed in the context of the braneworld concept. The monopole is formed with a hedgehoglike set of scalar fields φⁱ with a symmetry-breaking potential V depending on the magnitude φ² = φⁱφⁱ. All possible kinds of globally regular configurations are singled out without specifying the shape of V(φ). These variants are governed by the maximum value φ_m of the scalar field, characterizing the energy scale of symmetry breaking. If φ_m < φ_cr (where φ_cr is a critical value of φ related to the multidimensional Planck scale), the monopole reaches infinite radii, whereas in the “strong field regime,” when φ_m ≥ φ_cr, the monopole may end with a finite-radius cylinder or have two regular centers. The warp factors of monopoles with both infinite and finite radii may either exponentially grow or tend to finite constant values far from the center. All such configurations are shown to be able to trap test scalar matter, in striking contrast to RS2 type five-dimensional models. The monopole structures obtained analytically are also found numerically for the Mexican hat potential with an additional parameter acting as a cosmological constant.     

New nuclear three-body clusters φNN

Binding energies of three-body systems of the type φ + 2N are estimated. Due to the strong attraction between φ-meson and nucleon, suggested in different approaches, bound states can appear in systems like φ + np (singlet and triplet), φ + nn and φ + pp. This indicates the principal possibility of the formation of new nuclear clusters.     

From phenomenological thermodynamics to the canonical ensemble

Given the generic canonical probability in phase φ=exp[β(Ψ-H)], contact is traditionally made with phenomenological thermodynamics by comparing the identity δ〈φ〉=0 with the relationTδS=δU+δW, δ indicating an arbitrary infinitesimal variation of the thermodynamic coordinates and angular brackets ensemble means. This paper is concerned with the inverse problem of finding both the generic form of the phase functionw such thatS=〈w〉 and the explicit form φ=αexp[(F-H)/kT] of the canonical distribution on the basis of the requirement that the consequences of the phenomenological laws must be safeguarded, i.e., the relations between the quantities which are their concomitants must also be satisfied by their statistical representatives. Given the generic statistical formalism and specifically thatU=〈H〉, δW=?〈δH〉, the problem is soluble, granted the following generic assumption: “the statistical representative of the entropy is the ensemble mean of a function which depends upon the phase through φ alone.”     

The transformation between the mode representation and the generalized ray representation of a sound field

The “mode generation function” φ(ν), and the “generalized ray generation function” B(u) are introduced for a stratified wave-guide. It is proved that φ(ν) and B(u) are a Fourier transform pair when lateral waves do not appear. Mode representation and the “generalized ray” representation satisfy the Poisson summation formula. Furthermore, the “local conversion” relation between the mode and the ray is considered from the point of view of “member selection”. It is found that “local conversion” is just the result of using the stationary phase approximation in the Fourier transformation of φ(ν) and B(u). This is the same result as obtained by “selective processing” in which the constructive interference between adjoining members (of the ray or mode families) is used.     

Fluctuations and a rigorous uncertainty relation of trigonometric operators of the phase and the number of photons of an electromagnetic field for general quantum superpositions of coherent states

The quantum-statistical properties of states of an electromagnetic field of general superpositions of coherent states of the form of N _α,β(α?+e ^iξ β? are investigated. Formulas for the fluctuations (variances) of Hermitian trigonometric phase field operators ? ≡ côs φ, ? ≡ sîn φ (the so-called “Susskind–Glogower operators”) are found. Expressions for the rigorous uncertainty relations (Cauchy inequalities) for operators of the number of photons and trigonometric phase operators, as well as for operators ? and ?, are found and analyzed. The states of amplitude \({N_{\alpha ,\beta }}\left( {\left| {{{\sqrt {ne} }^{i\varphi }}\rangle + {e^{i\xi }}\left| {{{\sqrt {{n_\beta }e} }^{i\varphi }}\rangle } \right.} \right.} \right)\), φ = φ_α = φ_β, and phase \({N_{\alpha ,\beta }}\left( {\left| {{{\sqrt {ne} }^{i{\varphi _\alpha }}}\rangle + {e^{i\xi }}\left| {{{\sqrt {ne} }^{i{\varphi _\beta }}}\rangle } \right.} \right.} \right)\), n = n _α = n _β, superpositions of coherent states are considered separately. The types of quantum superpositions of meso- and macroscales (n _α, n _β » 1) are found for which the sines and/or cosines of the phase of the field can be measured accurately, since, under certain conditions, the quantum fluctuations of these quantities are close to zero. A simultaneous accurate measurement of cosφ and sinφ is possible for amplitude superpositions, while an accurate measurement of one of these trigonometric phase functions is possible in the case of certain phase superpositions. Amplitude superpositions of coherent states with a vacuum state are quantum states of the field with a “maximum” level of the quantum uncertainty both in the case of a mesoscopic scale and in the case of a macroscopic scale of the field with an average number of photons n _α/β ≈ 0, n _β/α » 1.     

Is there a quantization condition for the classical problem of charge and pole?

In elementary derivations of the quantization of azimuthal angular momentum the eigenfunction is determined to be exp(im φ), which is “oversensitive” to the rotation φ → φ+2π, unlessm is an integer. In a recent paper Kerner examined the classical system of charge and magnetic pole, and expressed Π, a vector constant of motion for the system, in terms of a physical angle ψ, to deduce a remarkable paradox. Kerner pointed out that Π(ψ) is “oversensitive” to ψ → ψ+2π unless a certain charge quantization condition is met. Our explicandum of this paradox highlights the distinction between coordinates in classical and quantum physics. It is shown why the single-valuedness requirement on Π(ψ) is devoid of physical significance. We are finally led to examine the classical analog of the quantum mechanical argument that demonstrates the quantization of magnetic charge, to show that there is “no hope” of a classical quantization condition.     

Continuous sample paths in quantum field theory

Nelson's free Markoff field on ? ^l+1 is a natural generalization of the Ornstein-Uhlenbeck process on ?¹, mapping a class of distributions φ(x,t) on ? ^l ×?¹ to mean zero Gaussian random variables φ with covariance given by the inner product \(\left( {\left( {m^2 - \Delta - \frac{{\partial ^2 }}{{\partial t^2 }}} \right)^{ - 1} \cdot , \cdot } \right)_2 \) . The random variables φ can be considered functions φ〈q〉=∝ φ(x,t)q(x,t)d x dt on a space of functionsq(x,t). In the O.U. case,l=0, the classical Wiener theorem asserts that the underlying measure space can be taken as the space of continuous pathst →q(t). We find analogues of this, in the casesl>0, which assert that the underlying measure space of the random variables φ which have support in a bounded region of ? ^l+1 can be taken as a space of continuous pathst →q(·,t) taking values in certain Soboleff spaces.     

Temperature dependence of fluorescence quantum yields of some side-substituted anthracene sulphonates

Of the four anthracene sulphonates (Na-salt), anthracene-1-sulphonate (1-AS), anthracene-2-sulphonate (2-AS) and anthracene-1, 5-disulphonate (1, 5-AS) show temperature dependence of φ_f, whereas for anthracene-1, 8-disulphonate (1, 8-AS) φ_f is independent of temperature. E_a for 1-AS, 2-AS and 1, 5-AS are 939 cm^?1, 1144 cm^?1 and 445 cm^?1, respectively. A low energy T_nπ¹ level supplied by ?SO^?₃ group could be responsible for efficient ISC in 1, 8-AS of symmetry C_2v. The possibility of tunnelling due to molecular distortion i.e. “geometry factor” cannot be ruled out also.     

Phase of φω interference due to unitarity corrections to the amplitude of φω mixing

The phase of φω interference in the reaction e ⁺ e ^? → π⁺π^?π⁰ near the energy of the φ(1020) peak is calculated within an approach that is virtually independent of the model for φω mixing. A comparison with the phase measured recently (with a poor precision) shows that the deviation of the measured result from the expected value of 180° is associated largely with the effect of the right shoulder of the ω(782) peak in the region of the φ(1020) peak. The ω width at the energy equal to the φ mass is within the interval 120–200 MeV. The effect of the φω-state-induced unitarity corrections to the φ and ω coupling constants on the phase of ρπ interference is considered in detail.     

The nature of the adsorption bond between graphite islands and iridium surface

To reveal the nature of adsorption bonds between two-dimensional graphite islands and iridium (111) and (100) faces, a study has been made of the adsorption of potassium and cesium atoms on the surface of these systems, using thermal desorption and Auger electron spectroscopy, as well as surface ionization and thermionic emission techniques. The graphite islands are shown to be weakly bound to the iridium substrate by Van der Waals forces. The unsaturated valence bonds at the periphery of the graphite islands are “lowered down” on to the metal. The recess between the graphite layer and the metal is filled by adsorbing particles through defects in the graphite layer. The atoms can penetrate into the recess in two ways: at T > 1000 K directly from the flux incident on the surface, and at T < 1000 K also by migration from the graphite island surface. The adsorption capacity of this state is ～ (2?3) × 10¹⁴cm^-2. Thermal destruction of the islands at T > 1900 K liberates the potassium and cesium atoms from under the graphite islands. Our study suggests that the reason for the “raised” position of the islands lies in the valence bonds of the graphite layer being saturated, the valence bonds of the metal and its crystallographic orientation being less significant. Therefore one may expect the graphite layer to be raised also above other metals as well. The filling by cesium of the recess between the graphite layer and iridium and of the adsorption phase on the graphite surface, does not change the general “graphitic” shape of the carbon Auger peak. This cesium results, however, in a pronounced splitting of the negative spike on the carbon peak (which provides information on its location relative to the graphite layer) indicating the appearance in the valence band of graphite near the Fermi level of two narrow (～ 2?3 eV) regions with an enhanced density of states originating from the presence of the alkali metal.     

Coefficient of ultrasound transmission from liquid helium to aluminum in the intermediate state at <Emphasis Type="Italic">T</Emphasis> ≈ 0.1 K

The coefficient α(θ) of ultrasound transmission from liquid ⁴He to an aluminum single crystal in intermediate, superconducting, and normal states at a temperature T ≈ 0.1 K is measured as a function of the polar angle θ at the azimuthal angle φ = 0. The experimental technique is based on the measurement of the Kapitza temperature jump at the interface between two media. The dependences of the transmission coefficient for the Rayleigh modes on the sound frequency (in the range 13–194 MHz) and the magnetic field strength are determined. It is demonstrated that the integrated transmission coefficient of the aluminum single crystal in the intermediate state at an angle θ_R larger than the critical value increases with an increase in the magnetic field strength. The integrals of the transmission coefficient in magnetic fields close to the field H _c are independent of the frequency. In the vicinity of H = 0, the transmission coefficient at ν > 39 MHz increases only slightly with increasing frequency. At the lowest frequencies, the transmission coefficient increases anomalously as the frequency decreases. The experimental data are compared with the results obtained in the framework of the Andreev theory. Numerical calculations are performed and the dependences α(θ, φ) for bulk modes in the range corresponding to angles smaller than the critical value are constructed for the three principal planes of the crystal, i.e., the (001), (011), and (111) planes. The dependence α(θ) is obtained for the azimuthal angle φ = 0. The width of the Rayleigh peak is estimated.     

Magnetic states of the surface and bulk of ferrites near a phase transition at the Curie temperature

Investigations of the magnetic state of a surface layer ~200 nm thick and of the bulk in macroscopic ferrite crystals of the type Ba-M (BaFe₁₂O₁₉) are performed in the phase transition region around the Curie temperature (T _c). The method of simultaneous gamma, x-ray, and electron Mössbauer spectroscopy, which made it possible to compare directly the phase states of the surface and bulk of the sample, is used for the measurements. It is observed experimentally that in BaFe₁₂O₁₉ the transition of a surface layer ~200 nm thick to the paramagnetic state occurs at temperatures below T _c. It is established that the transition temperature T _c(L) of a thin layer localized at depth L from the surface of the crystal increases with distance from the surface and reaches the value T _c at the lower boundary of the “critical” surface layer. Therefore, near T _c a nonuniform state in which the crystal is magnetically ordered in the bulk but disordered at the surface is observed. A phase diagram of the states of the surface and of the bulk of macroscopic magnets near the Curie (or Néel) point is proposed on the basis of all the experimental results obtained in the present work as well as previously published results.     

Two-dimensional and layered structures in the discrete φ4 model

The properties of phase transitions in two-dimensional and layered systems are investigated on the basis of a discrete φ⁴ model by numerical and analytical methods. The only parameter a of the discrete φ⁴ model determines the behavior of the system and makes it possible to investigate phase transitions ranging from transitions of the displacement type (a → +0) to order-disorder type (a → +∞). The behavior of a two-dimensional system is investigated in a wide range of values of the parameter a. The temperature dependences of the squared order parameter η²(T) and the phase transition temperature T _c as a function of the thickness N of the system are obtained for three characteristic values of the parameter a using the Monte Carlo method. The properties of phase transitions in the discrete φ⁴ model are investigated on the basis of the mean-field approximation and the independent-mode approximation. The results obtained in the numerical experiments are compared with the analytical approximations. It is shown that the mean-field approximation qualitatively describes the behavior of the phase-transition temperature T _c as a function of the thickness N of the system for a wide range of values of the parameter a, and the independent-mode approximation describes quantitatively, to within 5%, the results of the numerical simulation for small values of a.     

Adsorption of gold on low index planes of rhenium

On atomically rough areas of a thermally cleaned rhenium field emitter, adsorbed gold behaves like it does on tungsten. The average work function $\text{}\text{?}$gf increases at low average gold coverage $\text{}\text{?}$gq due to formation of gold-rhenium dipoles, and at high coverage a structural transformation in the gold layer leads to a $\text{}\text{?}$gq-independent work function. Broadly similar behaviour is found for gold on the low-index planes of tungsten, but on low-index rhenium planes gold behaves rather differently. When thermally cleaned at > 2200 K and annealed below 800 K, the work function, φ(clean), of (101&#x0304;1&#x0304;) takes one of two values 5.25 ± 0.04 eV, and 5.36 ± 0.04 eV, which are tentatively attributed to the two possible structures of this plane. Similar behaviour is expected and observed for (101&#x0304;0),but the values taken by φ(clean) are not well defined. Both forms of (101&#x0304;1&#x0304;) are thought to undergo reconstruction above 800 K forming a single structure with φ(clean) = 5.55 ± 0.03 eV. (112&#x0304;0) and (112&#x0304;2&#x0304;) each have only one possible structure, and in keeping with this, φ(clean) has a single well-defined value for each plane. The flatness of (101&#x0304;1&#x0304;) and (101&#x0304;0) leads to field reduction at their centres which produces an increase in their measured work functions by up to 10%. The initial increase in φ produced by gold condensed at 78 K and spread at low equilibration temperatures T_s on (112&#x0304;2&#x0304;), (101&#x0304;1&#x0304;) and (112&#x0304;0) is attributed to gold-rhenium dipoles, which, on the latter two planes approximate to the Topping model, giving dipoles characterised by μ₀(1011) = 0.1 × 10^?30 C-m with α = 10 ų and μ₀(112&#x0304;0) = 0.32 × 10^?30 C-m with α = 22 ų, where μ₀ is the zero-coverage dipole moment and α its polarizability. Failure of the Topping model on (112&#x0304;2&#x0304;) is attributed to its atomically rough structure. No dipole effect is seen on (101&#x0304;0). Energy spectroscopy of electrons field emitted at (202&#x0304;1&#x0304;) and (101&#x0304;1&#x0304;) demonstrates the non-free character of electrons in rhenium, while the small effect of adsorbed gold strengthens the belief that gold is bound through a greatly broadened 6s level centred 5.6 eV below the Fermi level and the dipolar nature of the bond supports this model. At higher values of T_s and $\text{}\text{?}$gq gold appears to form states which are well-characterised by a coverage-independent work function. (101&#x0304;0), (101&#x0304;1&#x0304;) and (112&#x0304;0) each form two such states, one in the range 2 < $\text{}\text{?}$gq < 4 (state 1), and the second at $\text{}\text{?}$gq > 4 (state 2). The atomic radii of gold and rhenium are thought to be sufficiently similar to allow the possibility that state 1 is a replication of the Re plane structure by gold. The high work function and thermal stability of state 2, taken together with the observed temperature dependence of the transformation of state 1 to state 2, encourages the belief that state 2 results from atomic rearrangement of state 1 into a close-packed Au(111) structure. State 2 also forms on (112&#x0304;2&#x0304;) and the absence of state 1 on this plane suggests some surface alloying at coverages below 4 $\text{}\text{?}$gq.