Slow dynamics in glycerol: collective de gennes narrowing and independent angstrom motion

The slow dynamics of microscopic density correlations in supercooled glycerol was studied by time-domain interferometry using ⁵⁷Fe-nuclear resonant scattering gamma rays of synchrotron radiation. The dependence of the relaxation time at 250 K on the momentum transfer q is maximum near the first peak of the static structure factor S(q) at q ～ 15 nm ^?1. The q-dependent behavior of the relaxation time known as de Gennes narrowing was confirmed in glycerol. Conversely, de Gennes narrowing around the second and third peaks of S(q) at q ～ 26 nm ^?1 and 54 nm ^?1 was not detected. The q dependence of the relaxation time was found to follow a power-law equation with power-law index of 1.9(2) in the q region well above the first peak of S(q) up to ～ 60 nm ^?1, which corresponds to angstrom scale, within experimental error. This suggests that in the angstrom-scale dynamics of supercooled glycerol, independent motions dominate over collective motion.     

Some Families of the Incomplete H-Functions and the Incomplete $$\overline H $$ -Functions and Associated Integral Transforms and Operators of Fractional Calculus with Applications

Our present investigation is inspired by the recent interesting extensions (by Srivastava et al. [35]) of a pair of the Mellin–Barnes type contour integral representations of their incomplete generalized hypergeometric functions _p γ _q and _p Γ _q by means of the incomplete gamma functions γ(s, x) and Γ(s, x). Here, in this sequel, we introduce a family of the relatively more general incomplete H-functions γ _p,q ^m,n (z) and Γ _p,q ^m,n (z) as well as their such special cases as the incomplete Fox-Wright generalized hypergeometric functions _p Ψ _q ^(γ) [z] and _p Ψ _q ^(Γ) [z]. The main object of this paper is to study and investigate several interesting properties of these incomplete H-functions, including (for example) decomposition and reduction formulas, derivative formulas, various integral transforms, computational representations, and so on. We apply some substantially general Riemann–Liouville and Weyl type fractional integral operators to each of these incomplete H-functions. We indicate the easilyderivable extensions of the results presented here that hold for the corresponding incomplete \(\overline H \)-functions as well. Potential applications of many of these incomplete special functions involving (for example) probability theory are also indicated.     

Noncompact <Emphasis Type="Italic">u</Emphasis><Subscript>q</Subscript>(2, 1) quantum algebra: Discrete series of highest weight irreducible representations

The structure of unitary irreducible representations of the noncompact u_q(2, 1) quantum algebra that are related to a negative discrete series is examined. With the aid of projection operators for the su_q(2) subalgebra, a q analog of the Gelfand-Graev formulas is derived in the basis corresponding to the reduction u_q(2, 1) → su_q(2)×u(1). Projection operators for the su_q(1, 1) subalgebra are employed to study the same representations for the reduction u_q(2, 1) → u(1)×su_q(1, 1). The matrix elements of the generators of the u_q(2, 1) algebra are computed in this new basis. A general analytic expression for an element of the transformation brackets <U∣T>_q between the bases associated with the above two reductions (the elements of this matrix are referred to as q Weyl coefficients) is obtained for a general case where the deformation parameter q is not equal to a root of unity. It is shown explicitly that, apart from a phase, the q Weyl coefficients coincide with the q Racah coefficients for the su_q(2) quantum algebra.     

Fundamental Entangling Operators in Quantum Mechanics and Their Properties

For the first time, we introduce so-called fundamental entangling operators \(e^{iQ_{1} P_{2}}\) and \(e^{iP_{1} Q_{2} }\) for composing bipartite entangled states of continuum variables, where Q_i and P_i (i = 1, 2) are coordinate and momentum operator, respectively. We then analyze how these entangling operators naturally appear in the quantum image of classical quadratic coordinate transformation (q₁, q₂) → (Aq₁ + Bq₂, Cq₁ + Dq₂), where AD?BC = 1, which means even the basic coordinate transformation (Q₁, Q₂) → (AQ₁ + BQ₂, CQ₁ + DQ₂) involves entangling mechanism. We also analyse their Lie algebraic properties and use the integration technique within an ordered product of operators to show they are also one- and two- mode combinatorial squeezing operators.     

Feynman-Diagrammatic Description of the Asymptotics of the Time Evolution Operator in Quantum Mechanics

We describe the “Feynman diagram” approach to nonrelativistic quantum mechanics on \({\mathbb{R}^n}\), with magnetic and potential terms. In particular, for each classical path γ connecting points q ₀ and q ₁ in time t, we define a formal power series V _γ (t, q ₀, q ₁) in \({\hbar}\), given combinatorially by a sum of diagrams that each represent finite-dimensional convergent integrals. We prove that exp(V _γ ) satisfies Schrödinger’s equation, and explain in what sense the \({t \to 0}\) limit approaches the δ distribution. As such, our construction gives explicitly the full \({\hbar\to 0}\) asymptotics of the fundamental solution to Schrödinger’s equation in terms of solutions to the corresponding classical system. These results justify the heuristic expansion of Feynman’s path integral in diagrams.     

New forms of the Cauchy operator and some of their applications

In this paper, we first construct the Cauchy q-shift operator T(a, b;D _xy ) and the Cauchy q-difference operator L(a, b; θ _xy ). We then apply these operators in order to represent and investigate some new families of q-polynomials which are defined in this paper. We derive some q-identities such as generating functions, symmetry properties and Rogers-type formulas for these q-polynomials. We also give an application for the q-exponential operator R(bD _q ).     

Fermi Surface Topology in the Case of Spontaneously Broken Rotational Symmetry

The relation between the broken rotational symmetry of a system and the topology of its Fermi surface is studied for the two-dimensional system with the quasiparticle interaction f(p, p') having a sharp peak at |p ? p'| = q₀. It is shown that, in the case of attraction and q₀ = 2p_F the first instability manifesting itself with the growth of the interaction strength is the Pomeranchuk instability. This instability appearing in the L = 2 channel gives rise to a second order phase transition to a nematic phase. The Monte Carlo calculations demonstrate that this transition is followed by a sequence of the first and second order phase transitions corresponding to the changes in the symmetry and topology of the Fermi surface. In the case of repulsion and small values of q₀, the first transition is a topological transition to a state with the spontaneously broken rotational symmetry, namely, corresponding to the nucleation of L ? π(p_F/q₀ ? 1) small hole pockets at the distance p_F ? q₀ from the center and the deformation of the outer Fermi surface with the characteristic multipole number equal to L. At q₀ → 0, when the model under study transforms to the two-dimensional Nozières model, the multipole number characterizing the spontaneous deformation is L → ∞, whereas the infinitely folded Fermi curve acquires the Hausdorff dimension D = 2 which corresponds to the state with the fermion condensate.     

A model of classical thermodynamics based on the partition theory of integers,Earth gravitation,and semiclassical asymptotics. I

In the paper, a new construction of the theory of partitions of integers is proposed. The author defines entropy as the natural logarithm of the number of partitions of a number M into natural summands with repetitions allowed p(M) and repetitions forbidden q(M). The passage from ln p(M) to lnq(M) through the mesoscopic values M → 0 is studied. The topological transition from the mesoscopic lower levels of the Bohr–Kalckar construction to the macroscopic levels corresponding to the critical number of neutrons according to the consequence of Einstein’s inequality M ≤ c N _c , where c is determined for the particles of the given atomic nucleus. The role of quantum mechanics in establishing the new world outlook in physics is analyzed. It is pointed out that the main equations of thermodynamics in the volume “Statistical Physics” of the Landau–Lifshits treatise are obtained without appealing to the so-called “three main principles of thermodynamics”. It is also pointed out that Niels Bohr’s liquid model of the nucleus does not involve any interaction of particles in the form of attraction and is based on the presence of a common potential trough for all elements of the nucleus. The author constructs a new approach to thermodynamics, using quantum mechanics and the Earth’s gravitational attraction as a common potential trough.     

Evolution of surface morphology during the growth of amorphous and polycrystalline silicon films

The evolution of the surface morphology of LPCVD poly-Si films (deposition temperature 620°C), a-Si films (deposition temperature 550°C) and poly-Si films, obtained by the crystallization of a-Si is investigated in the thickness range 40–500 nm. It is found that upon an increase in the thickness from 40 to 500 nm, the surface roughness (parameters S _q , S _z , S _v ) is increased for poly-Si, while in the case of a-Si and poly-Si obtained by crystallization a-Si, on the contrary, decreases. The correlation length (S _al ) increases for all three types of silicon films. Poly-Si films, obtained by the crystallization of a-Si, as compared to LPCVD poly-Si films have a significantly lower surface roughness, respectively, S _q two times less at a thickness of 40 nm and sixteen times less at 500 nm. In contrast to thick films, thin a-Si films (at thicknesses of less than 40 nm) have a granular structure, which is especially pronounced at an average thickness of about 20 nm and there is a maximum on the dependence of the roughness S _q on the thickness.     

Inflation Driven by q-de Sitter

We propose a generalised de Sitter scale factor for the cosmology of early and late time universe, including single scalar field is called as inflaton. This form of scale factor has a free parameter q is called as nonextensivity parameter. When q = 1, the scale factor is de Sitter. This scale factor is an intermediate form between power-law and de Sitter. We study cosmology of such families. We show that both kinds of dark components, dark energy and dark matter simultaneously are described by this family of solutions. As a motivated idea, we investigate inflation in the framework of q-de Sitter. We consider three types of scenarios for inflation. In a single inflation scenario, we observe that, inflation ended without any specific ending inflation ?_end, the spectral index and the associated running of the spectral index are n_s ? 1 ～ ?2??, α_s ≡ 0. To end the inflation: we should have \(q=\frac {3}{4}\). We deduce that the inflation ends when the evolution of the scale factor is a(t) = e_3/4(t). With this scale factor there is no need to specify ?_end. As an alternative to have inflation with ending point, We will study q-inflation model in the context of warm inflation. We propose two forms of damping term Γ. In the first case when Γ = Γ₀, we show the scale invariant spectrum, (Harrison-Zeldovich spectrum, i.e. n_s = 1) may be approximately presented by (\(q=\frac {9}{10},~~N=70\)). Also there is a range of values of R and n_s which is compatible with the BICEP2 data where \(q=\frac {9}{10}\). In case Γ = Γ₁V(?), it is observed that small values of a number of e-folds are assured for small values of q parameter. Also in this case, the scale-invariant spectrum may be represented by \((q,N) = (\frac {9}{10},70)\). For \(q=\frac {9}{10}\) a range of values of R and n_s is compatible with the BICEP2 data. Consequently, the proposal of q-de Sitter is consistent with observational data. We observe that the non-extensivity parameter q plays a significant role in inflationary scenario.     

Models of spin structures in Sr<Subscript>2</Subscript>RuO<Subscript>4</Subscript>

The mean-field method is used to calculate the bands, Fermi surfaces, and spin susceptibilities of a three-band model of the RuO₄ plane of Sr₂RuO₄ rutinate for states with different spin structures. In particular, the spiral state is studied with the “incommensurate” vector Q=2π(1/3, 1/3) corresponding to the nesting of bands with the population n=4. This state proves to be the lowest with respect to energy among other (paramagnetic, ferromagnetic, antiferromagnetic, and periodic) solutions. In the spiral state, in addition to the main α, β, and γ sheets of the Fermi surface, shadow Fermi boundaries along the Γ(0, 0)-M(π, 0) line (previously observed in the ARPES experiments) are revealed and explained. This may change the interpretation of the data on dispersionless peaks in photoemission, previously ascribed to surface states. The spin susceptibilities of the spiral state exhibit peaks in the dependence Im?(q, ω) at q=Q in accordance with the observed magnetic peak in neutron scattering. The hypothesis of the presence of spin structures with q=Q in the normal state of Sr₂RuO₄ and the methods of checking this hypothesis are discussed.     

Asymptotic Behavior of a Network of Oscillators Coupled to Thermostats of Finite Energy

We study the asymptotic behavior of a finite network of oscillators (harmonic or anharmonic) coupled to a number of deterministic Lagrangian thermostats of finite energy. In particular, we consider a chain of oscillators interacting with two thermostats situated at the boundary of the chain. Under appropriate assumptions, we prove that the vector (p, q) of moments and coordinates of the oscillators in the network satisfies (p, q)(t) → (0, q _c ) as t → ∞, where q _c is a critical point of some effective potential, so that the oscillators just stop. Moreover, we argue that the energy transport in the system stops as well without reaching thermal equilibrium. This result is in contrast to the situation when the energies of the thermostats are infinite, studied for a similar system in [14] and subsequent works, where the convergence to a nontrivial limiting regime was established.The proof is based on a method developed in [22], where it was observed that the thermostats produce some effective dissipation despite the Lagrangian nature of the system.     

On the nature of the liquid-to-glass transition equation

Within the model of delocalized atoms, it is shown that the parameter δT_g, which enters the glasstransition equation qτ_g = δT_g and characterizes the temperature interval in which the structure of a liquid is frozen, is determined by the fluctuation volume fraction \({f_g} = {\left( {{{\Delta {V_e}} \mathord{\left/ {\vphantom {{\Delta {V_e}} V}} \right. \kern-\nulldelimiterspace} V}} \right)_{T = {T_g}}}\) frozen at the glass-transition temperature T_g and the temperature T_g itself. The parameter δT_g is estimated by data on f_g and T_g. The results obtained are in agreement with the values of δT_g calculated by the Williams–Landel–Ferry (WLF) equation, as well as with the product qτ_g—the left-hand side of the glass-transition equation (q is the cooling rate of the melt, and τ_g is the structural relaxation time at the glass-transition temperature). Glasses of the same class with f_g ≈ const exhibit a linear correlation between δT_g and T_g. It is established that the currently used methods of Bartenev and Nemilov for calculating δT_g yield overestimated values, which is associated with the assumption, made during deriving the calculation formulas, that the activation energy of the glass-transition process is constant. A generalized Bartenev equation is derived for the dependence of the glass-transition temperature on the cooling rate of the melt with regard to the temperature dependence of the activation energy of the glasstransition process. A modified version of the kinetic glass-transition criterion is proposed. A conception is developed that the fluctuation volume fraction f = ΔV_e/V can be interpreted as an internal structural parameter analogous to the parameter ξ in the Mandelstam–Leontovich theory, and a conjecture is put forward that the delocalization of an active atom—its critical displacement from the equilibrium position—can be considered as one of possible variants of excitation of a particle in the Vol’kenshtein–Ptitsyn theory. The experimental data used in the study refer to a constant cooling rate of q = 0.05 K/s (3 K/min).     

Temperature range of the liquid–glass transition

It has been shown that the currently used method for calculating the temperature range of δT_g in the glass transition equation qτ_g = δT_g as the difference δT_g = (T₁₂–T₁₃) results in overestimated values, which is explained by the assumption of a constant activation energy of glass transition in deriving the calculation equation (T₁₂ and T₁₃ are the temperatures corresponding to the logarithmic viscosity values of logη = 12 and logη = 13). The methods for the evaluation of δT_g using the Williams–Landel–Ferry equation and the model of delocalized atoms are considered, the results of which are in satisfactory agreement with the product qτ_g (q is the cooling rate of the melt and τ_g is the structural relaxation time at the glass transition temperature). The calculation of τ_g for inorganic glasses and amorphous organic polymers is proposed.     

Photoelectron Energy Loss in Al(002) Revisited: Retrieval of the Single Plasmon Loss Energy Distribution by a Fourier Transform Method

A Fourier transform (FT) algorithm is proposed to retrieve the energy loss function (ELF) of solid surfaces from experimental X-ray photoelectron spectra. The intensity measured over a broad energy range towards lower kinetic energies results from convolution of four spectral distributions: photoemission line shape, multiple plasmon loss probability, X-ray source line structure and Gaussian broadening of the photoelectron analyzer. The FT of the measured XPS spectrum, including the zero-loss peak and all inelastic scattering mechanisms, being a mathematical function of the respective FT of X-ray source, photoemission line shape, multiple plasmon loss function, and Gaussian broadening of the photoelectron analyzer, the proposed algorithm gives straightforward access to the bulk ELF and effective dielectric function of the solid, assuming identical ELF for intrinsic and extrinsic plasmon excitations. This method is applied to aluminum single crystal Al(002) where the photoemission line shape has been computed accurately beyond the Doniach–Sunjic approximation using the Mahan–Wertheim–Citrin approach which takes into account the density of states near the Fermi level; the only adjustable parameters are the singularity index and the broadening energy Г (inverse hole lifetime). After correction for surface plasmon excitations, the q-averaged bulk loss function, <Im[??1 / ε(E, q)]> _q , of Al(002) differs from the optical value Im[??1 / ε(E, q?=?0)] and is well described by the Lindhard–Mermin dispersion relation. A quality criterion of the inversion algorithm is given by the capability of observing weak interband transitions close to the zero-loss peak, namely at 0.65 and 1.65 eV in ε(E, q) as found in optical spectra and ab initio calculations of aluminum.     

A first order Tsallis theory

We investigate first-order approximations to both (i) Tsallis’ entropy S _q and (ii) the S _q -MaxEnt solution (called q-exponential functions e _q ). We use an approximation/expansion for q very close to unity. It is shown that the functions arising from the procedure (ii) are the MaxEnt solutions to the entropy emerging from (i). Our present treatment is motivated by the fact it is FREE of the poles that, for classic quadratic Hamiltonians, appear in Tsallis’ approach, as demonstrated in [A. Plastimo, M.C. Rocca, Europhys. Lett. 104, 60003 (2013)]. Additionally, we show that our treatment is compatible with extant date on the ozone layer.     

Spin fluctuations in the stacked-triangular antiferromagnet YMnO<Subscript>3</Subscript>

The spectrum of spin fluctuations in the stacked-triangular antiferromagnet YMnO₃ was studied above the Néel temperature using both unpolarized and polarized inelastic neutron scattering. We find an in-plane and an out-of-plane excitation. The in-plane mode has two components just above T _N : a resolution-limited central peak and a Debye-like contribution. The quasi-elastic fluctuations have a line width that increases with q as Dq ^z and the dynamical exponent z = 2.3. The out-of-plane fluctuations have a gap at the magnetic zone center and do not show any appreciable q dependence at small wave vectors.     

Ableitung der Quantenregeln auf nicht-quantenmäßiger Grundlage

The general law of probability interference is only the first step to quantum mechanics; it does not yet contain wave-like periodic traits. The latter enter the theory only through additional dynamical rules for the connection between coordinates and momenta, typified by the wave functionψ(p, q)=exp(2iπqp/h). This quantum-dynamical rule is shown to be derivable from a non-quantal, non-periodic requirement ofinvariance of certain quantities with respect to displacement of the zero point inq- andp-space.     

Imitating accelerated expansion of the Universe by matter inhomogeneities: corrections of some misunderstandings

A number of misunderstandings about modeling the apparent accelerated expansion of the Universe and about the ‘weak singularity’ are clarified: (1) Of the five definitions of the deceleration parameter given by Hirata and Seljak (HS), only q ₁ is a correct invariant measure of acceleration/deceleration of expansion. The q ₃ and q ₄ are unrelated to acceleration in an inhomogeneous model. (2) The averaging over directions involved in the definition of q ₄ does not correspond to what is done in observational astronomy. (3) HS’s equation (38) connecting q ₄ to the flow invariants gives self-contradictory results when applied at the centre of symmetry of the Lemaître–Tolman (L–T) model. The intermediate equation (31) that determines q _3' is correct, but approximate, so it cannot be used for determining the sign of the deceleration parameter. Even so, at the centre of symmetry of the L–T model, it puts no limitation on the sign of q _3'(0). (4) The ‘weak singularity’ of Vanderveld et al. is a conical profile of mass density at the centre—a perfectly acceptable configuration. (5) The so-called ‘critical point’ in the equations of the ‘inverse problem’ for a central observer in an L–T model is a manifestation of the apparent horizon (AH)—a common property of the past light cones in zero-lambda L–T models, perfectly manageable if the equations are correctly integrated.     

Quintessence Reissner Nordström Anti de Sitter Black Holes and Joule Thomson Effect

In this work we investigate corrections of the quintessence regime of the dark energy on the Joule-Thomson (JT) effect of the Reissner Nordström anti de Sitter (RNAdS) black hole. The quintessence dark energy has equation of state as p _q = ωρ _q in which \(-1<\omega <-\frac {1}{3}\). Our calculations are restricted to ansatz: ω = ??1 (the cosmological constant regime) and \(\omega =-\frac {2}{3}\) (quintessence dark energy). To study the JT expansion of the AdS gas under the constant black hole mass, we calculate inversion temperature T _i of the quintessence RNAdS black hole where its cooling phase is changed to heating phase at a particular (inverse) pressure P _i . Position of the inverse point {T _i , P _i } is determined by crossing the inverse curves with the corresponding Gibbons-Hawking temperature on the T-P plan. We determine position of the inverse point versus different numerical values of the mass M and the charge Q of the quintessence AdS RN black hole. The cooling-heating phase transition (JT effect) is happened for M > Q in which the causal singularity is still covered by the horizon. Our calculations show sensitivity of the inverse point {T _i , P _i } position on the T-P plan to existence of the quintessence dark energy just for large numerical values of the AdS RN black holes charge Q. In other words the quintessence dark energy dose not affect on position of the inverse point when the AdS RN black hole takes on small charges.