The influence of free quintessence on gravitational frequency shift and deflection of light with 4D momentum

On the basis of the 4D momentum, the influence of quintessence on the gravitational frequency shift and the deflection of light are examined in modified Schwarzschild space. We find that the frequency of a photon depends on the state parameter of the quintessence w _q: the frequency increases for −1<w _q<−1/3 and decreases for −1/3<w _q<0. Meanwhile, we adopt an integral power number a (a=3ω _q+2) to solve the orbital equation of photon. The photon’s potentials become higher with the decrease of ω _q. The behavior of the bending light sensitively depends on the state parameter ω _q. In particular, for the case of ω _q=−1, there is no influence on the deflection of light by quintessence. Furthermore, according to the H-masers of the GP-A redshift experiment and long-baseline interferometry, the constraints on the quintessence field in the solar system are presented here.     

Nonadiabatic effects in the phonon spectra of superconductors

The nonadiabatic corrections to the self-energy part Σ_s(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and Σ_s(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σ_s(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σ_s(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional line in the phonon spectral function S(q, ω)≈−π ⁻¹ Im D _s (q, ω), where D _s (q, ω) is the phonon Green’s function, at temperatures T<T _c . Zh. éksp. Teor. Fiz. 115, 1799–1817 (May 1999)     

Optical fiber tip in front of a phase conjugator: focused light spot with inclusion of evanescent field contribution

 Within the framework of electric dipole approximation, the focused light spot produced by a tiny optical fiber tip in front of a phase conjugate mirror is investigated numerically. The fiber tip is the probe of a reflection scanning near field optical microscope and the incident light is guided through the fiber. Intensity distribution of local field is calculated in the half space where the fiber tip locates. Both homogeneous (q _‖≤ω/c ₀) and part of inhomogeneous (ω/c ₀<q _‖≤ωn/c ₀) fields are included in establishing a field propagator (Green’s function) which is employed to calculate the local field distribution. The local field forms at the tip position a diffraction light spot with a finite central value and a finite size, and when the tip-surface distance is sufficient small, the strength and the shape of the light spot become a function of the distance, which is due to the contribution of evanescent field. Fairly good agreements are found with the existing experimental reports. Received: 30 April 1996/Accepted: 19 August 1996     

Localization effects and dispersion of the dielectric response function in one-dimensional metals

We report the results of calculations and analysis concerning the dependence of the dielectric response function(, q) on frequency and wave numberq in one-dimensional conductors. The localization of electron states leads to unusually complicated dependences of(, q) on andq in low-frequency and long-wavelength regions, while the spatial and time dispersions become closely interwoven with each other. The effect of geometric resonance is discussed. It appears as quasiharmonical oscillations of complex susceptibility as function of andq, owing to the hopping nature of electron conductivity in a nonuniform electromagnetic field.     

Specific heat of the harmonic oscillator within generalized equilibrium statistics

Summary Within the generalized equilibrium statistics recently introduced by Tsallis (p _n ∝[1−β(q−-1) _εn ]^1/(q−)), we calculate the thermal dependence of the specific heat corresponding to a harmonic-oscillator-like spectrum, namely ε _n ω(n−α) (∀ω>0,n=0,1,2,...). The influences ofq and α are exhibited. Physically inaccessible and/or thermally frozen gaps are obtained in the low-temperature region, and, forq>1, oscillations are observed in the high-temperature region. The specific heat of the two-level system is also shown.     

q-quantum plane,ψ(q)-umbral calculus, and all that

It is known that one can formulateq-extended finite operator calculus with help of “quantumq-plane”q-commuting variablesA, B : AB − qBA ≡ [A, B]q=0. We shall recall this simple fact in its natural entourage which is the so-calledψ(q)-extension of Rota’s finite operator calculus. We aim to convince the audience that this is a natural and elementary method for formulation and treatment ofq-extended and possiblyR-extended orψ(q)-extended models for quantum-likeψ(q)-deformed oscillators. Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001.     

Many-body study of van der Walls interaction involving lithium and rare-gas atoms and its contribution to hyperfine shifts

Using linked cluster many-body perturbation theory, the frequency-dependent dipole polarizabilitiesa(ω) has been calculated for the lithium atom. The value ofa(ω) at the static limit (169.04a ₀ ³ ) matches well with other available theoretical values and experimental results. These values have been used to calculate the van der Waals constants for interactions of lithium, helium and neon atoms. The values of the van der Waals constants for dipole-dipole interaction in atomic units are −22.9, −44.8, −1465.8, 184950.0, 2011.8, 3896.5, 30.3, 59.0 and 115.1 for Li-He, Li-Ne, Li-Li, Li-Li-Li, Li-Li-He, Li-Li-Ne, Li-He-He, Li-He-Ne and Li-Ne-Ne interactions respectively. Obtaining the suitable response functions for lithium and helium atoms, the long range contribution to Δa(r)/a ₀ in the study of fractional frequency shift in hyperfine pressure and temperature shift measurements is obtained as −541 atomic units.     

Modeling Galactic Halos with Predominantly Quintessential Matter

This paper discusses a new model for galactic dark matter by combining an anisotropic pressure field corresponding to normal matter and a quintessence dark energy field having a characteristic parameter ω _q such that -1 < w_q < -\frac13-1<\omega_{q}< -\frac{1}{3}. Stable stellar orbits together with an attractive gravity exist only if ω _q is extremely close to -\frac13-\frac{1}{3}, a result consistent with the special case studied by Guzman et al. (Rev. Mex. Fis. 49:303, 2003). Less exceptional forms of quintessence dark energy do not yield the desired stable orbits and are therefore unsuitable for modeling dark matter.     

Kroll-Watson-type theorem for potential scattering in a bichromatic laser field

Summary We show that for potential scattering of electrons in a bichromatic laser field a Kroll-Watson type of theorem can be derived in which the scatteringT-matrix element is composed of a renormalized on-shell matrix element for scattering without a field times a generalized Bessel function factor. The radiation field has two components of frequency ω₁ and sω₁ (s=2,3,…) and both components are out of phase by an angle ϕ. Our paper is a generalization of earlier investigations which were performed in the first-order Born approximation.     

Tails of the dynamical structure factor of 1D spinless fermions beyond the Tomonaga approximation

We consider one-dimensional (1D) interacting spinless fermions with a non-linear spectrum in a clean quantum wire (non-linear bosonization). We compute diagrammatically the 1D dynamical structure factor, S(ω,q), beyond the Tomonaga approximation focusing on it's tails, |ω| ≫vq, i.e. the 2-pair excitation continuum due to forward scattering. Our methodology reveals three classes of diagrams: two “chiral” classes which bring divergent contributions in the limits ω→±vq, i.e. near the single-pair excitation continuum, and a “mixed” class (so-called Aslamasov-Larkin or Altshuler-Shklovskii type diagrams) which is crucial for the f-sum rule to be satisfied. We relate our approach to the T=0 ones present in the literature. We also consider the case and show that the 2-pair excitation continuum dominates the single-pair one in the range: |q|T/k_F ≪ω±vq ≪T (substantial for q ≪k_F). As applications we first derive the small-momentum optical conductivity due to forward scattering: σ∼1/ω for T ≪ω and σ∼T/ω² for T ≫ω. Next, within the 2-pair excitation continuum, we show that the attenuation rate of a coherent mode of dispersion Ω_q crosses over from , e.g. γ_q ∼|q|³ for an acoustic mode, to , independent of Ω_q, as temperature increases. Finally, we show that the 2-pair excitation continuum yields subleading curvature corrections to the electron-electron scattering rate: , where V is the dimensionless strength of the interaction.     

Community overlays upon real-world complex networks

An approximation for the dynamic structure factor S(q, ω) of the linear harmonic chain with periodic boundary conditions is obtained from a recurrence relation approach. It is compared with (numerically) exact results for S(q, ω). Explicit expressions for the moments of the structure factor are obtained from the short time expansion up to order n = 12. For the long-wavelength as well as the deep-inelastic limit, simple expressions are derived permitting to some extent analytic results for S(q, ω). Introducing a linear regression, an approximation scheme is defined which shows excellent agreement with the numerical results.     

Zero bias anomaly in the density of states of low-dimensional metals

We consider the effect of Coulomb interactions on the average density of states (DOS) of disordered low-dimensional metals for temperatures T and frequencies ω smaller than the inverse elastic life-time 1/τ. Using the fact that long-range Coulomb interactions in two dimensions (2d) generate ln²-singularities in the DOS ν(ω) but only ln-singularities in the conductivity σ(ω), we can re-sum the most singular contributions to the average DOS via a simple gauge-transformation. If σ(ω) > 0, then a metallic Coulomb gapν(ω) ∝ |ω|/e ⁴ appears in the DOS at T = 0 for frequencies below a certain crossover frequency Ω ₂ which depends on the value of the DC conductivity σ(0). Here, - e is the charge of the electron. Naively adopting the same procedure to calculate the DOS in quasi 1d metals, we find ν(ω) ∝ (|ω|/Ω ₁)^1/2exp(- Ω ₁/|ω|) at T = 0, where Ω ₁ is some interaction-dependent frequency scale. However, we argue that in quasi 1d the above gauge-transformation method is on less firm grounds than in 2d. We also discuss the behavior of the DOS at finite temperatures and give numerical results for the expected tunneling conductance that can be compared with experiments. Received 28 August 2001 / Received in final form 28 January 2002 Published online 9 July 2002     

Periodic and Quasi-Periodic Orbits¶for the Standard Map

We consider both periodic and quasi-periodic solutions for the standard map, and we study the corresponding conjugating functions, i.e. the functions conjugating the motions to trivial rotations. We compare the invariant curves with rotation numbers ω satisfying the Bryuno condition and the sequences of periodic orbits with rotation numbers given by their convergents ω _N = p _N /q _N . We prove the following results for N→ ∞: (1) for rotation numbers ω _N N we study the radius of convergence of the conjugating functions and we find lower bounds on them, which tend to a limit which is a lower bound on the corresponding quantity for ω; (2) the periodic orbits consist of points which are more and more close to the invariant curve with rotation number ω; (3) such orbits lie on analytical curves which tend uniformly to the invariant curve. Received: 14 December 2001 / Accepted: 16 March 2002?Published online: 2 October 2002     

Validity of the equivalent-photon approximation for the production of massive spin-1 particles

We point out that the equivalent-photon approximation (EPA) for processes with massive spin-1 particles in the final state would have validity in a more restricted kinematic domain than for processes where it is commonly applied, viz., those with spin-1/2 or spin-0 particles in the final state. We obtain the criterion for the validity ofEPA for the two-photon production of a pair of charged, massive, point-like spin-1 particlesV ^±, each of massM and with a standard magnetic moment (κ=1). In a process in which one of the photons is real and the other virtual with four-momentumq, the condition for the validity ofEPA is |q ²|≪M ², in addition to the usual condition |q ²|≪W ²,W being theV ⁺ V ⁻ invariant mass. In a process in which both photons are virtual (with four-momentaq andq′), our condition is |q ²||q′²|W ⁴ ≪ 16M ⁸, in addition to |q ²| ≪M ², |q′²| ≪M ² and |q ²| ≪W ², |q′²| ≪W ². Even when these extra conditions permitting the use ofEPA are not fulfilled, convenient approximate expressions may still be obtained assuming merely |q ²| ≪W ² and |q′²| ≪W ². We also discuss how the extra conditions are altered when the vector bosons are incorporated in a spontaneously broken gauge theory. Examples ofW boson production in Weinberg-Salam model are considered for which the condition |q ²||q′²|W ⁴ ≪ 16M ⁸ is shown to be removed.     

On momentum dependence of the reaction π− p→ωn near threshold

We discuss the near–threshold behavior of the ω production amplitude in the reaction π⁻ p→ωn. In contrast to the results of earlier analyses we find that the averaged squared matrix element of the production amplitude must be a decreasing function of energy in order to describe the existing experimental data. Received: 11 August 1999     

On the energy spectra of one-dimensional anharmonic oscillators

In this paper we present explicit and simple analytical formulae for the energy eigenvaluesE _n (λ) of one-dimensional anharmonic oscillators characterized by the potentials 1/2mω ² x ²+λx ^2α withα=2, 3 and 4. A simple intuitive criterion supplemented by the requirement of correct asymptotic behaviour, has been employed in arriving at the formulae. Our energy values over a wide range ofn andλ are in good agreement with the numerical values computed by earlier workers through very elaborate techniques. To our knowledge this is the first time that formulae of such wide validity have been given. The results for pure power oscillators are trivially obtained by going over to theω→0 limit. Approximate analytic expressions for the low order even moments ofx are also given.     

Field-theoretical Renormalization-Group approach to critical dynamics of crosslinked polymer blends

We consider a crosslinked polymer blend that may undergo a microphase separation. When the temperature is changed from an initial value towards a final one very close to the spinodal point, the mixture is out equilibrium. The aim is the study of dynamics at a given time t, before the system reaches its final equilibrium state. The dynamics is investigated through the structure factor, S(q, t), which is a function of the wave vector q, temperature T, time t, and reticulation dose D. To determine the phase behavior of this dynamic structure factor, we start from a generalized Langevin equation (model C) solved by the time composition fluctuation. Beside the standard de Gennes Hamiltonian, this equation incorporates a Gaussian local noise, ζ. First, by averaging over ζ, we get an effective Hamiltonian. Second, we renormalize this dynamic field theory and write a Renormalization-Group equation for the dynamic structure factor. Third, solving this equation yields the behavior of S(q, t), in space of relevant parameters. As result, S(q, t) depends on three kinds of lengths, which are the wavelength q ⁻¹, a time length scale R(t) ∼ t ^1/z , and the mesh size ξ ^*. The scale R(t) is interpreted as the size of growing microdomains at time t. When R(t) becomes of the order of ξ ^*, the dynamics is stopped. The final time, t ^*, then scales as t ^* ∼ ξ ^{* z}, with the dynamic exponent z = 6−η. Here, η is the usual Ising critical exponent. Since the final size of microdomains ξ ^* is very small (few nanometers), the dynamics is of short time. Finally, all these results we obtained from renormalization theory are compared to those we stated in some recent work using a scaling argument.     

Packing of molecules and hole formation in lyotropic systems

A vector field q (the order parameter of the molecular packing) describing the packing (specifically, the orientation) of membrane-forming amphiphilic molecules is introduced to describe the structures of lyotropic phases constructed from membranes. In the general case q·n≠0 (where n is the unit normal vector) and therefore the singularities of the vector field q are not determined uniquely by the topology of the surface. The condition q·n=0 signifies disruption of the packing of the molecules. This corresponds to holes, which can form in membranes when lyotropic systems are diluted. As an illustration, the simplest type of such singularities, in which the distribution of the field q around a hole is described by a part of an instanton with unit topological charge, is studied. It is shown that such a distribution guarantees the existence of a local minimum under the condition that the tension per unit length λ of the hole boundary is small compared with the deformation energy of the field q: λh/K≪l (K is the modulus of the orientational elasticity of the field q and h is the thickness of the membrane). The radius of the hole which is formed equals L≈2.52(K/λh)^1/3 and the energy E≈59.79K(λh/K)^1/3. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 8, 575–580 (25 October 1996)     

q$$ \bar q $$ pair production in non-Abelian gauge fields

We calculate the q pair production probability in the colour-flux tube model by considering the effect of non-Abelian interactions in the theory. Non-Abelian interactions in the colour field are time-dependent and hence should oscillate with a characteristic frequency ω ₀, which depends on the amplitude of the field strength. Using the WKB approximation in complex time, we calculated the pair production probability. When the strength of the field is comparable to the quark masses, the corresponding pair creation probability is maximum, and for the static field ω ₀ → 0, we recovered the well-known Schwinger result.      

Propagation oscillations in the near-field response of traveling surface waves launched by metallic nanoapertures

We discuss the implications of a frequency-dependent complex dielectric function ε(ω) of a metal for the interpretation of scanning near-field optical microscopy (SNOM) measurements in the vicinity of metallic nanoapertures. For subwavelength slits in gold films we observe distinct spatial intensity oscillations in the near-field signal for specific wavelengths in the visible spectrum. These oscillations of the SNOM signal far away from the nanoslit are ascribed to a constructive interference between the propagating surface plasmon (SP) with light scattered parallel to the gold–air interface. In these spatial SNOM-signal oscillations information about the surface plasmon dielectric function is encoded which can be extracted, for example, in surface plasmon interferometry for applications as sensors or waveguides.