Phonon contribution to the shear viscosity of a superfluid Fermi gas in the unitarity limit

We present a detailed analysis of the contribution of small-angle Nambu–Goldstone boson (phonon) collisions to the shear viscosity, η$\eta$, in a superfluid atomic Fermi gas close to the unitarity limit. We show that the experimental values of the shear viscosity coefficient to entropy ratio, η/s$\eta /s$, obtained at the lowest reached temperature can be reproduced assuming that phonons give the leading contribution to η$\eta$. The phonon contribution is evaluated considering 1↔2$1\leftrightarrow 2$ processes and taking into account the finite size of the experimental system. In particular, for very low temperatures, T?0.1T_F$T?0.1T_F$, we find that phonons are ballistic and the contribution of phonons to the shear viscosity is determined by the processes that take place at the interface between the superfluid and the normal phase. This result is independent of the detailed form of the phonon dispersion law and leads to two testable predictions: the shear viscosity should correlate with the size of the optical trap and it should decrease with decreasing temperature. For higher temperatures the detailed form of the phonon dispersion law becomes relevant and, within our model, we find that the experimental data for η/s$\eta /s$ can be reproduced assuming that phonons have an anomalous dispersion law.     

Study of molecular motions in liquids by electron spin-lattice relaxation measurements,I: Semiquinone ions in hydrogen bonding solvents

The electron spin-lattice relaxation times (T ₁) of a variety of semiquinone ions in hydrogen bonding solvents have been measured by the pulsed saturation recovery technique as a function of temperature (T) and viscosity (η) of the solvent. Also linewidths (ΔH) have been measured in suitable cases in such solvents at low radical concentrations (～10^?4 M). It is observed that (i) the temperature and viscosity dependence ofT ₁ can be fitted to an equation of the form 1/T ₁=A(T/η)+Bexp(-ΔE/RT) whereA andB are constants and ΔE is an activation energy of the order of 1 kcal mole^?1 for these systems; (ii)T ₁ is essentially independent of the radical concentration within the range 10^?3 to 5×10^?2 M; (iii) the concentration independent part of the linewidth (ΔH) increases linearly with (η/T) at sufficiently low temperatures, and (iv) the (η/T) dependent part ofT ₁ is sensitive to the size of the semiquinone as well as that of the solvent molecule, whereas the linewidth which is proportional to (η/T) at high viscosity, low temperature region is not sensitive to the size of the semiquinone and that of the solvent. Based on these observations, it is postulated that in hydrogen bonding solvents, three types of motion contribute significantly to electron spin relaxation:

1. A restricted small step diffusional motion, not involving large changes in the orientation of the molecule, leading to the dominant viscosity dependent contributions toT ₁ and ΔH, due to spin rotation interaction;
2. a large amplitude reorientation of the semiquinone, coupled to translational diffusion, resulting in viscosity dependent contributions toT ₁ and ΔH, throughg-modulation;
3. a hindred rotation of the semiquinone within the solvent cage, contributing toT ₁ due to spin rotation interaction.

The fact thatT ₁ is not sensitive to the concentration of the radicals, is ascribed to the formation of the solvent cage that prevents the close approach of radicals, thereby rendering radical-radical interactions to be weak mechanisms for relaxation, even at relatively high radical concentrations.     

Shear viscosity of the Quark–Gluon Plasma from a virial expansion

We calculate the shear viscosity η in the quark–gluon plasma (QGP) phase within a virial expansion approach with particular interest in the ratio of η to the entropy density s, i.e. η/s. The virial expansion approach allows us to include the interactions between the partons in the deconfined phase and to evaluate the corrections to a single-particle partition function. In the latter approach we start with an effective interaction with parameters fixed to reproduce thermodynamical quantities of QCD such as energy and/or entropy density. We also directly extract the effective coupling α _V for the determination of η. Our numerical results give a ratio η/s≈0.097 at the critical temperature T _c, which is very close to the theoretical bound of 1/(4π). Furthermore, for temperatures T≤1.8T _c the ratio η/s is in the range of the present experimental estimates 0.1–0.3 at RHIC. When combining our results for η/s in the deconfined phase with those from chiral perturbation theory or the resonance-gas model in the confined phase we observe a pronounced minimum of η/s close to the critical temperature T _c.     

On the theory of rheological properties of magnetic suspensions

The paper deals with a theoretical study of influence of magnetic field on effective viscosity of suspension of non-Brownian magnetizable particles. It is supposed that experimentally observed magnetorheological effects are provided by chain-like aggregates, consisting of the particles. Unlike previous works on this subject, we take into account that the chains cannot be identical and estimate their size distribution. The following power law (η-η₀)/η₀∼Mn^-Δ, detected in many experiments, is obtained theoretically (η and η₀ are the suspension effective viscosity and the carrier liquid viscosity, respectively, Mn is the so-called Mason number, proportional to the shear rate and inversely proportional to the square of magnetic field). The calculated magnitude of the exponent Δ increases with the applied magnetic field from approximately 0.66 to 0.8-0.9 and slowly increases with the volume concentration ? of the particles. These results are in agreement with known experiments.     

Dispersive viscosity coefficient of nuclear matter

By application of Landau's kinetic theory of a Fermi liquid in non-equilibrium, we have deduced a dispersive, momentum and frequency dependent shear viscosity coefficient η(q, ω) for symmetric nuclear matter. The resulting formula for η is found to be complicated for arbitrary q, ω; however, simple interpretation is possible in the limit of small momentum q → 0. In the static limit, ω → 0, η reduces to the well known kinetic formula for the hydrodynamic viscosity coefficient η_o, while in the high frequency (zero sound) limit, ωτ ? 1, η(ω) is found proportional to (?iω)^? indicating elastic behaviour of nuclear matter. As is discussed shortly, application of these results to finite nuclei unfortunately does not seem justified.     

Analyzing powers Ayy , Axx , Axz and Ay in the dd → 3Hen reaction at 270 MeV

The data on the tensor A_yy, A_xx, A_xz and vector A_y analyzing powers in the dd → ^3Hen obtained at T _d = 270 MeV in the angular range 0^° - 110^° in the c.m. are presented. The observed negative sign of the tensor analyzing powers A_yy, A_xx and A_xz at small angles clearly demonstrate the sensitivity to the ratio of the D - and S -wave component of the ³He wave function. However, the one-nucleon exchange calculations by using the standard ³He wave functions have failed to reproduce the strong variation of the tensor analyzing powers as a function of the angle in the c.m.     

Rapid viscous flow of a nematic liquid crystal in the vicinity of the nematic-smectic <Emphasis Type="Italic">A</Emphasis> transition

The resistance to shear flow is investigated theoretically for polar liquid crystals, such as 4-n-octyl-4′-and 4-n-octyloxy-4′-cyanobiphenyls. It is established that the lowest resistance to shear flow at temperatures in the vicinity of the nematic-smectic A phase transition point T _NA is observed when the nematic director is oriented perpendicular to both the flow velocity vector and the flow velocity gradient. The three Miesowicz shear viscosity coefficients η_i (i=1–3) at temperatures close to the phase transition temperature (tens of millikelvins from T _NA ) and far from this transition are calculated in the framework of the Ericksen-Leslie theory. The decrease in the viscosity coefficients in the order η₂>η₁>η ₃ is explained by the fact that fluctuations of the local smectic order in the nematic phase lead to a singular behavior of the viscosity coefficient η₂, whereas the other two viscosity coefficients η₁ and η₃ are not affected by order parameter fluctuations.     

Effect of ultrasound treatment on steady and dynamic shear properties of glucomannan based salep dispersions: optimization of amplitude level, sonication time and temperature using response surface methodology

The present study investigated effect of different amplitude levels (40, 70 and 100%), sonication temperatures (40, 50 and 60 °C) and exposure times (3, 7 and 11 min) on steady shear properties; apparent viscosity (η), shear stress (σ), consistency coefficient (K), flow behavior index (n) and dynamic shear properties; storage modulus (G′), loss modulus (G″), complex viscosity (η^∗), complex modulus (G^∗) and loss tangent (tan δ) values of glucomannan based salep solution (SS) and salep drink (SD) samples. In addition, the steady and dynamic shear properties were optimized using ridge analysis in terms of amplitude level, sonication temperature and exposure times levels. Increasing amplitude level and sonication time decreased considerably the η, σ, K, G′, G″ and η^∗ values of salep dispersions (SS and SD samples). However, sonication temperature did not have a remarkable effect on these properties.     

Third sound detection of superfluid transitions in 3He-4He films

Experiments in ³He⁴He films using the torsional oscillator method suggest the existence of two superfluid transitions. We only detect the low temperature superfluid transition T_A by third sound velocity measurement, which raises the question of the existence of percolation between superfluid clusters at T>T_A.     

Energy dependence of tensor analyzing powers in deuteron elastic scattering from 208Pb

Differential cross section and all four analyzing powers iT₁₁, T₂₀, T₃₁ and T₂₂ have been measured for deuteron elastic scattering from ²⁰⁸Pb at incident energies from 10 to 23 MeV. The energy dependence of the tensor analyzing powers was investigated. A considerable deviation of the data from optical-model calculations including a T_r-type tensor potential is found near the Coulomb barrier.     

Tensor interaction in heavy-ion scattering: (I). The turning-point model

The Heidelberg shape-effect model for heavy-ion tensor interactions is reformulated and generalized using the Hooton-Johnson formulation. The generalized semiclassical model (the turning-point model) predicts that the components of the tensor analysing power $\text{T}{}_{\mathrm{2q}}$ have certain relations with each other for each type of tensor interaction (T_R, T_P and T_L types). The predicted relations between the $\text{T}{}_{\mathrm{2q}}$ are very simple and have a direct connection with the properties of the tensor interaction at the turning point. The model predictions are satisfied in quantum-mechanical calculations for ⁷Li and ²³Na elastic scattering from ⁵⁸Ni in the Fresnel-diffraction energy region. As a consequence of this model, it becomes possible to single out effects from a T_P? or T_L-type tensor interaction in polarized heavy-ion scattering. The presence of a T_P-type tensor interaction is suggested by measured $\text{T}{}_{20}\text{/}\text{T}{}_{22}$ ratios for ⁷Li+⁵⁸Ni scattering. In the turning-point model the three types of tensor operator are not independent, and this is found to be true also in a quantum-mechanical calculation. The model also predicts relations between the components of higher-rank tensor analysing power in the presence of a higher-rank tensor interaction. The rank-3 tensor case is discussed in detail.     

Viscosity of strong and fragile glass-forming liquids investigated by means of principal component analysis

The Vogel—Fulcher-Tammann-Hesse (VFTH) equation has been the most widespread tool for describing the temperature dependence with viscosity for strong, moderate and fragile glass-forming liquids. In this work, the VFTH equation was applied over a wide temperature range (between the glass transition temperature, T_g, and the melting point, T_m) for 38 oxide glasses, considering simple, binary and ternary compositions of silicate and borate systems. The Levenberg-Marquart non-linear fitting procedure was used to assess VFTH viscosity parameters B and T₀, maintaining A=−5 fixed (in Pa·s) to reduce the number of adjustable parameters. Regarding this restriction, the VFTH formula has shown to adjust very well to experimental data in a wide temperature range. Previous assertions revealed that there is statistical correlation between B and T₀. Principal component analysis (PCA) was used in the present study to verify the correlation between the B and T₀ parameters [J. F. Mano, E. Pereira, J. Phys. Chem. A 108 (2004) 10824], as well as between T_g and T_m. In brief, PCA is a mathematical method aimed at reorganizing information from data sets. The results have shown that it is possible to map either borate (and almost fragile) or silicate (usually strong up to near fragile) systems. As a statistical tool, PCA justifies the use of B, T₀ and T_g as the main parameters for the fragility indexes m=d(log₁₀η)/d(T_g/T)|_T=Tg and D=B/T₀, where η is the viscosity and T the absolute temperature.     

Elastic scattering of 56 MeV polarized deuterons on 4He

The differential cross section and the vector and tensor analyzing powers A_y, A_xx, A_yy and A_xz were measured for the d-⁴He elastic scattering at 56 MeV. The measurement of A_xz was performed using a deuteron beam polarized in the horizontal plane. An optical-model analysis of the experimental data was carried out. The magnitude of the tensor analyzing powers could not be reproduced without the tensor potential. By including the T_R type tensor potential, the optical-model calculations give a reasonable reproduction of the experimental data at θ_c.m. < 120°. The obtained T_R tensor potential was much stronger than that predicted by the folding model. The strength of the real T_R potential was roughly in accordance with that obtained from the optical-model analysis of d-⁴He elastic scattering at 20.2 MeV.     

Universal behavior of shear viscosity near the freezing point

The dynamics of liquids above the freezing point is studied. It is demonstrated that the available experimental data on shear viscosity of simple liquids can be described in the framework of the so-called weak crystallization theory. The theory predicts that, in the main approximation, shear viscosity is proportional to the (T/T _*−1)^−3/2, where T _* is the temperature close to the freezing temperature. This prediction is in good agreement with experimental data for many substances.     

Universal behavior of shear viscosity near the freezing point

The dynamics of liquids above the freezing point is studied. It is demonstrated that the available experimental data on shear viscosity of simple liquids can be described in the framework of the so-called weak crystallization theory. The theory predicts that, in the main approximation, shear viscosity is proportional to the (T/T _*−1)^−3/2, where T _* is the temperature close to the freezing temperature. This prediction is in good agreement with experimental data for many substances. The text was submitted by the author in English.     

Static viscosity of nuclear matter

The static shear viscosity η₀ of symmetric nuclear matter is estimated. It is found, that for reasonable nuclear temperatures the mean free path connected with η_o is considerably larger than the nuclear radii. We therefore conclude, that the concept of viscosity cannot be applied to nuclear fission and heavy ion collisions without taking into account the nuclear surface.     

Specific features of the BCS-BEC crossover and thermodynamics in the 2D resonant Fermi gas with p-wave pairing

The 2D resonant Fermi gas with p-wave pairing is considered n the BCS-BEC regime. For the 2D analog of the superfluid A1 phase, the Leggett equations [1] for superfluid gap Δ and chemical potential μ are analytically solved at T = 0 and the spectrum of the collective excitations (acoustic waves) is analyzed in the BCS regime (μ > 0), where the triplet Cooper pairs emerge; in the BEC regime (μ < 0), where the triplet local pairs (molecules) emerge; and in the transition region, where μ → 0. At low temperatures, the contribution of the superfluid Fermi quasiparticles of the resonant gas to heat capacity C _v and the density of normal component ρ_n is also calculated. At μ = 0, the fermionic contribution to ρ_n and C _v are represented as power functions of temperature (ρ_n ～ T ³ and C _v ～ T ²). However, similar power contributions to these quantities are related to phonons (bosonic acoustic oscillations). The possibility of the experimental observation of the nontrivial topological term with the charge Q = 1 in the BCS regime of the 2D A1 phase is briefly discussed.     

Spin-state transition, magnetic, electrical and thermal transport properties of the perovskite cobalt oxide Gd0.7Sr0.3CoO3

The magnetization, resistivity ρ, thermoelectric power (TEP) S, and thermal conductivity κ in perovskite cobalt oxide Gd_0.7Sr_0.3CoO₃ have been investigated systematically. Based on the temperature dependence of susceptibility χ_g(T) and Seebeck coefficient S(T), a combination of the intermediate-spin (IS) state for Co³⁺ and the low-spin (LS) state for Co⁴⁺ can be suggested. A metal-insulator transition (MIT) caused by the hopping of σ* electrons (localized or delocalized e_g electrons) from the IS Co³⁺ to the LS Co⁴⁺ is observed. Meanwhile, S(T) curve also displays an obvious phonon drag effect. In addition, based on the analysis of the temperature dependence of S(T) and ρ(T), the high-temperature small polaron conduction and the low-temperature variable-range-hopping conduction are suggested, respectively. As to thermal conduction κ(T), rather low κ values in the whole measured temperature range is attributed to unusually large local Jahn-Teller (JT) distortion of Co³⁺O₆ octahedra with IS state.     

Inclusive ηp and ηn charged-current neutrino reactions below 6 GeV

Results are presented of a study of inclusive ηp and ηn interactions from threshold to 6 GeV. The data show a rapid approach to the distributions expected in the naive quark-parton model. The charged-current η deuteron total cross section is fit by the expression σ_T(ηd) = (0.76 ± 0.03) × 10^?38E_η cm² per GeV per nucleon. For E_η > 1.5 GeV, we measure σ_T(ηn)/σ_T(ηp) = (2.02 ± 0.23). The distributions in the scaling variables x and y are given and discussed.