RPA instabilities in finite nuclei at low density

Early development of the instabilities in a dilute nuclear source is investigated using a finite temperature quantal RPA approach for different systems. The growth rates of the unstable collective modes are determined by solving a dispersion relation, which is obtained by parametrizing the transition density in terms of its multipole moments. Under typical conditions of a dilute finite system at moderate temperatures the dispersion relation exhibits an ultraviolet cut-off. As a result, only a finite number of multipole modes becomes unstable, and the number of the unstable collective modes increases with the size of the source. Calculations indicate that for an expanding source, unstable modes show a transition from surface to volume character.     

Mechanical and chemical spinodal instabilities in finite quantum systems

Self-consistent quantum approaches are used to study the instabilities of finite nuclear systems. The frequencies of multipole density fluctuations are determined as a function of dilution and temperature for several isotopes. The spinodal region of the phase diagrams is determined, and it appears that instabilities are reduced by finite size effects. The role of surface and volume instabilities is discussed. It is indicated that the important chemical effects associated with mechanical disruption may lead to isospin fractionation.     

Dynamic instabilities of fracture under biaxial strain using a phase field model

We present a phase-field model of the propagation of fracture under plane strain. This model, based on simple physical considerations, is able to accurately reproduce the different behavior of cracks (the principle of local symmetry, the Griffith and Irwin criteria, and mode-I branching). In addition, we test our model against recent experimental findings showing the presence of oscillating cracks under biaxial load. Our model again reproduces well observed supercritical Hopf bifurcation and is therefore the first simulation which does so.     

Application of finite strain theory to non-cubic crystals

The application of finite strain theory to a crystal of orthorhombic or higher elastic symmetry, which is subjected to a purely extensional deformation parallel to the crystallographic axes, yields stress-strain relations and effective elastic constants for hydrostatic stresses. Alternative formulations of the theory are obtained when the free energy is written as Taylor series in E, the invariant analogue of the Eulerian strain tensor, or η, the Lagrangian strain tensor. In most cases, the formulation in terms of E provides a better approximation when the Taylor series are truncated at the second or third order. In the case of cubic crystals, the stress-strain relations reduce to the Birch equation. For non-cubic crystals, the P-V relations calculated using the non-cubic and Birch equations will differ due to the effects of elastic anisotropy. A comparison between the second-order approximations of the non-cubic stress-strain relations and the cubic Birch equation suggests that the difference in volume will be less than 1% for most materials. The difference in volume is reduced when the third-order approximations are used. When the third-order terms are retained, the stress-strain relations calculated using the Eulerian formulation agree with measured linear compression data for quartz to 150 kbar $\text{(}\text{P}\text{K}{}_0\text{= 0.4).}$ For zinc, the calculated pressure-volume relation agrees with the shock-wave Hugoniot up to 750 kbar $\text{(}\text{P}\text{K}{}_0\text{= 1.2),}$ although both calculated and Hugoniot P-V relations disagree with X-ray compression data. At pressures greater than 300 kbar, the calculated axial ratio of zinc approaches that for other hexagonal metals $\text{(}\text{c}\text{a}\text{? 1.63).}$     

Quasi-harmonic finite strain equations of state of solids

Thomsen's ‘fourth-order anharmonic’ theory, which explicitly evaluates thermal effects in finite strain equations of elasticity according to the fourth-order approximation in lattice dynamics, is reconsidered for the special case of isotropic stresses and strains. It is shown that the approximations made in the finite strain theory are independent from those made in the lattice dynamics theory, with the result that strain dependence may be described in terms of any frame-indifferent strain tensor, not just the ‘Lagrangian’ strain tensor, η, and that the finite strain expansions may be taken to any order, not just the fourth. This result is valid for general stresses and strains. Illustrative pressure-volume equations are derived in terms of three strain measures, including η and the frame-indifferent analogue, E, of the ‘Eulerian’ strain tensor, ε. The reference state is here left arbitrary, rather than identifying it with the ‘rest’ state. This results in greater convenience in applying the equations. Not being restricted to fourth order, the present equations do not depend for their application on knowing the second pressure derivatives of the bulk modulus. Expressions are obtained for isentropes and Hugoniots in terms of the same parameters as enter the original equations, which have the form of isotherm. Ultrasonic, thermal expansion and calorimetric data for MgO are used to evaluate the parameters of third-order equations of state of MgO. The equations of state are tested and refined with Hugoniot data. The third-order ‘E’ Hugoniot is much closer to the data than the third-order ‘η’ Hugoniot. Inclusion of fourth-order terms allows both ‘E’ and ‘ρ’ Hugoniots to fit the data within their scatter. The separation of Hugoniots corresponding to different initial densities is predicted within the accuracy of the data by the thermal part of this theory.     

Gross features of finite nuclei at finite temperatures

A simple expression is obtained for the low-temperature behaviour of the energy and entropy of finite nuclei for 20 ￡ \leq A ￡ \leq 250 . The dependence on A of these quantities is for the most part due to the presence of the asymmetry energy.     

Axial anomaly at finite temperature and finite density

TheU(1) axial anomaly in a hot fermion medium is investigated by using the real time Green's function method. After calculating the lowest order triangle diagrams, we find that finite temperature as well as finite fermion density does not affect the axial anomaly. The higher order corrections for the axial anomaly are discussed.     

Quasi-particles at finite temperatures

We study the consequences of the KMS-condition on the properties of quasi-particles, assuming their existence. We establish

1. If the correlation functions decay sufficiently, we can create them by quasi-free field operators.
2. The outgoing and incoming quasi-free fields coincide, there is no scattering.
3. There are may age-operatorsT conjugate toH. For special forms of the dispersion law ε(k) of the quasi-particles there is aT commuting with the number of quasi-particles and its time-monotonicity describes how the quasi-particles travel to infinity.

     

QCD at finite temperature

Quantum chromodynamics is studied at finite temperatures and densities using the temperature Green functions method. For the Green functions the renormalized Schwinger-Dyson equations are obtained and their qualitative properties are discussed. The equality of the renormalization constants for the equations obtained at T, μ ≠ 0 with those for quantum field theory is pointed out. General properties of the gluon polarization tensor are investigated at T, μ ≠ 0. The temperature Green functions are calculated within the one-loop approximation using both relativistic and axial gauges. The fulfilment of the Slavnov-Taylor identities is verified. The asymptotic behaviour of the polarization tensor at T, μ ≠ 0 is established and the excitation spectrum of quark-gluon plasma is found. Both Fermi and Bose excitations are considered and the gauge invariance of the spectra is demonstrated. The renormalization group extension of the dispersion laws into the regions of high temperatures and densities is presented. The exact representation of the thermodynamical potential in QCD is found in terms of the temperature Green functions. For the quark-gluon plasma the thermodynamical potential is calculated with the g³-term taken into account. The equation of state of the hot quark-gluon plasma is found and its properties are discussed. The complete evolutional diagram of the hadronic matter is outlined. The phase curve asymptotics, which put bounds on the quark-gluon plasma domain, are found for the two limiting cases (μ = 0, T → T₀; T = 0, μ → μ₀). The phase transition of the hot quark-gluon plasma placed in external Abelian field is studied. The instability of such plasma has been found and the program of its stabilization is indicated. The infrared behaviour of the non-Abelian gauge theory is studied for finite temperatures when power divergencies are essential. The propagator of transverse gluons is shown to be singular for momenta |p| ˜ g²T and this cannot be avoided by summing the simplest bubble chains. The infrared asymptotic behaviour of the tree-gluon vertex is found and the results obtained are checked using the Slavnov-Taylor identities. The Green functions asymptotics found indicate either an instability of the quark-gluon plasma in the infrared momentum domain or the inconsistency of the perturbational methods. A non-perturbative approach to the infrared problem in QCD is developed within the axial gauge. The closed equations for the structure functions that determine the gluon polarization tensor are obtained by using the Slavnov-Taylor identities to found approximately the three-gluon vertex. It is shown that the solution of the equations obtained by iterations does not remove the infrared singularity from the temperature Green functions. The nonperturbative solution of such equations is discussed.     

Merons at finite temperature

We prove the existence of solutions to the SU(2) Yang—Mills equations on IR⁴, periodic in time, with meron singularities along the time-axis.Supported in part by the Icelandic Science Foundation.     

Tunneling at finite temperature

In a two-dimensional scalar field theory the rate of the metastable vacuum decay at finite temperature is calculated.     

On the theory of instabilities arising at quark-gluon plasma formation

Collisions of two degenerate quark Fermi liquids are studied. It is shown that there arise instabilities, which manifest themselves in propagation of growing oscillations corresponding to the modes existing in a Fermi liquid at rest. Quark jets are likely to appear in the directions of the growing oscillations propagation.

The instabilities studied in this work are similar to the beam instability in ordinary electron plasma.     

Local excitation-lateral inhibition interaction yields oscillatory instabilities in nonlocally interacting systems involving finite propagation delay

The work studies wave activity in spatial systems, which exhibit nonlocal spatial interactions at the presence of a finite propagation speed. We find analytically propagation delay-induced oscillatory instabilities for various local excitatory and lateral inhibitory spatial interactions. Further, the work shows for general nonlocal interactions analytically that the first kernel Fourier moment defines the stability thresholds. The final numerical simulation confirms the analytical results.     

Magnetohydrodynamic instabilities at Comet P/Halley: Giotto observations

Summary We examine the plasma parameters observed by the ion mass spectrometer of the Giotto JPA experiment, downstream the bow shock and up to the closest approach of comet P/Halley. From the analysis of the observations we have identified two regions where the ΔV between the proton and water group ion bulk velocities is first parallel and later perpendicular, respectively, to the magnetic-field direction. In the parallel region, a strong MHD turbulence is observed that we suppose to be generated by a firehose instability mechanism driven by the velocity difference. At about 5·10⁵ km from closest approach, the center of mass switches from solar-wind protons to the cometary ions, while the velocity difference becomes perpendicular to the magnetic field, causing the quenching of the isstability and the disappearing of the plasma fluctuations. Paper presented at the V Cosmic Physics National Conference, S. Miniato, November 27–30, 1990.     

$$\bar K$$ optical potential at finite temperatureoptical potential at finite temperature

The \(\bar K\) optical potential is microscopically calculated from the \(\bar K\)N effective interaction in nuclear matter at T=0 and finite temperature, with the aim to adapt our calculations to the experimental conditions in heavy-ion collisions. In the rank of densities (0-2_ρ0), the finite temperature \(\bar K\) optical potential shows a smoother behaviour compared to the T=0 case. The model has also been applied to the study of the ratio between K⁺ and K^? produced at GSI with T around 70 MeV. The results point at the necessity of introducing an attractive \(\bar K\) optical potential.