A. Alastuey

Nuclear reaction rate enhancement in dense stellar matter

The enhancement factor for the rate of thermonuclear reactions in dense stellar matter is calculated in the one-component, strongly coupled plasma model. The nuclear reaction rate is related to the short-range behavior of the quantum-mechanical pair correlation function. Within the range of parameters which is investigated here, the pair correlation function is expressed in terms of classical quantities, which are known from existing computer results; the classical potential of mean force is found to play an important role, from the practical point of view. Numerical results are given.

Decay of correlations in classical fluids with long-range forces

We show with simple arguments that, as a consequence of the Poisson equation, the correlations of a charged system at equilibrium decay faster than any inverse power, if they are integrable and monotonous at infinity. For all other longrange systems (with potentialφ(x)∼b¦x¦−s, ¦x¦ → ∞, 0<s<v,s≠} 2), the decay is bounded below by an inverse power.

Magnetic properties of a nearly classical one-component plasma in three or two dimensions: II. Strong field

Abstract The equilibrium statistical mechanics of a nearly classical one-component plasma, submitted to a strong magnetic field, is studied, in three or two dimensions, by a suitable expansion of the Wigner distribution function. A strong magnetic field quenches the quantum fluctuations transverse to the field. The situation is especially simple for a two-dimensional plasma, which has a classical behaviour in the strong-field limit; as a consequence, a classical Wigner crystallization can be induced by the magnetic field.

Correlations in the Kosterlitz-Thouless phase of the two-dimensional Coulomb gas

The particle and charge correlations of the two-dimensional Coulomb gas are studied in the dielectric phase. A term-by-term analysis of the low-fugacity expansions suggests that the large-distance behaviors of the particle correlations are governed by multipolar interactions, similar to what happens in a system of permanent dipoles. These behaviors are compatible with the asymptotic structure of the BGY hierarchy equations; on the other hand, a new identity for the dielectric constant ɛ is used to show that the four-particle correlations decay as the dipole-dipole potential 1/r2 when two neutral pairs are separated by a large distancer. Near the zero-density critical point of the Kosterlitz-Thouless transition, we resum the low-fugacity expansions of both 1/ɛ and the charge correlation C(r). We thus retrieve the coupling constant flow equations of the renormalization group as well as the effective interaction energy of the iterated mean-field theory by Kosterlitz and Thouless. The coupling constant at the RG fixed point is then identified with 1/ɛ. The nonanalyticity of 1/ɛ at the transition turns out to coincide with the divergence of the low-fugacity series for this quantity. The leading term in the large-distance behavior of C(r) is found to be the same as for external charges. Moreover, we exhibit the subleading terms which also contribute to 1/ɛ.

Absence of Exponential Clustering for the Static Quantum Correlations and the Time-Displaced Correlations in Charged Fluids

The 4-term in the Wigner-Kirkwood expansion of the equilibrium charge-charge correlations of a quantum one-component plasma (OCP) is found to decay like 1/r10. The t8-term in the small time expansion of the time displaced charge-charge correlations of a classical OCP also decays like 1/r10. Thus both correlations decay algebraically for all values of the thermodynamic parameters. Furthermore we show by an analysis of the hierarchy equations for the correlations that the corresponding tails are bounded by 1/r6.

Part II. Algebraic tails in three-dimensional quantum plasmas

We review various exact results concerning the presence of algebraic tails in three-dimensional quantum plasmas. First, we present a solvable model of two quantum charges immersed in a classical plasma. The effective potential between the quantum charges is shown to decay as 1/r6 at large distances r. Then, we mention semiclassical expansions of the particle correlations for charged systems with Maxwell-Boltzmann statistics and short-ranged regularization of the Coulomb potential. The quantum corrections to the classical quantities, from orderh4 on, also decay as 1/r6. We also give the result of an analysis of the charge correlation for the one-component plasma in the framework of the usual many-body perturbation theory; some Feynman graphs beyond the random phase approximation display algebraic tails. Finally, we sketch a diagrammatic study of the correlations for the full many-body problem with quantum statistics and pure 1/r interactions. The particle correlations are found to decay as 1/r6, while the charge correlation decays faster, as 1/r10. The coefficients of these tails can be exactly computed in the low-density limit. The absence of exponential screening arises from the quantum fluctuations of partially screened dipolar interactions.

Part I. The 2D classical Coulomb gas near the zero-density Kosterlitz-Thouless critical point: Correlations and critical line

The 2D classical Coulomb gas undergoes the famous Kosterlitz-Thouless (KT) transition between a high-temperature conducting phase and a low-temperature insulating phase. We present various studies of the correlations in the insulating phase near the zero-density critical point. First, we briefly recall the phenomenological approach of Kosterlitz and Thouless. This theory predicts that the decay of the charge correlation is entirely controlled by the bare Coulomb potential between opposite charges only renormalized by the dielectric constante. Then, we present an analysis of the low-fugacity expansions of the correlations. The particle correlations are found to decay as 1/r4. The large-distance decay of the charge correlation is shown to be tightly related to the behavior of l/s in the regime of interest. Systematic resummations allow one to recover the algebraic decay predicted by the heuristic KT model. This settles on a rigorous basis various assumptions of this model. In particular, the nested pair mechanism naturally arises in the resummation scheme. Finally, we describe the phase diagram of the system according to the most recent calculations which include finite-density effects.

ABSENCE OF EXPONENTIAL SCREENING IN QUANTUM MECHANICAL PLASMAS

Publisher Summary This chapter presents evidence that the equilibrium correlations of quantum mechanical charges do not cluster exponentially fast, irrespective of the value of the density and of the temperature. Thus, the Debye screening does not exist in real matter. The evidence for the absence of exponential screening rely on the following two approaches. In a study described in the chapter, the large-distance behavior of the quantum corrections to the classical correlations for both an OCP and a multicomponent system described by Maxwell-Boltzmann statistics was investigated. This investigation gives algebraic lower bounds for the decay of the quantum correlations (for instance, the particle-particle correlations should not decay faster than 1/r6 in a multicomponent system). A simplified model was also studied where only two quantum charges are immersed in a classical plasma. The exact asymptotic behavior of the correlations of these two charges was determined, which was found as 1/r6 when r → ∞.