The quasiclassical approach to superfluid 3He

We present a unified description of the high temperature phase of QCD, the so-called quark-gluon plasma, in a regime where the effective gauge coupling g is sufficiently small to allow for weak coupling calculations. The main focuss is the construction of the effective theory for the collective excitations which develop at a typical scale gT , which is well separated from the typical energy of single particle excitations which is the temperature T . We show that the short wavelength thermal fluctuations, i.e., the plasma particles, provide a source for long wavelength oscillations of average fields which carry the quantum numbers of the plasma constituents, the quarks and the gluons. To leading order in g, the plasma particles obey simple gauge-covariant kinetic equations, whose derivation from the general Dyson-Schwinger equations is outlined. By solving these equations, we effectively integrate out the hard degrees of freedom, and are left with an effective theory for the soft collective excitations. As a by-product, the "hard thermal loops" emerge naturally in a physically transparent framework. We show that the collective excitations can be described in terms of classical fields, and develop for these a Hamiltonian formalism. This can be used to estimate the effect of the soft thermal fluctuations on the correlation functions. The effect of collisions among the hard particles is also studied. In particular we discuss how the collisions affect the lifetimes of quasiparticle excitations in a regime where the mean free path is comparable with the range of the relevant interactions. Collisions play also a decisive role in the construction a Member of CNRS. E-mail: blaizot@spht.saclay.cea.fr b Member of CNRS. E-mail: iancu@spht.saclay.cea.fr c Laboratoire de la Direction des Sciences de la Matière du Commissariatà l'Energie Atomique of the effective theory for ultrasoft excitations, with momenta ∼ g 2 T , a topic which is briefly addressed at the end of this paper.

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“…[144,86,87,12,13,14] for equilibrium situations, and in Refs. [88,43,89,90,91,92,93] for the non-equilibrium ones.…”

Section: Quantum Fields Near Thermal Equilibriummentioning

confidence: 99%

“…) From these identities, we get easily: 89) and, more generally: In particular, the average field induced in the system by the external current can be expanded as:…”

Section: Retarded Response Functionsmentioning

confidence: 99%

The quark–gluon plasma: collective dynamics and hard thermal loops

Blaizot¹,

Iancu²

2002

Physics Reports

511

714

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“…We will discuss the superconducting phase by means of the quasiclassical theory of superconductivity [18,19,20].…”

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Nuclear magnetic relaxation rate in a noncentrosymmetric superconductor

et al. 2006

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For a noncentrosymmetric superconductor such as CePt3Si, we consider a Cooper pairing model with a two-component order parameter composed of spin-singlet and spin-triplet pairing components. We demonstrate that such a model on a qualitative level accounts for experimentally observed features of the temperature dependence of the nuclear spin-lattice relaxation rate T −1 1 , namely a peak just below Tc and a line-node gap behavior at low temperatures.Inversion symmetry is one of the key points for the formation of Cooper pairs in superconductors. Unusual properties arise in superconductors whose crystal structure does not possess an inversion center (e.g., Refs. [1,2,3,4,5], and references therein). The recent discovery of superconductivity in the noncentrosymmetric heavy Fermion compound CePt 3 Si has initiated much interest, as experimental data revealed various intriguing features [6,7,8]. The essential element in modelling noncentrosymmetric systems is the presence of antisymmetric spin-orbit coupling [9,10]. One of the characteristic features in the superconducting phase is the mixing of the spin-singlet and spin-triplet Cooper pairing channels which are otherwise distinguished by parity [2]. This is likely responsible for the surprisingly high value of the upper critical field H c2 which exceeds the paramagnetic limit [3,6,8,11,12]. CePt 3 Si displays further intriguing properties. Recent nuclear magnetic resonance (NMR) experiments found an overall anomalous temperature dependence of the nuclear spin-lattice relaxation rate T −1 1 [8,13,14]. The behavior of T −1 1 shows a (Hebel-Slichter) peak just below the superconducting critical temperature T c , and simultaneously a T 3 dependence at low temperatures indicating line nodes in the quasiparticle gap. Such a gap with line nodes is also suggested by measurements of the London penetration depth [8]. At first sight, those experimental results seem to be mutually contradicting, as the features of unconventional Cooper pairing (line nodes) and of conventional superconductivity (peak in T −1 1 due to the coherence effect) are implied at the same time by the temperature dependence of T −1 1 [8,13,14].In the present study, we demonstrate that these apparently conflicting behaviors can be reconciled by taking account of the mixing of the pairing channels with opposite parity, which naturally occurs in superconductors without inversion center. For this purpose, we consider a pairing model with a two-component order parameter consisting of spin-singlet and spin-triplet pairing components. Such a model contains the necessary ingredients to account for the observed features of T −1 1 , i.e., the linenode behavior at low temperatures and the coherence effect just below T c . At the same time, the pairing model would also explain the temperature dependence of the London penetration depth qualitatively and be consistent with earlier studies of H c2 [3,15].We base our analysis on a Hamiltonian considered in Ref. [3], in which the lack of inversion symmetry is incorporated ...

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“…5 We solve the Eilenberger transport equation for the quasiclassical propagator, g(p, R; ε m ), in the Matsubara formalism,…”

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Domain Walls in Superfluid 3He-B

Vorontsov¹,

Sauls²

2005

J Low Temp Phys

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We consider domain walls between regions of superfluidThe order parameter of superfluid 3 He is suppressed near an impurity or in the vicinity of walls and interfaces. 1,2,3,4 This happens because the order parameter breaks the rotational symmetry of the normal phase, and because particle-hole coherence is destroyed when quasiparticles, which move in the presence of the order parameter, are scattered from one point on the Fermi surface to another. Here we consider a related problem in which the order parameter varies strongly in space, so that quasiparticles move in this spatially varying order parameter even when they propagate along straight trajectories. Consider an order parameter that varies along some axis and has one bulk solution on the far left, and another possible bulk solution on far right. The region separating these two degenerate bulk solutions is the domain wall. Since the order parameter is different on the two sides the superfluid will be strongly deformed in the vicinity of the domain wall. Although domain walls are not energetically favorable in bulk 3 He, we will argue that inhomogeneous structures formed from domain walls may be the favorable solutions for 3 He in confined geometries.To determine the order parameter and to calculate the corresponding free energy of a domain wall we use the quasiclassical theory. 5 We solve the Eilenberger transport equation for the quasiclassical propagator, g(p, R; ε m ),

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The quasiclassical approach to superfluid 3He

Cited by 602 publications

References 91 publications

The quark–gluon plasma: collective dynamics and hard thermal loops

The quark–gluon plasma: collective dynamics and hard thermal loops

Nuclear magnetic relaxation rate in a noncentrosymmetric superconductor

Domain Walls in Superfluid 3He-B

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