The RPA correlations in the presence of thermal fluctuations

Rossignoli, R.; Canosa, N.

doi:10.1016/s0370-2693(97)00029-4

Cited by 35 publications

(54 citation statements)

References 32 publications

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“…Some of them exploit the concept of small amplitude vibrations about some given thermal state of the system, like RPA at finite temperature (see e.g. [29]) or the variants of the "Static Path Approximation" such as the P(erturbed)SPA of [30] or the C(orrelated)SPA of [31]. Also there separable two body interactions similar to the one given in (2) are exploited (with the k being some given constant, it is understood).…”

Section: Inferences For the High Temperature Limitmentioning

confidence: 99%

“…It is seen that the structure of the homogeneous parts follow from that of (28), for which reason the q 2 c (t) etc. satisfy the set (29) to (31) with the inhomogeneities D qp , D pp put equal to zero. For any finite value of these diffusion coefficients D qp and D pp the fluctuations will become finite in the course of time.…”

Section: Harmonic Approximation For First and Second Momentsmentioning

confidence: 99%

See 1 more Smart Citation

A Self-Consistent Treatment of Damped Motion for Stable and Unstable Collective Modes

Hofmann

Kiderlen

1998

Int. J. Mod. Phys. E

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We address the dynamics of damped collective modes in terms of first and second moments. The modes are introduced in a self-consistent fashion with the help of a suitable application of linear response theory. Quantum effects in the fluctuations are governed by diffusion coefficients D µν . The latter are obtained through a fluctuation dissipation theorem generalized to allow for a treatment of unstable modes. Numerical evaluations of the D µν are presented. We discuss briefly how this picture may be used to describe global motion within a locally harmonic approximation. Relations to other methods are discussed, like "dissipative tunneling", RPA at finite temperature and generalizations of the "Static Path Approximation".

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Section: Inferences For the High Temperature Limitmentioning

confidence: 99%

Section: Harmonic Approximation For First and Second Momentsmentioning

confidence: 99%

A Self-Consistent Treatment of Damped Motion for Stable and Unstable Collective Modes

Hofmann

Kiderlen

1998

Int. J. Mod. Phys. E

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“…In this figure, we see that, except for the small systematic difference observed for the gap, the FT-VAP approach provides a perfect description of the thermodynamics of a system with fixed particle number in any range of temperature. None of the limitations [14,15] appearing in other mean-field based theories are seen. In particular, the entropy, that is an approximation in FT-VAP, perfectly matches the exact one.…”

Section: Description Of the Methods And Applications To The Richardsonmentioning

confidence: 87%

Pairing and thermodynamics properties of finite-systems with fixed number of particles

Gambacurta

Lacroix

2012

EPJ Web of Conferences

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Abstract.A canonical description of the thermodynamical pairing properties of small systems is achieved by using the Variation After Projection approach at finite temperature. The minimization of the free energy is made by a direct evaluation of the energy and full diagonalization of the entropy. We use the Richardson -pairing model whose exact solution allows to study the reliability of different approaches. We show that the Projection After Variation approach, that is usually performed at zero temperature with rather good success, provides a quite poor description at finite temperature. On the contrary, the Variation After Projection applied at finite temperature provides a perfect reproduction of the exact canonical properties of odd or even systems from very low to high temperature.

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“…The latter leads to a random-phase-approximation-like (RPA-like) correction to the SPA result for each ∆ 0 . This technique is known as the SPA+RPA approach [32,33,34,35,36]. The number of electrons in the grain is essentially fixed by the large charging energy, leading to the odd-even effects discussed above.…”

Section: Superconducting Nanoparticles In the Absence Of Spin-orbit Smentioning

confidence: 99%

Mesoscopic superconductivity in ultrasmall metallic grains

Alhassid¹,

Nesterov²

2014

AIP Conference Proceedings

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Abstract.A nano-scale metallic grain (nanoparticle) with irregular boundaries in which the single-particle dynamics are chaotic is a zero-dimensional system described by the so-called universal Hamiltonian in the limit of a large number of electrons. The interaction part of this Hamiltonian includes a superconducting pairing term and a ferromagnetic exchange term. Spin-orbit scattering breaks spin symmetry and suppresses the exchange interaction term. Of particular interest is the fluctuation-dominated regime, typical of the smallest grains in the experiments, in which the bulk pairing gap is comparable to or smaller than the single-particle mean-level spacing, and the Bardeen-Cooper-Schrieffer (BCS) mean-field theory of superconductivity is no longer valid. Here we study the crossover between the BCS and fluctuation-dominated regimes in two limits. In the absence of spin-orbit scattering, the pairing and exchange interaction terms compete with each other. We describe the signatures of this competition in thermodynamic observables, the heat capacity and spin susceptibility. In the presence of strong spin-orbit scattering, the exchange interaction term can be ignored. We discuss how the magnetic-field response of discrete energy levels in such a nanoparticle is affected by pairing correlations. We identify signatures of pairing correlations in this response, which are detectable even in the fluctuation-dominated regime.

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The RPA correlations in the presence of thermal fluctuations

Cited by 35 publications

References 32 publications

A Self-Consistent Treatment of Damped Motion for Stable and Unstable Collective Modes

A Self-Consistent Treatment of Damped Motion for Stable and Unstable Collective Modes

Pairing and thermodynamics properties of finite-systems with fixed number of particles

Mesoscopic superconductivity in ultrasmall metallic grains

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