Nonequilibrium relaxation in neutral BCS superconductors: Ginzburg-Landau approach with Landau damping in real time

Alamoudi, S. M.; Boyanovsky, D.; Wang, Shang-Yung

doi:10.1103/physrevb.66.184502

Cited by 5 publications

(5 citation statements)

References 45 publications

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“…Then they defined a complex order parameter whose modulus is the square root of the density. Their main result is a nonlinear Schrödinger equation describing this complex order parameter, which is different from the result obtained by Aitchison et al Very recently Alamoudi et al used the Keldysh formulation to treat non-equilibrium systems 19) and computed the response of the order parameter to an external perturbation added to the system in equilibrium. All these works 16)-19) are based on the Keldysh theory in the Grassmann number path-integral formulation and the introduction of the auxiliary fields through the Hubbard-Stratonovich transformation.…”

Section: §1 Introductionmentioning

confidence: 85%

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Space-Time Dependence of the BCS Order Parameter in Non-Equilibrium Systems

Toyoda

2005

Progress of Theoretical Physics

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A partial differential equation in time and space variables for the BCS order parameter for a non-equilibrium system is derived within the framework of nonperturbative canonical quantum many-body theory. The derivation is rigorous and no approximation is employed. The ensemble average used to define the order parameter is characterized by an arbitrary density matrix that satisfies the quantum Liouville equation. §1. IntroductionSince Ginzburg and Landau proposed an extremely successful phenomenological model of superconductivity, 1) formulating a microscopic derivation of that model has been one of the central problems in the study of superconductivity. 2) Two years after the proposal of the BCS theory, 3) Gor'kov refined it by introducing "anomalous" Matsubara Green functions 4) and derived the Ginzburg-Landau model with various approximations for temperatures near T c . 5) An extension of the Gor'kov theory to the time-dependent case was carried out by Abrahams and Tsuneto, 6) who used the Martin-Schwinger theory of Matsubara Green functions 7) and the Kadanoff-Baym formulation of non-equilibrium quantum many-body problems. 8) They carried out a Taylor expansion of the integral kernel in the integral form of the Gor'kov equation in momentum-frequency space and obtained a diffusion-type equation in the vicinity of the critical temperature and a wave-like equation at zero temperature for the superconducting order parameter.Recently, Stoof 9) reformulated Abrahams-Tsuneto theory using the Keldysh theory 10) in the Grassmann number 11) path-integral form and the Hubbard-Stratonovich transformation 12)-14) to introduce the pair fields and derived an effective Lagrangian for the phase of the order parameter. Stoof's effective Lagrangian yields a wave equation. Aitchison et al. 15) criticized Stoof's work on the ground that it violates Galilean invariance and derived an effective Lagarangian for the phase of the order parameter, which is manifestly Galilean invariant and very different from Stoof's result. From the effective Lagrangian, they constructed a density and a current in terms of the phase variable. Then, they identified the square root of the density as the modulus of the complex order parameter. They showed that a nonlinear Schrödinger Lagrangian for the complex order parameter actually yields the assumed forms of the density and current. Their result strongly suggests that the equation describing the behavior of the superconducting order parameter is a nonlinear Schrödinger equation. Their work was further developed for application to finite temperatures. 16), 17) De Palo et al. extended their work by introducing the density, which was introduced

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Section: §1 Introductionmentioning

confidence: 85%

“…8) has a term |Ψ 0 | 2 Ψ (x) that corresponds to the nonlinear terms observed in previous papers. 16)- 19) The term I(x) can be similarly approximated in terms of F (x, x ). It should be noted here that the exact equation (4 .…”

Section: ) the Equal-time Commutator Of λ(X) With H A (T) Yieldsmentioning

confidence: 99%

Space-Time Dependence of the BCS Order Parameter in Non-Equilibrium Systems

Toyoda

2005

Progress of Theoretical Physics

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“…In a ferroelectric phase transition, the relaxation process exhibits critical behaviour in the vicinity of the dielectric peak temperature [40]. The phenomena related to the critical slowing down were observed in many condensed matters having meta-stability, such as nanosized ferroelectric particles [41], quasicrystalline systems [42], superconductors having non-equilibrium phenomena [43] and granular ferromagnets [44], by using dynamical measurements such as dielectric dispersion, NMR measurements, Mössbauer spectra and light scattering. The observation in the lead nitrate crystal gives new information about the phenomena of the critical slowing down in condensed matter having meta-stability.…”

Section: S(t)mentioning

confidence: 99%

Electrical properties of lead nitrate single crystals

Isoda

Kawashima

2007

Physica Status Solidi (b)

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The measured alternating current (ac) electrical conductivity of lead nitrate [Pb(NO 3 ) 2 ] crystals in the frequency range 20 -10 6 Hz at temperature varying from 200 to 320 K shows anomalous temperature dependence, having meta-stability in the temperature range from 240 to 300 K. The dynamic properties have been extracted from these ac electrical data. The frequency exponents derived from the power law of the conductivity exhibit a singularity in this temperature variation range. A critical slowing down has been observed at temperatures near 275 K.

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“…Apart from the fact that the derivation of such an effective Lagrangian at T = 0 for either the complex order parameter or only the Goldstone mode is rather tricky even at quadratic level [2][3][4][5][6], this nonlocal formulation makes it difficult to simulate numerically the real time evolution of non-equilibrium processes, such as oscillations of trapped Fermi gases.…”

Section: Introductionmentioning

confidence: 98%

“…The effective description at finite temperature of the broken symmetry phase of a Fermi gas in the BCS-BEC crossover is complicated by the effect of Landau damping, which results in a highly nonlocal time-dependent Ginzburg-Landau theory [1]. Apart from the fact that the derivation of such an effective Lagrangian at T = 0 for either the complex order parameter or only the Goldstone mode is rather tricky even at quadratic level [2,3,4,5,6], this nonlocal formulation makes it difficult to simulate numerically the real time evolution of non-equilibrium processes, such as oscillations of trapped Fermi gases.…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian formulation of the effective kinetic theory for superfluid Fermi liquids

Valle

2011

Physics Letters A

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We present in a local form the time dependent effective description of a superfluid Fermi liquid which includes Landau damping effects at T = 0. This is achieved by the introduction of an additional variable, the quasiparticle distribution function, which obeys a simple kinetic equation. The transport equation is coupled with first order equations for the Goldstone mode and the particle density. We prove that a main feature of this formulation is its Hamiltonian structure relative to a certain Poisson bracket. We construct the Hamiltonian to quadratic order.

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Nonequilibrium relaxation in neutral BCS superconductors: Ginzburg-Landau approach with Landau damping in real time

Cited by 5 publications

References 45 publications

Space-Time Dependence of the BCS Order Parameter in Non-Equilibrium Systems

Space-Time Dependence of the BCS Order Parameter in Non-Equilibrium Systems

Electrical properties of lead nitrate single crystals

Hamiltonian formulation of the effective kinetic theory for superfluid Fermi liquids

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