Effective Lagrangians for BCS superconductors at<i>T</i>=0

Aitchison, I. J. R.; Ao, Ping; Thouless, D. J.; Zhu, Xiaowei

doi:10.1103/physrevb.51.6531

Cited by 101 publications

(179 citation statements)

References 17 publications

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“…The system that we have in mind is the dilute Bose gas, which is governed by the Gross-Pitaevskii equation [8,9] at temperatures sufficiently low that the system may be described as a superfluid. It should, however, be noted that this type of equation is applicable to a wider class of systems than just zero-temperature dilute gases [10,11].…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamic approach to vortex lifetimes in trapped Bose condensates

Lundh

2000

Phys. Rev. A

110

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We study a vortex in a two-dimensional, harmonically trapped Bose-Einstein condensate at zero temperature. Through a variational calculation using a trial condensate wave function and a nonlinear Schrödinger Lagrangian, we obtain the effective potential experienced by a vortex at an arbitrary position in the condensate, and find that an off-center vortex will move in a circular trajectory around the trap center. We find the frequency of this precession to be smaller than the elementary excitation frequencies in the cloud.We also study the radiation of sound from a moving vortex in an infinite, uniform system, and discuss the validity of this as an approximation for the trapped case. Furthermore, we estimate the lifetime of a vortex due to imperfections in the trapping potential.

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Section: Introductionmentioning

confidence: 99%

Hydrodynamic approach to vortex lifetimes in trapped Bose condensates

Lundh

2000

Phys. Rev. A

110

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“…The tadpole to one-loop order is given by (4.7). From the explicit form of the one-loop self-energies in the static limit (5.9), find that 10) which is an exact relationship to one-loop order, obtained for arbitrary ∆ 0 . Upon collecting the above results, we find to one-loop order that…”

Section: Ward Identity and Static Self-energiesmentioning

confidence: 99%

“…While previous efforts, notably by Aitchison et al [10,14], focused on the long-wavelength, low-frequency effective action well below the critical temperature for 0 < T < 0.6 T c our goal is to study the critical region |∆ 0 (T )| ≪ T c with ∆ 0 (T ) the finite-temperature gap. Our study is different from previous attempts in several respects: (i) We implement the Schwinger-Keldysh formulation of nonequilibrium field theory [28] along with the recently introduced tadpole method [31] to obtain the equations of motion for small amplitude fluctuations of the order parameter in real time.…”

Section: Introductionmentioning

confidence: 99%

“…Whereas the effective Ginzburg-Landau (GL) [4] description in the static limit was derived by Gor'kov [5,6], the effective time dependent Ginzburg-Landau description is still the focus of a substantial theoretical effort. There is a large body of work that established the validity of a time-dependent nonlinear Schroedinger equation that describes the dynamics of the order parameter at zero temperature [7,8,9,10,11,12].…”

Section: Introductionmentioning

confidence: 99%

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

Alamoudi¹,

Boyanovsky²,

Wang³

2002

Phys. Rev. B

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We present a field-theoretical method to obtain consistently the equations of motion for small amplitude fluctuations of the order parameter directly in real time for a homogeneous, neutral BCS superconductor. This method allows to study the nonequilibrium relaxation of the order parameter as an initial value problem. We obtain the Ward identities and the effective actions for small phase the amplitude fluctuations to one-loop order. Focusing on the long-wavelength, low-frequency limit near the critical point, we obtain the time-dependent Ginzburg-Landau effective action to one-loop order, which is nonlocal as a consequence of Landau damping. The nonequilibrium relaxation of the phase and amplitude fluctuations is studied directly in real time. The long-wavelength phase fluctuation (Bogoliubov-Anderson-Goldstone mode) is overdamped by Landau damping and the relaxation time scale diverges at the critical point, revealing critical slowing down.

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“…As it was shown earlier [15,13], in 2D case it is convenient to pass from φ and φ * fields to new variables, namely: the absolute value ρ and the phase θ, where φ(x) = ρ(x) exp[−2iθ(x)], and to perform simultaneously the spinor transformation…”

Section: Model and Main Equationsmentioning

confidence: 99%

Phase diagram in 2D Fröhlich model of metal at arbitrary carriers density: pseudogap versus doping

Локтев

Sharapov

Turkowski

1998

Physica C: Superconductivity

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It is shown that in 2D system of the fermions with simplest indirect boson-induced attraction (through the Einstein phonon exchange as an example) along with the normal and superconducting phases there arises a new (called "abnormal normal" or pseudogap) one where the absolute value of the order parameter is finite but its phase is a random quantity. It is important that this new phase really exists at low carriers density only, i.e. it shrinks when doping increases. The relevance of the results obtained with dependence of pseudogap on doping in high-temperature superconductors is speculated.

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Effective Lagrangians for BCS superconductors atT=0

Cited by 101 publications

References 17 publications

Hydrodynamic approach to vortex lifetimes in trapped Bose condensates

Hydrodynamic approach to vortex lifetimes in trapped Bose condensates

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

Phase diagram in 2D Fröhlich model of metal at arbitrary carriers density: pseudogap versus doping

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