Coupling mechanisms for damped vortex motion in superfluids

Cataldo, H. M.; Despósito, M. A.; Hernández, E. S.; Jezek, D. M.

doi:10.1103/physrevb.56.8282

Cited by 4 publications

(8 citation statements)

References 16 publications

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“…In previous works 27,28,29 we derived, by means of a standard reduction-projection procedure and a weak-coupling Markov approximation, a generalized master equation for the density operator of the vortex. Our aim was to obtain an equation of motion for the mean value of the complex vortex position operator R = x + iy.…”

Section: Vortex Equation Of Motion Markov Approximation and The Limit...mentioning

confidence: 99%

Memory Effects in Superfluid Vortex Dynamics

Cataldo

Jezek

2004

Journal of Low Temperature Physics

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The dissipative dynamics of a vortex line in a superfluid is investigated within the frame of a non-Markovian quantal Brownian motion model. Our starting point is a recently proposed interaction Hamiltonian between the vortex and the superfluid quasiparticle excitations, which is generalized to incorporate the effect of scattering from fermion impurities ( 3 He atoms). Thus, a non-Markovian equation of motion for the mean value of the vortex position operator is derived within a weakcoupling approximation. Such an equation is shown to yield, in the Markovian and elastic scattering limits, a 3 He contribution to the longitudinal friction coefficient equivalent to that arising from the Rayfield-Reif formula. Simultaneous Markov and elastic scattering limits are found, however, to be incompatible, since an unexpected breakdown of the Markovian approximation is detected at low cyclotron frequencies. Then, a non-Markovian expression for the longitudinal friction coefficient is derived and computed as a function of temperature and 3 He concentration. Such calculations show that cyclotron frequencies within the range 0.01−0.03 ps −1 yield a very good agreement to the longitudinal friction figures computed from the Iordanskii and Rayfield-Reif formulas for pure 4 He, up to temperatures near 1 K. A similar performance is found for nonvanishing 3 He concentrations, where the comparison is also shown to be very favorable with respect to the available experimental data. Memory effects are shown to be weak and increasing with temperature and concentration.

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Section: Vortex Equation Of Motion Markov Approximation and The Limit...mentioning

confidence: 99%

Memory Effects in Superfluid Vortex Dynamics

Cataldo

Jezek

2004

Journal of Low Temperature Physics

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“…(5)), was found to be the only linear combination of vortex position and momentum operators leading to a dynamics in agreement with a drag force of the form (2). 18 It is instructive to identify the scattering processes embodied in the interaction potential (8); in fact if we replace the velocity from Eqs. (6), we find that the interaction consists of terms of the form a † a † k a q and a a † k a q , i.e.…”

Section: The Modelmentioning

confidence: 99%

“…( 9) was derived, i.e., a Markov approximation to second order in the coupling parameter. Finally, replacing the form (18) in Eq. ( 16) and taking the limit Ω → 0 we have,…”

Section: The Modelmentioning

confidence: 99%

Friction force on a vortex due to the scattering of superfluid excitations in helium II

Cataldo¹,

Jezek²

2002

Phys. Rev. B

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The longitudinal friction acting on a vortex line in superfluid 4 He is investigated within a simple model based on the analogy between such vortex dynamics and that of the quantal Brownian motion of a charged point particle in a uniform magnetic field. The scattering of superfluid quasiparticle excitations by the vortex stems from a translationally invariant interaction potential which, expanded to first order in the vortex velocity operator, gives rise to vortex transitions between nearest Landau levels. The corresponding friction coefficient is shown to be, in the limit of elastic scattering (vanishing cyclotron frequency), equivalent to that arising from the Iordanskii formula. Proposing a simple functional form for the scattering amplitude, with only one adjustable parameter whose value is set in order to get agreement to the Iordanskii result for phonons, an excellent agreement is also found with the values derived from experimental data up to temperatures about 1.5 K. Finite values of the cyclotron frequency arising from recent theories are shown to yield similar results. The incidence of vortex-induced quasiparticle transitions on the friction process is estimated to be, in the roton dominated regime, about 50 % of the value of the friction coefficient, ∼8 % of which corresponds to roton-phonon transitions and ∼42 % to roton R + ↔ R − ones.

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“…In what follows we shall consider the excitations to be at rest, so that the velocity of the normal fluid vanishes. In a previous work [5] we have considered an interaction Hamiltonian of the form…”

mentioning

confidence: 99%

“…In order to obtain an equation of motion for the mean value of the complex vortex position operator R = x + iy, in previous works [3,5] we have derived by means of a standard reduction-projection procedure, a generalized master equation for the density operator of the vortex. We have employed a usual weak-coupling approximation, in which the vortex dynamics is affected by the reservoir degrees of freedom only through the second order time correlation tensor B(t)B , where the angular brackets indicate an average over the reservoir equilibrium ensemble and B(t) denotes a free time evolution for the reservoir operators.…”

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Longitudinal and transverse forces on a vortex in superfluid⁴He

Cataldo¹,

Despósito²,

Jezek³

1999

J. Phys.: Condens. Matter

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We examine the transverse and longitudinal components of the drag force upon a straight vortex line due to the scattering of liquid 4 He excitations. For this purpose, we consider a recently proposed Hamiltonian that describes the dissipative motion of a vortex, giving an explicit expression for the vortex-quasiparticle interaction. The involved dissipative coefficients are obtained in terms of the reservoir correlation function. Most of our explicit calculations are concerned to the range of temperatures below 0.4 K, at which the reservoir is composed by phonon quasiparticle excitations. We also discuss some important implications in the determination of possible scattering processes leading to dissipation, according to the values of vortex mass found in the literature.

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Coupling mechanisms for damped vortex motion in superfluids

Cited by 4 publications

References 16 publications

Memory Effects in Superfluid Vortex Dynamics

Memory Effects in Superfluid Vortex Dynamics

Friction force on a vortex due to the scattering of superfluid excitations in helium II

Longitudinal and transverse forces on a vortex in superfluid⁴He

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Coupling mechanisms for damped vortex motion in superfluids

Cited by 4 publications

References 16 publications

Memory Effects in Superfluid Vortex Dynamics

Memory Effects in Superfluid Vortex Dynamics

Friction force on a vortex due to the scattering of superfluid excitations in helium II

Longitudinal and transverse forces on a vortex in superfluid4He

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Longitudinal and transverse forces on a vortex in superfluid⁴He