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Relativistic superfluidity at arbitrary temperature, chemical potential and (uniform) superflow is discussed within a self-consistent field-theoretical approach. Our starting point is a complex scalar field with a $\varphi^4$ interaction, for which we calculate the 2-particle-irreducible effective action in the Hartree approximation. With this underlying microscopic theory, we can obtain the two-fluid picture of a superfluid, and compute properties such as the superfluid density and the entrainment coefficient for all temperatures below the critical temperature for superfluidity. We compute the critical velocity, taking into account the full self-consistent effect of the temperature and superflow on the quasiparticle dispersion. We also discuss first and second sound modes and how first (second) sound evolves from a density (temperature) wave at low temperatures to a temperature (density) wave at high temperatures. This role reversal is investigated for ultra-relativistic and near-non-relativistic systems for zero and nonzero superflow. For nonzero superflow, we also observe a role reversal as a function of the direction of the sound wave.Comment: 32 pages, 9 figures, v2: expanded discussion of renormalization, conclusions unchanged, version to appear in Phys. Rev.

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“…(For a zero-temperature calculation of the sound velocities in the presence of a superflow in 4 He see Ref. [63]. )…”

Section: Results Iii: Sound Modesmentioning

confidence: 99%

Role reversal in first and second sound in a relativistic superfluid

et al. 2014

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“…(15)-(17) are the mean constant equilibrium values, from which there are small perturbations of temperature and relative velocity, which propagate with velocities (15)- (17). Velocities (15) and (16) correspond to the second sound propagation velocities, which were found in [14] for arbitrary values of relative velocity w. Particularly, at w = 0, we obtain V 1,2 = ∓c/ √ 3 which is the well-known phonon second sound velocity, when ρ n ≪ ρ. Specific features of second sound in anisotropic phonon systems with w = 0, i.e.…”

Section: Second Sound Simple Waves In Phonon Systemsmentioning

confidence: 98%

“…where r = (r 1 , r 2 , r 3 ) is a eigenvector of matrix (10) of system (9), which corresponds to the eigenvalueṼ . The equations (14) determine the functional dependence between the variables Θ, u x , and u 2 in the corresponding simple wave solution of system (9), (10). It follows from Eqs.…”

Section: Second Sound Simple Waves In Phonon Systemsmentioning

confidence: 99%

“…They define the propagation of second sound waves and the transverse wave, at arbitrary values of the equilibrium relative velocity w, when ρ n ≪ ρ. The dispersion relation for this case is studied in [14]. For a phonon system with a linear energy-momentum relation ε = cp, where c 2 = (∂P )/(∂ρ) and c is the first sound velocity of helium, we have [12]:…”

Section: Introductionmentioning

confidence: 99%

“…The power of the applied heat pulses was such that the normal density ρ n was very small, ρ n ≪ ρ. In this case the superfluid velocity and variations of pressure can be neglected when we study phonon propagation [14]. Taking into account the approximate relation v n = w + v s ≈ w in Eqs.…”

Section: Introductionmentioning

confidence: 99%

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Formation of a Mesa Shaped Phonon Pulse in Superfluid 4He

2010

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We present a theory for the formation of a mesa shaped phonon pulse in superfluid 4 He. Starting from the hydrodynamic equations of superfluid helium, we obtain the system of equations which describe the evolution of strongly anisotropic phonon systems. Such systems can be created experimentally. The solution of the equations are simple waves, which correspond to second sound in the moving phonon pulse. Using these exact solutions, we describe the expansion of phonon pulses in superfluid helium at zero temperature. This theory gives an explanation for the mesa shape observed in the measured phonon angular distributions. Almost all dependencies of the mesa shape on the system parameters can be qualitatively understood.

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From a complex scalar field to the two-fluid picture of superfluidity

et al. 2013

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The hydrodynamic description of a superfluid is usually based on a two-fluid picture. We compute the basic properties of the relativistic two-fluid system from the underlying microscopic physics of a relativistic ϕ 4 complex scalar field theory. We work at nonzero but small temperature and weak coupling, and we neglect dissipation. We clarify the relationship between different formulations of the two-fluid model, and how they are parameterized in terms of partly redundant current and momentum 4-vectors. As an application, we compute the velocities of first and second sound at small temperatures and in the presence of a superflow. While our results are of a very general nature, we also comment on their interpretation as a step towards the hydrodynamics of the color-flavor locked state of quark matter, which, in particular in the presence of kaon condensation, appears to be a complicated multi-component fluid.

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Second sound in an anisotropic quasiparticle system of superfluidH4e

Cited by 4 publications

References 20 publications

Role reversal in first and second sound in a relativistic superfluid

Role reversal in first and second sound in a relativistic superfluid

Formation of a Mesa Shaped Phonon Pulse in Superfluid 4He

From a complex scalar field to the two-fluid picture of superfluidity

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