Strong coupling corrections to the GinzburgLandau theory of superfluid {sup 3}He
Abstract
In the GinzburgLandau theory of superfluid {sup 3}He, the free energy is expressed as an expansion of invariants of a complex order parameter. Strong coupling effects, which increase with increasing pressure, are embodied in the set of coefficients of these orderparameter invariants [A. J. Leggett, Rev. Mod. Phys. 47, 331 (1975); E. V. Thuneberg, Phys. Rev. B 36, 3583 (1987); J. Low Temp. Phys. 122, 657 (2001)]. Experiments can be used to determine four independent combinations of the coefficients of the five fourthorder invariants. This leaves the phenomenological description of the thermodynamics near T{sub c} incomplete. Theoretical understanding of these coefficients is also quite limited. We analyze our measurements of the magnetic susceptibility and the NMR frequency shift in the B phase which refine the four experimental inputs to the phenomenological theory. We propose a model based on existing experiments, combined with calculations by Sauls and Serene [Phys. Rev. B 24, 183 (1981)] of the pressure dependence of these coefficients, in order to determine all five fourthorder terms. This model leads us to a better understanding of the thermodynamics of superfluid {sup 3}He in its various states. We discuss the surface tension of bulk superfluid {sup 3}He and predictions formore »
 Authors:
 Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208 (United States)
 Publication Date:
 OSTI Identifier:
 20957837
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. B, Condensed Matter and Materials Physics; Journal Volume: 75; Journal Issue: 17; Other Information: DOI: 10.1103/PhysRevB.75.174503; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; CORRECTIONS; ELASTIC SCATTERING; FREE ENERGY; GINZBURGLANDAU THEORY; HELIUM 3; MAGNETIC SUSCEPTIBILITY; NUCLEAR MAGNETIC RESONANCE; ORDER PARAMETERS; POROUS MATERIALS; PRESSURE DEPENDENCE; QUASI PARTICLES; SILICA; STRONGCOUPLING MODEL; SUPERFLUIDITY; SURFACE TENSION; THERMODYNAMICS
Citation Formats
Choi, H., Davis, J. P., Pollanen, J., Haard, T. M., and Halperin, W. P.. Strong coupling corrections to the GinzburgLandau theory of superfluid {sup 3}He. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVB.75.174503.
Choi, H., Davis, J. P., Pollanen, J., Haard, T. M., & Halperin, W. P.. Strong coupling corrections to the GinzburgLandau theory of superfluid {sup 3}He. United States. doi:10.1103/PHYSREVB.75.174503.
Choi, H., Davis, J. P., Pollanen, J., Haard, T. M., and Halperin, W. P.. Tue .
"Strong coupling corrections to the GinzburgLandau theory of superfluid {sup 3}He". United States.
doi:10.1103/PHYSREVB.75.174503.
@article{osti_20957837,
title = {Strong coupling corrections to the GinzburgLandau theory of superfluid {sup 3}He},
author = {Choi, H. and Davis, J. P. and Pollanen, J. and Haard, T. M. and Halperin, W. P.},
abstractNote = {In the GinzburgLandau theory of superfluid {sup 3}He, the free energy is expressed as an expansion of invariants of a complex order parameter. Strong coupling effects, which increase with increasing pressure, are embodied in the set of coefficients of these orderparameter invariants [A. J. Leggett, Rev. Mod. Phys. 47, 331 (1975); E. V. Thuneberg, Phys. Rev. B 36, 3583 (1987); J. Low Temp. Phys. 122, 657 (2001)]. Experiments can be used to determine four independent combinations of the coefficients of the five fourthorder invariants. This leaves the phenomenological description of the thermodynamics near T{sub c} incomplete. Theoretical understanding of these coefficients is also quite limited. We analyze our measurements of the magnetic susceptibility and the NMR frequency shift in the B phase which refine the four experimental inputs to the phenomenological theory. We propose a model based on existing experiments, combined with calculations by Sauls and Serene [Phys. Rev. B 24, 183 (1981)] of the pressure dependence of these coefficients, in order to determine all five fourthorder terms. This model leads us to a better understanding of the thermodynamics of superfluid {sup 3}He in its various states. We discuss the surface tension of bulk superfluid {sup 3}He and predictions for novel states of the superfluid such as those that are stabilized by elastic scattering of quasiparticles from a highly porous silica aerogel.},
doi = {10.1103/PHYSREVB.75.174503},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 17,
volume = 75,
place = {United States},
year = {Tue May 01 00:00:00 EDT 2007},
month = {Tue May 01 00:00:00 EDT 2007}
}

We first discuss the generalized Eilenberger equations for superfluid /sup 3/He in the presence of a magnetic field and for uniform rotation of the system. These equations determine the spacedependent Green's function, the free energy density, and the supercurrent density at all temperatures. From these equations we derive the generalized GinzburgLandau series expansions in powers of spatial derivatives and the order parameter. This is in contrast to Cross' generalized GinzburgLandau approach, which takes into account only spatial derivatives up to second order. Explicit expressions are given for the corrections of order (1T/T/sub c/) to the wellknown expressions for the bendingmore »

Spinfluctuation theory of strong coupling corrections to the free energy in superfluid /sup 3/He
Previous spinfluctuation theories yielding the strong coupling corrections ..delta..betabar/sub i/ to the five coefficients of the fourthorder invariants in the free energy functional are extended. First, the superfluid part of the susceptibility is calculated up to order ..delta../sup 4/for all momenta and frequencies and the contribution arising from pwave fluctuations of the order parameter is included. Then the frequency sums yielding the ..delta..betabar/sub i/ are calculated by taking into account the full momentum and frequency dependence of the superfluid susceptibility and the spin fluctuation propagator. The results for the ..delta..betabar/sub i/ are plotted vs. a cutoff q/sub c/ on themore » 
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Spin/entropy wave in superfluid {sup 3}He A{sub 1}: Anomalous attenuation and strong coupling corrections
A mass superflow in A{sub 1} phase carries both fully polarized nuclear spin flow and zero entropy simultaneously. The second sound in A{sub 1} is then a hybrid spin/entropy wave propagation. The authors have studied the spin/entropy wave propagation in fields up to 5 T between 10 and 30 bar. When A{sub 1} makes transition into the superfluid A{sub 2} phase, the spin/entropy wave is expected to disappear abruptly. Unexpectedly the authors observe that there is a {open_quotes}critical{close_quotes} region within A{sub 1} phase over which the attenuation gradually increases. The observation might be an evidence for presence of minority spinmore »