# Strong coupling corrections to the Ginzburg-Landau theory of superfluid {sup 3}He

## Abstract

In the Ginzburg-Landau 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 order-parameter 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 fourth-order 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 fourth-order 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; GINZBURG-LANDAU THEORY; HELIUM 3; MAGNETIC SUSCEPTIBILITY; NUCLEAR MAGNETIC RESONANCE; ORDER PARAMETERS; POROUS MATERIALS; PRESSURE DEPENDENCE; QUASI PARTICLES; SILICA; STRONG-COUPLING 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 Ginzburg-Landau 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 Ginzburg-Landau 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 Ginzburg-Landau theory of superfluid {sup 3}He". United States.
doi:10.1103/PHYSREVB.75.174503.
```

```
@article{osti_20957837,
```

title = {Strong coupling corrections to the Ginzburg-Landau 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 Ginzburg-Landau 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 order-parameter 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 fourth-order 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 fourth-order 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}

}