Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Unitary Thermodynamics from Thermodynamic Geometry II: Fit to a Local-Density Approximation

Unitary Thermodynamics from Thermodynamic Geometry II: Fit to a Local-Density Approximation Strongly interacting Fermi gasses at low density possess universal thermodynamic properties that have recently seen very precise PVT measurements by a group at MIT. This group determined local thermodynamic properties of a system of ultracold $$^6\text{ Li }$$ 6 Li atoms tuned to Feshbach resonance. In this paper, I analyze the MIT data with a thermodynamic theory of unitary thermodynamics based on ideas from critical phenomena. This theory was introduced in the first paper of this sequence and characterizes the scaled thermodynamics by the entropy per particle $$z= S/N k_B$$ z = S / N k B and the energy per particle Y(z), in units of the Fermi energy. Y(z) is in two segments, separated by a second-order phase transition at $$z=z_c$$ z = z c : a “superfluid” segment for $$z<z_c$$ z < z c and a “normal” segment for $$z>z_c$$ z > z c . For small z, the theory obeys a series $$Y(z)=y_0+y_1 z^{\alpha }+y_2 z^{2 \alpha }+\cdots ,$$ Y ( z ) = y 0 + y 1 z α + y 2 z 2 α + ⋯ , where $$\alpha $$ α is a constant exponent and $$y_i$$ y i ( $$i\ge 0$$ i ≥ 0 ) are constant series coefficients. For large z, the theory obeys a perturbation of the ideal gas $$Y(z)= \tilde{y}_0\,\text{ exp }[2\gamma z/3]+ \tilde{y}_1\,\text{ exp }[(2\gamma /3-1)z]+ \tilde{y}_2\,\text{ exp }[(2\gamma /3-2)z]+\cdots $$ Y ( z ) = y ~ 0 exp [ 2 γ z / 3 ] + y ~ 1 exp [ ( 2 γ / 3 - 1 ) z ] + y ~ 2 exp [ ( 2 γ / 3 - 2 ) z ] + ⋯ , where $$\gamma $$ γ is a constant exponent and $$\tilde{y}_i$$ y ~ i ( $$i\ge 0$$ i ≥ 0 ) are constant series coefficients. This limiting form for large z differs from the series used in the first paper and was necessary to fit the MIT data. I fit the MIT data by adjusting four free independent theory parameters: $$(\alpha ,\gamma ,\tilde{y}_0,\tilde{y}_1)$$ ( α , γ , y ~ 0 , y ~ 1 ) . This fit process was augmented by trap integration and comparison with earlier thermal data taken at Duke University. The overall match to both the data sets was good and had $$\alpha =1.21(3)$$ α = 1.21 ( 3 ) , $$\gamma =1.21(3)$$ γ = 1.21 ( 3 ) , $$z_c=0.69(2)$$ z c = 0.69 ( 2 ) , scaled critical temperature $$T_c/T_F=0.161(3)$$ T c / T F = 0.161 ( 3 ) , where $$T_F$$ T F is the Fermi temperature, and Bertsch parameter $$\xi _B=0.368(5)$$ ξ B = 0.368 ( 5 ) . I also discuss the virial expansion in the context of this thermodynamic geometric theory. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Low Temperature Physics Springer Journals

Unitary Thermodynamics from Thermodynamic Geometry II: Fit to a Local-Density Approximation

Journal of Low Temperature Physics , Volume 181 (2) – Jul 22, 2015

Loading next page...
 
/lp/springer-journals/unitary-thermodynamics-from-thermodynamic-geometry-ii-fit-to-a-local-ePXpWm6DHm

References (2)

Publisher
Springer Journals
Copyright
Copyright © 2015 by Springer Science+Business Media New York
Subject
Physics; Condensed Matter Physics; Characterization and Evaluation of Materials; Magnetism, Magnetic Materials
ISSN
0022-2291
eISSN
1573-7357
DOI
10.1007/s10909-015-1327-5
Publisher site
See Article on Publisher Site

Abstract

Strongly interacting Fermi gasses at low density possess universal thermodynamic properties that have recently seen very precise PVT measurements by a group at MIT. This group determined local thermodynamic properties of a system of ultracold $$^6\text{ Li }$$ 6 Li atoms tuned to Feshbach resonance. In this paper, I analyze the MIT data with a thermodynamic theory of unitary thermodynamics based on ideas from critical phenomena. This theory was introduced in the first paper of this sequence and characterizes the scaled thermodynamics by the entropy per particle $$z= S/N k_B$$ z = S / N k B and the energy per particle Y(z), in units of the Fermi energy. Y(z) is in two segments, separated by a second-order phase transition at $$z=z_c$$ z = z c : a “superfluid” segment for $$z<z_c$$ z < z c and a “normal” segment for $$z>z_c$$ z > z c . For small z, the theory obeys a series $$Y(z)=y_0+y_1 z^{\alpha }+y_2 z^{2 \alpha }+\cdots ,$$ Y ( z ) = y 0 + y 1 z α + y 2 z 2 α + ⋯ , where $$\alpha $$ α is a constant exponent and $$y_i$$ y i ( $$i\ge 0$$ i ≥ 0 ) are constant series coefficients. For large z, the theory obeys a perturbation of the ideal gas $$Y(z)= \tilde{y}_0\,\text{ exp }[2\gamma z/3]+ \tilde{y}_1\,\text{ exp }[(2\gamma /3-1)z]+ \tilde{y}_2\,\text{ exp }[(2\gamma /3-2)z]+\cdots $$ Y ( z ) = y ~ 0 exp [ 2 γ z / 3 ] + y ~ 1 exp [ ( 2 γ / 3 - 1 ) z ] + y ~ 2 exp [ ( 2 γ / 3 - 2 ) z ] + ⋯ , where $$\gamma $$ γ is a constant exponent and $$\tilde{y}_i$$ y ~ i ( $$i\ge 0$$ i ≥ 0 ) are constant series coefficients. This limiting form for large z differs from the series used in the first paper and was necessary to fit the MIT data. I fit the MIT data by adjusting four free independent theory parameters: $$(\alpha ,\gamma ,\tilde{y}_0,\tilde{y}_1)$$ ( α , γ , y ~ 0 , y ~ 1 ) . This fit process was augmented by trap integration and comparison with earlier thermal data taken at Duke University. The overall match to both the data sets was good and had $$\alpha =1.21(3)$$ α = 1.21 ( 3 ) , $$\gamma =1.21(3)$$ γ = 1.21 ( 3 ) , $$z_c=0.69(2)$$ z c = 0.69 ( 2 ) , scaled critical temperature $$T_c/T_F=0.161(3)$$ T c / T F = 0.161 ( 3 ) , where $$T_F$$ T F is the Fermi temperature, and Bertsch parameter $$\xi _B=0.368(5)$$ ξ B = 0.368 ( 5 ) . I also discuss the virial expansion in the context of this thermodynamic geometric theory.

Journal

Journal of Low Temperature PhysicsSpringer Journals

Published: Jul 22, 2015

There are no references for this article.