TL;DR: In this article, the authors used a capillary technique for small samples to measure the isothermal compressibility κ T of water to −26°C and showed that the anomalous characteristics are due to the sensitivity of the volume to temperature changes, suggesting a geometrical basis for the cooperative behavior.
Abstract: Using a capillary technique for small samples, the isothermal compressibility κ T of water has been measured to −26°C. Accelerating increases of κ T at the lower temperatures can be described by an expression of the form κ T =Aeγ [where e= (T−T s )/T s ], which is known to describe anomalies encountered in the vicinity of a thermodynamic singularity located at T s . The implication that the thermodynamic and certain other properties of water at lower temperatures may be decomposed into a normal component and an anomalous component which diverges at T s =−45°C is supported by analysis of numerous other thermodynamic and relaxation data which extend into the supercooled regime. The anomalous characteristics are shown to originate primarily in the sensitivity of the volume to temperature changes, suggesting a geometrical basis for the cooperative behavior. The singularity at T s =−45°C may be a lambda transition associated with the cooperative formation of an open hydrogen‐bonded network, but the near coincidence of T s with the experimental homogeneous nucleation temperature suggests, as an alternative, that T s may correspond to the limit of mechanical stability for the supercooled liquid phase.
TL;DR: The superfluid phase transition in a strongly interacting Fermi gas is observed by high-precision measurements of the local compressibility, density, and pressure, which completely determine the universal thermodynamics of these gases without any fit or external thermometer.
Abstract: Fermi gases, collections of fermions such as neutrons and electrons, are found throughout nature, from solids to neutron stars. Interacting Fermi gases can form a superfluid or, for charged fermions, a superconductor. We have observed the superfluid phase transition in a strongly interacting Fermi gas by high-precision measurements of the local compressibility, density, and pressure. Our data completely determine the universal thermodynamics of these gases without any fit or external thermometer. The onset of superfluidity is observed in the compressibility, the chemical potential, the entropy, and the heat capacity, which displays a characteristic lambda-like feature at the critical temperature T(c)/T(F) = 0.167(13). The ground-state energy is 3/5ξN E(F) with ξ = 0.376(4). Our measurements provide a benchmark for many-body theories of strongly interacting fermions.
TL;DR: In this paper, it is shown from first principles that liquid He4 should exhibit a transition analogous to the transition in an ideal Bose-Einstein gas, and the exact partition function is written as an integral over trajectories, using the space-time approach to quantum mechanics.
Abstract: It is shown from first principles that, in spite of the large interatomic forces, liquid He4 should exhibit a transition analogous to the transition in an ideal Bose-Einstein gas. The exact partition function is written as an integral over trajectories, using the space-time approach to quantum mechanics. It is next argued that the motion of one atom through the others is not opposed by a potential barrier because the others may move out of the way. This just increases the effective inertia of the moving atom. This permits a simpler form to be written for the partition function. A rough analysis of this form shows the existence of a transition, but of the third order. It is possible that a more complete analysis would show that the transition implied by the simplified partition function is actually like the experimental one.
TL;DR: In this paper, high-precision measurements of the local compressibility, density, and pressure of strongly interacting Fermi gases have been obtained without any fit or external thermometer.
Abstract: Fermi gases, collections of fermions such as neutrons and electrons, are found throughout nature, from solids to neutron stars. Interacting Fermi gases can form a superfluid or, for charged fermions, a superconductor. We have observed the superfluid phase transition in a strongly interacting Fermi gas by high-precision measurements of the local compressibility, density, and pressure. Our data completely determine the universal thermodynamics of these gases without any fit or external thermometer. The onset of superfluidity is observed in the compressibility, the chemical potential, the entropy, and the heat capacity, which displays a characteristic lambda-like feature at the critical temperature T(c)/T(F) = 0.167(13). The ground-state energy is 3/5ξN E(F) with ξ = 0.376(4). Our measurements provide a benchmark for many-body theories of strongly interacting fermions.
TL;DR: In this article, a general dynamical scaling theory of phase transitions is established by exploiting the absence of a characteristic length in an extended system at its phase transition, which imposes strong constraints on the frequency and wave-number dependence of the fluctuation spectrum and leads to unambiguous predictions concerning the critical properties.