Thermodynamics and hydrodynamics of ³He-⁴He mixtures

The specific heat of liquid 3He–4He mixtures is usually written in terms of the sum of the specific heat of a 3He-quasiparticle gas and the specific heat of the pure 4He component. The thermodynamics based on this starting point is derived. Relations of important quantities and their low- and high-temperature limits are given. These are used to derive expressions for the velocity of second sound. This latter quantity is a very important source of information for the Fermi gas properties. Finally, the Fermi gas parameters are summarized in the chapter. The experimental aspects of the 3He–4He hydrodynamics are treated. The appearance of mutual friction that has long been neglected in this field is discussed, together with the properties of the critical velocities. The phenomenological equations of motion are given. The occurrence of mutual friction is a strong indication that 4He vortices play an important role in 3He–4He hydrodynamics. From the equation of motion of quantized 4He vortices, the observed cubic velocity dependence of the 4He chemical potential difference is explained on purely dimensional grounds. A differential equation is given from which the temperature profile in a cylindrical tube in which 3He flows through superfluid 4He can be calculated

Disorder Effects in Superconducting Multiple Loop Quantum Interferometers

A theoretical study is presented on a number N of resistively shunted Josephson junctions connected in parallel as a disordered 1D array by superconducting wiring in such a manner that there are N-1 individual SQUID loops with arbitrary shape formed.Comment: 4 pages, 2 figure

Thermodynamics of liquid 3He−4He mixtures

The osmotic pressure of 3He−4He solutions is shown to follow in a natural way from the separation of the specific heat in a quasiparticle contribution and a 4He-contribution. Expressions for important thermodynamic properties such as the chemical potentials, the internal energy, the entropy, specific heat, osmotic pressure, etc. are given for the case the quasiparticle gas can be treated as a nearly-ideal Fermi gas. The zero kelvin and the high-temperature limits are tabulated. A first-order approximation is given for the effect of the 3He quasiparticle contribution to the second-sound velocity in the high-temperature limit

Thermodynamics and hydrodynamics of ³He-⁴He mixtures

The specific heat of liquid 3He–4He mixtures is usually written in terms of the sum of the specific heat of a 3He-quasiparticle gas and the specific heat of the pure 4He component. The thermodynamics based on this starting point is derived. Relations of important quantities and their low- and high-temperature limits are given. These are used to derive expressions for the velocity of second sound. This latter quantity is a very important source of information for the Fermi gas properties. Finally, the Fermi gas parameters are summarized in the chapter. The experimental aspects of the 3He–4He hydrodynamics are treated. The appearance of mutual friction that has long been neglected in this field is discussed, together with the properties of the critical velocities. The phenomenological equations of motion are given. The occurrence of mutual friction is a strong indication that 4He vortices play an important role in 3He–4He hydrodynamics. From the equation of motion of quantized 4He vortices, the observed cubic velocity dependence of the 4He chemical potential difference is explained on purely dimensional grounds. A differential equation is given from which the temperature profile in a cylindrical tube in which 3He flows through superfluid 4He can be calculated

Aspects of tunneling in high-Tc superconductors: WKB revisited

We discuss the merits of WKB for calculating I-V characteristics of high-resistance contacts to high-Tc superconductors. The I-V curves of these contacts (kΩ regime) formed with at least one high-Tc superconductor show a parabolic shape above and below Tc which is remarkably similar for many different type of contacts. This similarity can be attributed to normal electrons tunneling through a trapezoidal potential barrier. Usually the probability of electrons tunneling through such a barrier is calculated using the WKB method. We will show that the barrier width, height and shape as well as densities of states involved do not justify the use of a WKB approach. We therefore advocate the transmission-reflection formalism (TRF), which has the additional advantage of being applicable to a wide range of contacts

Tunnelling characteristics of point contacts with high Tc material

The I-V characteristics of point contacts formed by pressing two pieces of bulk material against each other are considered. One side of the contact consists of a ceramic superconductor. The other side can be either a ceramic superconductor, a normal metal or a classical superconductor. The I-V characteristics of the contacts formed with these different materials often show a remarkable similarity: the I-V characteristics can be very well described by the phenomenological equation IR0 = V{1 + (V/V0)α}, where the exponent α is of the order of one and V0 of the order of 100 mV. The parameters V0 and α determine the shape of the curve. The temperature dependence of the curves is dominated by the temperature dependence of R0. No significant changes are observed at the critical temperature of the superconducting materials. In this paper we show that the observations can be explained by assuming that normal electron tunnelling takes place across a trapezoidal potential barrier