Quantum liquid

Pines, D. and Nozieres, P. (1966) The Theory of Quantum Liquids, Benjamin, Reading, Mass. 

Let us first consider physical systems, in which quantum effects might be important, in order of decreasing effect. The prototype quantum liquid is liquid helium with its well-known exotic properties. This liquid requires a full quantum... 

Table 2.2 clearly shows the strong differences between the two quantum liquids . It is worth noting that both isotopes have very low boiling and critical temperatures and a low density (the molar volume is more than the double than that corresponding to a classic liquid). Figure 2.4 shows the p-T phase diagrams besides the presence of a superfluid phases it is to be noted for both isotopes the missing of a triple point. 

D. Pines and P. Nozieres. The Theory of Quantum Liquids. Vol. I. New-York Benjamin, 1966. 

It is known that the classical molecular field theory discussed above is not suited for describing a close vicinity of the critical point. Experimentally obtained values of the parameter (3 (called the critical exponent) are essentially less than (3q = 1/2 predicted by the mean-field theory. On the other hand, the experimental values of (3 = 0.33-0.34 turn out to be universal for many different systems (except for quantum liquid-helium where (3... 

Although mi completely satisfactory single theory of liquid helium has yet been formulated, one can say that most of the remarkable properties are qualitatively understood and are due 10 Ihe predominance nl quantum effects, including the dillerence in the statistics of the even and odd isotopes. Titus helium is the one example in nature of a quantum liquid, ail olher liquids showing only minor deviations from classical behavior. 

The SAPT potential for the He-C02 complex was also used in the calculations of the rovibrational spectra of the He -CC clusters 366. High resolution experimental data were also reported in this paper. Comparison of the theoretical and experimental effective rotational constants B and other spectroscopic characteristics as functions of the cluster size N is shown on Figure 1-9. Again, the agreement between the theory and experiment is impressive showing that theory can describe with trust spectroscopic characteristics of small clusters He -CO This especially true for the effective rotational constant and the frequency shift of the C02 vibration due to the solvation by the helium atoms. One may note in passing that the clusters HeA,-C02 with the number of helium atoms N around 20 do not exhibit all the properties of the C02 molecule in the first solvation shell of the (quantum) liquid helium at very low temperatures. 

Superfluid. Liquid helium (more precisely the 2He4 isotope) has a "lambda point" transition temperature of 2.17 K, below which it becomes a superfluid ("Helium-II"). This superfluid, or "quantum liquid," stays liquid down to 0 K, has zero viscosity, and has transport properties that are dominated by quantized vortices thus 2He4 never freezes at lbar. Above 25.2 bar the superfluid state ceases, and 2He4 can then freeze at 1K. The other natural helium isotope, 2He3, boils at 3.19 K and becomes a superfluid only below 0.002491 K. 

To reach temperatures below 4.2 K, one can partially evacuate a He reservoir using a high-capacity vacuum pump this works down to the lambda point of liquid He (2.1768 K) below this temperature the 2He4 turns into a superfluid quantum liquid, which cannot be cooled any further. The minority isotope, 2He3 remains a normal fluid down to 0.002491 K this allows cooling down to about 1K. 

The consequence of Eq. (5.2.19) is that if T — 0 K, as all systems become solids (except for the "quantum liquid" or superfluid 2He4 at 1 atm hydrostatic pressure), and if in the resulting solids there is perfect order (except for the quantum-mechanically mandated zero-point vibration for molecules), then > 1 and S > 0. This, again, is the Third Law of Thermodynamics. 

Noziferes P. and Pines D., The Theory of Quantum Liquids, (Perseus, Cambridge, Massachusetts, 1999). 

The LDM was extended [128] to incorporate quantum effects advancing a quantum hquid drop model (QLDM). The relation between the discrete dispersion curves for elementary excitation and the density fluctuations in quantum clusters was established in an elegant work [128] based on the hydrodynamic form of the Hamiltonian for a Bose quantum liquid [Eq. (14)]. The procedure [128] was based on the expansion of the Hamiltonian //(p) and was second-order in density fluctuations 5p(r) setting the boundary conditions 8p(r = Rq) = 0, and on the expansion of 5p(r), v(r), and < )(r, E) = 8p(r)8p(r ) in spherical Bessel functions. The discrete dispersion curves for Gfmn kin) Were obtained in the form [128]... 

P. Nozieres and D. Pines, The Theory of Quantum Liquids (Addison Wesley, New York, revised printing 1989). 

Such decoupling in the liquid may be strictly justified only in the long-wave approximation.In this sense, such a procedure is justified for the macroscopic description. However, one should remember that this is the correct method in a number of cases also for short wavelengths. For example, this is the case for phonons in solids. In other cases, such as the electron gas in metals (plasmons), acoustic phonons in quantum liquids and so on, this decoupling may be considered as the self-consistent field method or the random phase approximation (the analog of the superposition approximation in the classical theory of liquids). 

Collisions (Nuclear physics) 2. Low temperatures. 3. Quantum solids. 4. Quantum liquids. 5. Coidgases. 6. Molecular dynamics. I. Krems, Roman. II. Friedrich, Bretislav. 

---