Quantum liquids, helium

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... 

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. 

Liquid Helium-4. Quantum mechanics defines two fundamentally different types of particles bosons, which have no unpaired quantum spins, and fermions, which do have unpaired spins. Bosons are governed by Bose-Einstein statistics which, at sufficiently low temperatures, allow the particles to coUect into a low energy quantum level, the so-called Bose-Einstein condensation. Fermions, which include electrons, protons, and neutrons, are governed by Fermi-DHac statistics which forbid any two particles to occupy exactly the same quantum state and thus forbid any analogue of Bose-Einstein condensation. Atoms may be thought of as assembHes of fermions only, but can behave as either fermions or bosons. If the total number of electrons, protons, and neutrons is odd, the atom is a fermion if it is even, the atom is a boson. 

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... 

C. N. Yang, Concept of off-diagonal long-range order and quantum phases of liquid helium and... 

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 most positive aspect was the extraordinary intellectual ferment coupled with open-mindedness which permeated the whole place . There was no distinction between high and low brow, it was all one intellectual adventure. That is how polymers eventually slotted in between quantum mechanics, dislocations, particle physics, liquid helium, design of new optical in-... 

At x = 2 and T < 80K this state of H2 in the gap can be treated as quazy-liquid monolayer . At temperatures of liquid helium molecular hydrogen in the van der Waals gap and layer crystal forms a supperlattice consisting from a layered crystal lattice and a lattice of molecular hydrogen cryocrystal built in its van-der-Waals gap. At x>2 atomic hydrogen begins to incorporate into interstices of the crystal lattice due to quantum-size effects arise in the gap and strong repulsion of between H2 molecules. 

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. 

Although we have explained Bose-Einstein condensation as a characteristic of an ideal or nearly ideal gas, i.e., a system of non-interacting or weakly interacting particles, systems of strongly interacting bosons also undergo similar transitions. Liquid helium-4, as an example, has a phase transition at 2.18 K and below that temperature exhibits very unusual behavior. The properties of helium-4 at and near this phase transition correlate with those of an ideal Bose-Einstein gas at and near its condensation temperature. Although the actual behavior of helium-4 is due to a combination of the effects of quantum statistics and interparticle forces, its qualitative behavior is related to Bose-Einstein condensation. 

Low temperature experiments have shown the formation of hypso intermediates from several species [99,103,105-107]. The study of early photoconversion processes in squid [108], which also involved the evaluation of the relative quantum yields among the four pigments (squid rhodopsin, squid batho-, hypso- and isorhodopsin) showed that hypsorhodopsin is a common intermediate of rhodopsin and isorhodopsin there is no direct conversion between rhodopsin and isorhodopsin bathorhodopsin is not converted directly to hypsorhodopsin and both rhodopsin and isorhodopsin convert more efficiently to bathorhodopsin than to hypsorhodopsin. While a temperature dependence of the relaxation processes from the excited state of rhodopsin, and an assumption that batho could be formed from one of the high vibrational levels of the ground state hypso have been invoked to explain these findings [108], the final clarification of this matter awaits results from subpicosecond laser photolysis experiments at liquid helium temperature. 

Because of its small size (collision diameter 0.20 nm), helium would appear to be a useful probe molecule for the study of uitramicroporous carbons. The experimental difficulty of working at liquid helium temperature (4.2 K) is the main reason why helium has not been widely used for the characterization of porous adsorbents. In addition, since helium has some unusual physical properties, it is to be expected that its adsorptive behaviour will be abnormal and dependent on quantum effects. 

At even lower temperatures, some unusual properties of matter are displayed. Consequently, new experimental and theoretical methods are being created to explore and describe chemistry in these regimes. In order to account for zero-point energy effects and tunneling in simulations, Voth and coworkers developed a quantum molecular dynamics method that they applied to dynamics in solid hydrogen. In liquid helium, superfluidity is displayed in He below its lambda point phase transition at 2.17 K. In the superfluid state, helium s thermal conductivity dramatically increases to 1000 times that of copper, and its bulk viscosity drops effectively to zero. Apkarian and coworkers have recently demonstrated the disappearance of viscosity in superfluid helium on a molecular scale by monitoring the damped oscillations of a 10 A bubble as a function of temperature. These unique properties make superfluid helium an interesting host for chemical dynamics. 

The simple expression or the more complicated ones can be used to describe solvent perturbations on infrared spectra. They do not explain solvent shifts, since their explanation requires a priori calculations of 17, C7",. This kind of calculation demands a detailed quantum mechanical examination of the intricate many-body interactions between the electrons and nuclei of the solvent and those of the dissolved molecule. Such calculations may be just barely possible for, say, a system of hydrogen atoms dissolved in liquid helium. They are not tractable for most solvent-solute systems unless drastic approximations are made. 

Physical details relating to the isomerization of the stilbenes (12) have been determined.A study of the photophysical properties of the styrylstiIbenes (13) has shown that quantum yields for trans-cis isomerism are low from the singlet but high from the triplet state. The photochemical isomerization of the alkene (14) in an ethanol glass affords the trans-isomer with high efficiency even at liquid helium temperatures. Photochemical cis-trans-isomerization of cis-1,2-di-l-naphthylethylene (14) has also been studied in the crystalline phase. A study of the photochemical isomerization of a series of styryl phenanthrenes has been reported. The mechanism of the reaction involved was discussed. ... 

S. Nakajima. Elementary quantum theory of light in liquid helium. Progr. Theor. Phys., 45 353-364 (1971). 

Note Liquid helium has unique thermodynamic properties too complex to be adequately described here. Liquid He I has refr index 1.026,dO.l 25, and is called a quantum fluid because it exhibits atomic properties on a macroscopic scale. Its bp is near absolute zero and viscosity is 25 micropoises (water = 10,000). He II, formed on cooling He I below its transition point, has the unusual property of superfluidity, extremely high thermal conductivity, and viscosity approaching zero. 

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