On the superfluidity of classical liquid in nanotubes,III

Solutions of equations in variations presented in the previous paper are refined.     

On the superfluidity of classical liquid in nanotubes,I. Case of even number of neutrons

We show that the superfluidity effect in nanotubes arises in a classical liquid (regarded as the limit as h → 0 of the quantum liquid) and involves not only the Bogolyubov “running waves,” but also a “standing wave.” This is obtained from the variational equations in the context of ultrasecondary quantization. It is stressed that the “atomic” size of the nanotube plays a crucial role in the phenomena.     

On the superfluidity of classical liquid in nanotubes,II. Case of odd number of neutrons

We show that the superfluidity effect in nanotubes arises in a classical liquid (regarded as the limit as h → 0 of the quantum liquid) and involves not only the Bogolyubov “running waves,” but also a “standing wave.” This is obtained from the variational equations in the context of ultrasecondary quantization. We consider cases of Bose and Fermi liquids.     

On the theory of superfluidity

We investigate the properties of dispersion spectra of one-dimensional periodic Bose systems with repulsive interparticle interactions. These systems with sufficient large interactions can support metastable supercurrent states, which correspond to the local minima of the dispersion spectra at non-zero momenta. The existence of local minima in the spectra and the energy barriers, which separate the minima, can be explained in terms of Bose exchange symmetry. We extend our study to the case of higher dimensional Bose systems. We suggest that superfluidity could be understood as a Bose exchange effect.     

On the mechanisms of superfluidity in atomic nuclei

A system of equations is obtained for the Cooper gap in nuclei. The system takes two mechanisms of superfluidity into account in an approximation quadratic in the phonon-production amplitude: a Bardeen-Cooper-Schrieffer (BCS)-type mechanism and a quasiparticle-phonon mechanism. These equations are solved for ¹²⁰Sn in a realistic approximation. If the simple procedures proposed are used to determine the new particle-particle interaction and to estimate the average effect, then the contribution of the quasiparticle-phonon mechanism to the observed width of the pairing gap is 26% and the BCS-type contribution is 74%. This means that at least in semimagic nuclei pairing is of a mixed nature — it is due to the two indicated mechanisms, the first being mainly a surface mechanism and the second mainly a volume mechanism. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 10, 669–674 (25 May 1999)     

Spectroscopic evidence for superfluidity in liquid He droplets

A beam of liquid He _N droplets (N≈5000) is prepared by a cryogenic free jet expansion, doped with single molecules and studied via laser spectroscopy. The spectra consist of sharp lines (Δν?0.003–0.1 cm^?1) and show rotational structure (for SF₆), providing the first information on the droplet temperature, which is 0.37 K for⁴He _N and 0.14 K for³He _N . The rotational constants give information on the microscopic interaction of the molecule with the He environment. Each of the sharp vibronic lines of the elecronic S₁←S₀ transition in glyoxal (C₂O₂H₂) is accompanied by a phonon sideband, showing a distinct gap followed by a sharp peak at the roton energy (8.1 K) and a second weaker maxon peak followed by a broad multiphonon wing. These provide the first evidence for superfluidity in⁴He _N predicted theoretically.     

Kinetic theory of classical liquids. IV. Numerical results on the density fluctuations in liquid rubidium

Based on a general theory given in an earlier paper, we present results of extensive calculations of the dynamical structure factor S(qω) for liquid rubidium. Detailed comparisons are made with experimental and molecular dynamics data. Comparisons are also made with earlier calculations for liquid argon, based on the same theory.     

On the role of the uncertainty principle in superconductivity and superfluidity

We discuss the general interplay between the uncertainty principle and the onset of dissipationless transport phenomena such as superconductivity and superfluidity. We argue that these phenomena are possible because of the robustness of many-body quantum states with respect to the external environment, which is directly related to the uncertainty principle as applied to coordinates and momenta of the carriers. In the case of superconductors, this implies relationships between macroscopic quantities such as critical temperature and critical magnetic field, and microscopic quantities such as the amount of spatial squeezing of a Cooper pair and its correlation time. In the case of ultracold atomic Fermi gases, this should be paralleled by a connection between the critical temperature for the onset of superfluidity and the corresponding critical velocity. Tests of this conjecture are finally sketched with particular regard to the understanding of the behaviour of superconductors under external pressures or mesoscopic superconductors, and the possibility to mimic these effects in ultracold atomic Fermi gases using Feshbach resonances and atomic squeezed states.     

Correlation entropy in a classical liquid

A statistical formula is presented for the entropy of a classical monatomic liquid, including effects of multiparticle correlations. This theory applies to the liquid state, which has small density fluctuations, and which is distinct from the gas state. The statistical entropy is found to agree well with the thermodynamic entropy for liquid sodium at temperatures from 378 to 823 K.     

Narrow-gap Luttinger liquid in carbon nanotubes

Electron interactions reinforce minigaps induced in metallic nanotubes by an external field and turn the gap field dependence into a universal power law. An exactly solvable Gross-Neveau model with an SU(4) symmetry is derived for neutral excitations near half filling. Charge excitations, described by a sine-Gordon perturbation of Luttinger liquid theory, are composite solitons formed by the charged and neutral fields with two separate length scales. Charge compressibility at finite density, evaluated in terms of intersoliton interaction, exhibits a crossover from overlapping to nonoverlapping soliton state. Implications for the Coulomb blockade measurements are discussed.     

Solitons,Bose-Einstein condensation,and superfluidity in helium II

The analytic form of a wave propagating with a constant velocity and a permanent profile is inferrred for a weakly interacting Bose gas, using an exact (rather than asymptotic) solution of the field equation of the self-consistent Hartree model. The significance of this approach is indicated, especially when realistic interatomic potentials are used. In addition, the general relation between solitons and Bose-Einstein condensation is underlined by invoking the profound insight recently acquired in studies of the quantum liquids involved in the living state. It is concluded that solitons may occur in He II, and may play a significant role in the phenomenon of superfluidity.On leave of absence from the Department of Physics, Universidad Simón Bolívar, Caracas, Venezuela. Also at Instituto Internacional de Estudios Avanzados, Ap. 17606 Caracas 1015-A.     

超流研究的历史回顾

回顾了超流发现的历史，介绍了超流的一些现象、理论以及新近的研究结果。强调指出超流与超导一样是一种宏观量子现象。     

He superfluidity in the presence of aerogel

Aerogels introduce disorder into the p-wave-paired superfluid ³He and suppress T_c. Quantifiable (by small angle X-ray scattering) differences in the long-range structure of two identical density aerogels are primarily responsible for their different transition temperatures. We also demonstrate that alteration of the short-range correlations by the addition of ⁴He does not strongly affect T_c. Acoustic measurements of the fast and slow modes of ³He in aerogel are described. These can be used to explore the superfluid component. We also outline future prospects.     

Stability analysis of the Luttinger liquid fixed-point in metallic nanotubes

We study the stability of a Luttinger liquid in a metallic single-walled nanotube against generic backscattering and Umklapp perturbations. Analizing the renormalization group equations we identify nontrivial particular solutions that lay in the same universality class of the Luttinger liquid. We describe in detail the mechanism of instability generation in that electron liquid and discuss under which conditions it governs the physical properties in the presence of low frequency or temperature cutoffs.     

On the indistinguishability of classical particles

If no property of a system of many particles discriminates among the particles, they are said to be indistinguishable. This indistinguishability is equivalent to the requirement that the many-particle distribution function and all of the dynamic functions for the system be symmetric. The indistinguishability defined in terms of the discrete symmetry of many-particle functions cannot change in the continuous classical statistical limit in which the number density n and the reciprocal temperature become small. Thus, microscopic particles like electrons must remain indistinguishable in the classical statistical limit although their behavior can be calculated as if they move following the classical laws of motion. In the classical mechanical limit in which quantum cells of volume (2)³ are reduced to points in the phase space, the partition functionTr{exp(–) for N identical bosons (fermions) approaches (2)^–3N(N!) ... d³r₁ d³p₁ ... d³r_N d³p_N exp(–H). The two factors, (2)^–3N and (N!)^–1, which are often added in anad hoc manner in many books on statistical mechanics, are thus derived from the first principles. The criterion of the classical statistical approximation is that the thermal de Broglie wavelength be much shorter than the interparticle distance irrespective of any translation-invariant interparticle interaction. A new derivation of the Maxwell velocity distribution from Boltzmann's principle is given with the assumption of indistinguishable classical particles.