Nonlinear third sound in thin superfluid helium films

Summary The nature of nonlinear third-sound waves and the concomitant nonlinear dispersion of a thin superfluid film, subject to the van der Waals interaction due to a substrate, are investigated.

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Riassunto Si studiano la natura delle onde non lineari del terzo suono e la concomitante dispersione di un film sottile superfluido, soggetto all'interazione di Van der Waals dovuta al substrato.

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Резюме Исследуется природа нелинейного третьего звука и сопутствуюзей нелинейной дисперсии в тонкой сверхтекучуй пленке жидкого гелия, испытывающей взаимодствие Ван дер Ваальожкой.

     

The two-fluid model with superfluid entropy

Summary The two-fluid model of liquid helium is generalized to the case that the superfluid fraction has a small entropy content. We present theoretical arguments in favour of such a small superfluid entropy. In the generalized two-fluid model various sound modes of He II are investigated. In a superleak carrying a persistent current the superfluid entropy leads to a new sound mode which we call sixth sound. The relation between the sixth sound and the superfluid entropy is discussed in detail.     

Nucleation of vortices in superfluid helium-4

Summary Nucleation of vortices and strings is studied in superfluid helium in the context of phase transitions in this system. It is shown that the formation of these structures depends on the homotopy groups of the manifold of degenerate condensed states. The subsequent evolution of these structures is investigated and then impact on the superfluid nature of this system is analysed. The cross-section for the scattering of quasi-particles is estimated. This is exploited to find the effect of scatterings on the dynamics of shrinking vortex. During the editorial procedure we came to know that this author deceased.     

Coherent state in the roton region of superfluid helium-4

Summary Coherent states in the roton region of superfluid He⁴ are studied with a view to determine the transition probability from phonon to roton states. These states are formed in such a way that they are found to be identical to those of the angular-momentum states. During the editorial procedure we came to know that this author deceased.     

Goldstone excitation and symmetry-breaking mechanism in superfluid-He4

Summary The form of Goldstone excitation in superfluid He⁴ is envisaged by the formalism of scaling transformation. This is achieved within the framework of symmetry-breaking mechanism which is akin to that of the relativistic quantum field theory. During the editorial procedure we came to know that this author deceased     

Paired-phonon analysis of impurities in bose fluids

Summary The paired-phonon analysis for boson mixtures is employed in conjunction with the hypernetted-chain approximation to study the ground-state properties of an impurity embedded in liquid⁴He. Chemical potentials, volume coefficients and other thermodynamic quantities as well as some of the most interesting optimal correlation functions are calculated for various impurities interacting with the⁴He background atoms via Lennard-Jones potentials of differing strength. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Thermodynamic conditions for a symmetric form of superfluid's equations

Summary Going on with a research started in a previous paper, we examine carefully Putterman's system of superfluid hydrodynamic equations, assuming as viewpoint the theory of quasi-linear hyperbolic symmetric systems with constraints. We prove that such a system is always hyperbolic. It can be put in a symmetric form, provided suitable thermodynamic conditions, ensuring the convexity of the entropy function, hold.

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Riassunto Si approfondisce l'esame, iniziato in un precedente lavoro, del sistema di equazioni idrodinamiche del superfluido di Putterman dal punto di vista della teoria dei sistemi quasi lineari iperbolici simmetrici e con vincoli. Si dimostra che tale sistema è sempre iperbolico e può essere posto in forma simmetrica quando siano soddisfatte opportune condizioni termodinamiche che assicurano la convessità della funzione entropia.

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Резюме Углубляется начатое в одной из предыдущих работ исследование системы гидродинамических уравнений супержидкости Паттермана с точки зрения теории систем квазилинейных гиперболических симметрических и со связями. Доказывается, что такая система является всегда гиперболической и может быть приведена к симметрической форме, когда выполнены соответствующие термодинамические условия, обеспечивающие вьшуклость функции энергии.

     

Microscopic theory of quantum fluid at nonzero temperature. The momentum distribution,liquid-structure factor and ground-state energy of liquid4He

Summary Employing theU-matrix theory in the present form we have presented a microscopic theory of an interactingN-boson system at nonzero temperature. The Hamiltonian includes a term describing the external influence, a term for a two-particle interaction and one pertaining to the dipole-type interaction. To study the ground state of liquid⁴He, only the two-particle interaction is included. Based on scattering data, we have deduced the two-particle potential function. With that we calculate numerically the momentum atT=1.1 K for several sets of parameters. It is shown that the theoretical curves agree well with the observed results. The corresponding liquid-structure-factor curves fit the measured data very well and the best result for the ground-state energy is −7.12K.

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Riassunto Impiegando la teoria della matriceU nella forma presente, abbiamo presentato una teoria microscopica di un sistema interagente diN bosoni a temperatura non nulla. L'hamiltoniana include un termine che descrive l'influenza esterna, un termine per un'interazione a 2 particelle e une che riguarda l'interazione di tipo dipolare. Per studiare lo stato fondamentale dell'⁴He liquido s'include solo l'interazione a 2 particelle. Basandoci su dati di scattering, abbiamo dedotto la funzione potenziale a 2 particelle. Con quella, calcoliamo numericamente la distribuzione dell'impulso aT=1.1K per diversi gruppi di parametri. Si mostra che le curve teoriche sono in buon accordo con i risultati osservati. Le corrispondenti curve del fattore di struttura del liquido si adattano benissimo ai dati misurati e il risultato migliore per l'energia dello stato fondamentale è − 7.12K.

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Резюме Используь теориюU-матрицы, мы предлагаем микроскопическую теорию взаимодеюствующейN-бозонной системы при ненулевых температурах. Гамильтониан включает член, описывающий внешнее влияние, член двух-частичного взаимодействия и член, относящийся к дипольному типу взаимодействия. При исследовании основного состояния шидкого⁴He учитяватся только двух-частичное взаимодействие. Основываясь на данных по рассеянию, мы выводим двух-частичную потенциальную функцию. Мы численно определяем распределение по импульсам приT=1.1K для некоторых систем параметров. Показывается, что теоретические кривые согласуются с наблюденными результатами. Соответст вующий структурный фактор зидкости хорошо согласуется с экспериментальными данными. Полученная величина энергии основного состояния составляет −7.12 K.

     

Dynamics of uniform quantum gases, I: Density and current correlations

A unified approach valid for any wavenumber q, frequency ω, and temperature T is presented for uniform ideal quantum gases allowing for a comprehensive study of number density and particle-current density response functions. Exact analytical expressions are obtained for spectral functions in terms of polylogarithms. Also, particle-number and particle-current static susceptibilities are presented which, for fugacity less than unity, additionally involve Kummer functions. The q- and T-dependent transverse-current static susceptibility is used to show explicitly that current correlations are of long range in a Bose-condensed uniform ideal gas but for bosons at T>T_c and for Fermi and Boltzmann gases at all temperatures these correlations are of short range. Contact repulsive interactions for systems of neutral quantum particles are considered within the random phase approximation. The expressions for particle-number and transverse-current susceptibilities are utilized to discuss the existence or nonexistence of superfluidity in the systems under consideration.     

Lowest breathing mode of bosonic helium clusters

We analyze various microscopic calculations of vibrational frequencies for ⁴He_N clusters, N = 3-728. The lowest breathing frequency with total angular momentum J = 0 varies smoothly as a function of N, with a maximum around N = 50-120. Received 11 July 2001     

Surface tension of liquid helium

We calculated the surface tension of liquid helium using a relation between the condensate fraction and surface tension. The paired-phonon model for the condensate fraction results in calculated surface tension in excellent agreement with experiment at low temperatures.     

UCN production in superfluid helium

Ultra-cold neutrons (UCN) are produced in superfluid helium by single- and multi-phonon excitation. The UCN production rate density R _II via multiphonons can be larger than that by one-phonon excitation R _I being due to the dependence of the incident neutron spectral flux density dφ/dλ on the wavelength λ. Received: 28 March 2002 / Accepted: 19 December 2002 / Published online: 11 March 2003 RID="a" ID="a"e-mail: wschott@e18.physik.tu-muenchen.de RID="b" ID="b"On leave of absence from PNPI, Gatchina, Russia Communicated by T. Walcher     

Surface tension of pure liquid helium isotopes

The effects caused by vapor inhomogeneity over liquid helium are considered. Both pure isotopes have surface levels, whose population increases with temperature T. We separated their contribution to the temperature dependence of surface tension σ₃(T) and σ₄(T) and compared our theoretical results with the results of Japanese experimental works [1–3]. For liquid He³, one has σ₃(T)=σ₃(0)?σ ₃ ^∞ T² at 0.2 K<T<1 K and σ₃(T)=σ₃(0)?α ₃ ⁰ T²exp(?Δ₃/T) at T<0.2 K, with Δ₃≈0.25 K. For liquid He⁴, σ₄(T)=σ₄(0)?AT^7/3? α ₄ ⁰ T²exp(?Δ₄/T) at T<2 K, where A is the Atkins constant and Δ₄≈4 K. The parameters α ₃ ⁰ , α ₃ ^∞ , and α ₄ ⁰ depend on the fluid properties.     

Thermodynamic inequalities of superfluid helium

We have obtained the thermodynamic inequalities warranting the stability of the equilibrium states of superfluid helium.     

Evolution from BCS superconductivity to Bose condensation: analytic results for the crossover in three dimensions

We provide an analytic solution for the mean-field equations and for the relevant physical quantities at the Gaussian level, in terms of the complete elliptic integrals of the first and second kinds, for the crossover problem from BCS superconductivity to Bose-Einstein condensation of a three-dimensional system of free fermions interacting via an attractive contact potential at zero temperature. This analytic solution enables us to follow the evolution between the two limits in a particularly simple and transparent way, as well as to verify the absence of singularities during the evolution. Received: 9 May 1997 / Revised: 4 August 1997 / Accepted: 6 November 1997     

Electron impact ionization of thymine clusters embedded in superfluid helium droplets

Embedding molecules in helium clusters has become a powerful technique for the preparation of cold targets for spectroscopy experiments, as well as for the assembly of complex, fragile molecular species. We have recently developed a helium cluster source and a pick-up cell to produce neutral beams of doped helium droplets, to be used as targets in studies on electron collisions with molecules of biological relevance. In the present work we present the results of a series of experiments on electron-impact ionization of helium clusters doped with thymine and 1-methylthymine, where several interesting phenomena were observed, i.e., (i) electron impact ionization of molecular clusters inside the helium droplets leads predominantly to protonated clusters; (ii) the appearance energies are close to the ionization threshold of the helium atom but ionization efficiency curves in addition extend down by several eV; (iii) ionized molecular clusters can undergo metastable decay via the loss of one neutral monomer.     

Neutron-detected tomography of impurity-seeded superfluid helium

We describe a neutron radiography technique that can be used to map the distribution of 3He impurities in liquid 4He, providing direct and quantitative access to underlying transport processes. Images reflecting finite normal- and superfluid-component 4He velocity fields are presented.     

Anisotropic system of quasiparticles in superfluid helium

The thermodynamic properties of anisotropic quasiparticle systems of He II are considered for all degrees of anisotropy. It is shown that the thermodynamic functions of a strongly anisotropic phonon-roton system are mainly determined by rotons at all temperatures. Analytical expressions for the roton thermodynamic functions are obtained for all degrees of anisotropy. The maximum anisotropy is limited by the criterion for thermodynamic stability, which is here derived for the whole temperature range.