Creation of superfluid helium rotons by a solid’s phonons incident normal to the interface

We solve the one-dimensional problem of quasiparticles’ transfer through the interface between a solid and superfluid helium. Superfluid helium is treated as a continuous medium with correlations. When a solid’s phonon is incident on the interface, phonons, R⁻ and R⁺rotons are created in helium, and their creation probabilities are obtained. When a quasiparticle of superfluid helium is incident, it can be reflected as any one of the three quasiparticles, and the corresponding probabilities are derived. The R⁻ rotons creation and detection probability are both shown to be small, and this explains why they could not be detected experimentally for a long time.Ми розв’язали одновимірну задачу про проходження квазічастинок через границю між твердим тілом та надплинним гелієм. Надплинний гелій описується як суцільне середовище із кореляціями. Отримано ймовірності того, що фонон твердого тіла при падінні на границю народжує фонон, R⁻ або R⁺ ротони надплинного гелію. Також обчислено ймовірності, з якими відбивається одна з трьох можливих квазічастинок при падінні на границю заданої квазічастинки надплинного гелію. Показано, що ймовірності народження й реєстрації R⁻ ротону малі, і, таким чином, дано пояснення тому, що протягом довгого часу вони не були експериментально зареєстровані.Мы решаем одномерную задачу о прохождении квазичастиц через границу между твердым телом и сверхтекучим гелием. Сверхтекучий гелий описывается как сплошная среда с корреляциями. Получены вероятности того, что фонон твердого тела при падении на границу рождает фонон, R⁻ или R⁺ ротон сверхтекучего гелия. Также вычислены вероятности, с которыми отражается одна из трех возможных квазичастиц при падении на границу заданной квазичастицы сверхтекучего гелия. Показано, что вероятности рождения и регистрации R⁻ ротона малы, и, таким образом, дано объяснение тому, что в течение долгого времени они не были экспериментально зарегистрированы

On the suprathermal distribution in an anisotropic phonon system in He II

The equation that describes the suprathermal distribution of high-energy phonons (h phonons) created in anisotropic phonon systems in superfluid helium is obtained. The solution of this equation enables the derivation of the value of suprathermal ratio S as the ratio of the actual distribution to the Bose-Einstein one, its dependences on the momentum of the h phonons, the anisotropy parameters, and the temperature of the low-energy phonons from which the h phonons are created. We analyze this equation to obtain an estimate of the value of the ratio between the h-phonon number density in anisotropic and isotropic phonon systems and draw conclusions about the dependence of S on the relevant parameters

Collective modes in superfluid helium when there is a relative velocity between the normal and superfluid components

Collective modes are studied in superfluid helium when the normal and superfluid components have a relative velocity w. In this paper the general dispersion relation for first and second sound modes is obtained for arbitrary values of w, and we have found the relationship between the amplitudes of the oscillating variables for first sound. It is shown in a first sound wave, that both temperature and pressure can oscillate, and moreover, the normal fluid velocity can exceed the superfluid velocity in the wave. In the general case of first sound, the normal fluid not only has a velocity component parallel to the wave vector, but also a transverse velocity component. It is shown that when there is only a phonon system in the helium, the amplitude of the temperature oscillation in a first sound wave in an anisotropic phonon system, can exceed that in a second sound wave in an isotropic phonon system, for similar values of the normal fluid density

Evolution of a pulse of noninteracting quasiparticles with dispersion and initial angular width

The evolution of a pulse of noninteracting quasiparticles, caused by their different velocities and angular distribution of momenta, is studied theoretically. Equations are found that describe the shape of the pulse surface at any time. The time of the beginning, end and duration of the density of the quasiparticle energy flux is determined at a general spatial point. The quasiparticle energy density is considered at all times and positions, and it is shown that the region of high energy density, in the middle of the pulse, is equal to the initial energy density under certain conditions. These theoretical results are discussed in relation to experimental data on the evolution of a pulse of noninteracting phonons in superfluid helium

Four and three-phonon scattering in isotropic superfluid helium

We analyse the important role of four-phonon processes (4pp) in isotropic phonon systems of superfluid helium. The matrix elements and the rate of four-phonon processes are calculated. Special consideration is given to the 4pp in the momentum range where three-phonon processes are allowed. In this momentum range, we show that the 4pp scattering rate, at small angles, is equal to the scattering rate due to three-phonon processes. Then we show that the coefficient of first viscosity of superfluid helium is caused by two processes, the first is due to the transverse relaxation caused by many three-phonon processes and the second is due to four-phonon processes. The relaxation time that governs the viscosity is obtained from the sum of the rates from these two processes. The temperature dependence of the attenuation coefficient of a pulse of high-energy phonons in He II, due to scattering with thermal phonons, is also calculated. The theoretical results are compared with experimental data and found to be in good agreement

Phonons, rotons and ripplons at interfaces

We use dispersive hydrodynamics to describe thermal excitations of superfluid helium 4. Dispersion relation of the bulk quasiparticles, phonons and rotons, acts as an input parameter of the theory. Wiener and Hopf method is used to solve nonlocal equations of the fluid in half-space. The dispersion relation helium surface excitations, ripplons, is derived and analyzed; numerical solution reveals its new unusual branch. The same method applies to the description of bulk quasiparticles’ interaction with the interface with a solid. All quasiparticles creation probabilities are derived and weak interaction of rotons with negative dispersion with interfaces is explained.Для описания тепловых возбуждений сверхтекучего гелия 4 используется нелокальная гидродинамика, в которой дисперсионное соотношение является входным параметром. Для решения нелокальных уравнений жидкости в полупространстве используется метод Винера-Хопфа. Вычислено дисперсионное соотношение поверхностных мод гелия, риплонов; численное решение выявляет существование новой ветви. Это же решение описывает взаимодействие фононов и ротонов с границей раздела с твердым телом. Найдены все вероятности рождения квазичастиц и объяснена слабость взаимодействия ротонов с отрицательной дисперсией с границей раздела.Для опису теплових збуджень надплинного гелію 4 використовується нелокальна гідродинаміка, в якій дисперсійне співвідношення є вхідним параметром. Для розв'язку нелокальних рівнянь рідини в півпросторі використовується метод Вінера-Хопфа. Обчислено дисперсійне співвідношення поверхневих мод гелію, ріплонів; чисельний розв'язок виявляє їх нову гілку. Те ж рішення описує взаємодію фононів і ротонів із границею розподілу із твердих тілом. Знайдені всі вірогідності народження квазічастинок та пояснена слабкість взаємодії ротонів з від'ємною дисперсією із границею розподілу

A new ripplon branch in He II

We analyse the dispersion relation of ripplons, on the surface of superfluid helium, using the dispersive hydrodynamics approach and find a new ripplon branch. We obtain analytical equation for the dispersion relation and analytic expressions for the limiting cases. The probabilities of decay of unstable ripplons above the roton gap into rotons are derived. A numerical solution for the ripplon dispersion curve is obtained. The new ripplon branch is found at energies just below the instability point of the bulk spectrum, and is investigated; its stability is discussed

The unusual properties of anisotropic systems of quasiparticles in superfluid ⁴He

We discuss a number of unusual phenomena, which have been discovered recently in anisotropic quasiparticle systems in superfluid ⁴He. These include the creation of high-energy phonons by a pulse of low-energy phonons, the suprathermal distribution of high-energy phonons in long phonon pulses, the mesa shape of the angular distribution of low-energy phonons, the creation of a «hot line» when two-phonon pulses cross. The thermodynamic properties of anisotropic quasiparticle systems of He II are derived for all degrees of anisotropy

The theory of kinetic processes in anisotropic phonon systems

We present a theoretical investigation of the kinetic properties of strongly anisotropic phonon systems. Such systems can be created in superfluid helium by heat pulses. The general expression for the rates of four-phonon processes are obtained. This expression shows that there is an asymmetry between the creation and decay of the high-energy phonons in the anisotropic phonon systems. Solutions of this expression are then considered. The results presented in this work explain the phenomena which are observed in the anisotropic phonon systems and they will stimulate the conception of new experiments

Three-phonon relaxation in isotropic and anisotropic phonon systems of liquid helium at different pressures

Starting from the kinetic equation for phonons in superfluid helium, expressions for the rates of three-phonon scattering in isotropic and anisotropic phonon systems were obtained for different pressures. These expressions are valid in the whole range of energies where three-phonon processes are allowed. Limiting cases were analysed and compared with the results of previous theoretical investigations. The obtained pressure and angular dependence of three phonon scattering rate allows one to explaine of the experimental data on interaction of phonon pulses