Recent Progress in Thin 3He–4He Films

Anderson, R. H.; Li, David Z.; Miller, Michael David

doi:10.1007/s10909-012-0640-5

Cited by 3 publications

(5 citation statements)

References 47 publications

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“…In the usual manner, [9][10][11] we can introduce a Fourier representation: W σ σ (cos θ ) = ∞ =0 α T (cos θ )W σ σ . In the following, we shall restrict ourselves to including only the = 0 term.…”

Section: A Quasiparticle-quasiparticle Collisionsmentioning

confidence: 99%

“…2 Thin films of normal 3 He have been studied experimentally for many years as prototypical two-dimensional Fermi liquids. [3][4][5][6][7][8] In a recent series of papers [9][10][11] [Li, Anderson, and Miller (LAM)], we have utilized a perturbation-theory-based approach to study the properties of thin, arbitrarily polarized Fermi-liquid films. Perturbation theory was applied to the low-density Fermi gas in three dimensions by Khalatnikov and Abrikosov (KA).…”

Section: Introductionmentioning

confidence: 99%

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Zero sound and first sound in thin arbitrarily polarized Fermi-liquid films

Anderson

Miller

2013

Phys. Rev. B

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We study the propagation and attenuation of zero sound and first sound in thin, arbitrarily polarized Fermi-liquid films. Following Khalatnikov and Abrikosov, we solve Landau's linearized kinetic equation in the relaxation-time approximation for a complex speed of sound. Analytic solutions are obtained in the hydrodynamic and ballistic limits for arbitrary polarization. By solving the collision integral in two dimensions, we find the well-known result that quasiparticle-quasiparticle collisions contribute to the collision frequencies 1/τ σ , with a low-temperature term proportional to T 2 ln (T F σ /T ), where σ = ↑, ↓ is the spin state. If the films are adsorbed to a dynamic substrate, we find additional possible contributions to the collision frequency that come from quasiparticle-phonon interactions. We show, however, that for 3 He thin films, the mismatch between possible maximum values of the Fermi velocity and the substrate speed of sound freezes this contribution out at usual experimental temperatures. Thus, we can conclude that zero sound propagates at absolute zero in this type of adsorbed Fermi-liquid film. By utilizing previous results for the Landau parameters of an arbitrarily polarized 3 He film, we compute numerical solutions for the sound speeds and attenuation in the hydrodynamic and ballistic regimes, thereby studying the transition from first sound to zero sound as a function of temperature.

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Section: A Quasiparticle-quasiparticle Collisionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Zero sound and first sound in thin arbitrarily polarized Fermi-liquid films

Anderson

Miller

2013

Phys. Rev. B

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“…Вивчення термодинамiчних властивостей 4 He сьогоднi проводиться не тiльки для рiдкого [19,18,17] чи газоподiбного стану [20], багато робiт присвяченi i твердому стану [25,24,23,22,21]. Активно вивчається термодинамiка плiвок [28,26,27] та сумiшей [30,29], а також поведiнка 4 He в рiзних середовищах [33,32,31].…”

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Internal energy of the many-boson system with three- and four-particle direct correlations taken into account

Vakarchuk¹,

Hryhorchak²

2015

J. Phys. Stud.

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In this paper we calculate kinetic, potential and full energy with three-and four-particle direct correlations taken into account at wide temperature region on the base of the density matrix of the interacting Bose-particles [I. O. Vakarchuk, O. I. Hryhorchak, Journ. Phys. Stud. 3, 3005 (2009)]. In the low temperature limit the obtained expression for the full energy is equal to the wellknown expression for ground state energy in the approximation of "two sums over the wave vector". The results of this work can be applied for the numeric calculation of the heat capacity of liquid 4 He in order to check the theoretical and experimental results quantatively, especially in the λ-transition region. 1 Вступ Розрахунок внутрiшньої енергiї такої багатобозонної системи, як рiдкий 4 He має доволi давню iсторiю. Великою мiрою це пов'язано iз прагненням теоретично описати λ-подiбний хiд кривої теплоємностi в околi точки фазового переходу. Першi кроки були зробленi в напрямi наближеного обчислення енергiї основного стану i енергетичного спектру цiєї системи ще Боголюбовим [1] майже сiмдесят рокiв тому. Пiзнiше вiн разом iз Зубарєвим у роботi [2] знайшли хвильову функцiю основного стану, а також хвильовi функцiї нижнiх збуджених рiвнiв для слабонеiдеального бозе-газу з допомогою методу колективних змiнних. В границi зникаюче малої взаємодiї енергiя основного стану бозе-системи була вперше коректно знайдена в роботi [3]. Розрахунок проводився з використанням псевдотенцiалу.Дослiдження термодинамiчних функцiй основного стану рiдкого 4 He, зокрема внутрiшньої енергiї, в наближеннi вищому, нiж наближення Боголюбова, було проведено в рядi робiт [4,5,6,7]. Завдяки цим роботам було показано, що врахування три-та чотиричастинкових кореляцiй покращує значення для енергiї основного стану.Трохи згодом в роботах [8,9] з допомогою двочасових температурних функцiй Грiна були отриманi вирази для термодинамiчних функцiй рiдкого 4 He в широкотемпературному дiапазонi. В пiдходi колективних змiнних термодинамiчнi функцiї багатобозонної системи в широкотемпературнiй областi були знайденi в роботi [10]. Розрахунок проводився за допомогою уcереднення з матрицею густини взаємодiючих бозе-частинок в наближеннi парних кореляцiй. Узгодження з експериментальними даними отриманих результатiв для кiнетичної, потенцiальної та повної енергiї є досить добрим [11,12,13,14], однак неповним. Це великою мiрою пов'язано з тим, що для матрицi густини було взято лише наближення парних кореляцiї. Для бiльш точних результатiв потрiбно врахувати три-та чотиричастинковi кореляцiї. Як вiдомо [15,16], їх внесок в значення термодинамiчних функцiй може виявитися досить значним. Врахування внескiв три-i чотиричастинкових кореляцiй у внутрiшню енергiю багатобозонної системи i є предметом цiєї роботи. 1 arXiv:1506.03987v1 [cond-mat.quant-gas]

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“…Finally, we derive the behavior of the the sound speeds and attenuation in the weak-coupling and strong-coupling limits for both approximations. In section 3, using Landau parameters [9][10][11] and quasiparticle lifetimes [3] determined previously, we shall compute sound speeds and attenuation for the system of thin 3 He films at arbitrary polarization for both approximations, and compare their results. In section 4, the conclusion, we shall discuss among other matters the effects on the attenuation and first-sound speeds of using a state-dependent relaxation time approximation for the collision integral.…”

Section: J Stat Mech (2014) P07021mentioning

confidence: 99%

“…In Sec. III, using Landau parameters [7][8][9] and quasiparticle lifetimes 2 determined previously, we shall compute sound speeds and attenuation for the system of thin 3 He films at arbitrary polarization for both among other matters the effects on the attenuation and first-sound speeds of using a statedependent relaxation time approximation for the collision integral. Finally, we shall point out that there are notable advantages of the SBW method especially for systems at non-zero polarization, and also in the zero-sound limit.…”

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confidence: 99%

Competing solutions of Landau’s kinetic equation for zero sound and first sound in thin arbitrarily polarized Fermi-liquid films

Li¹,

Anderson²,

Miller³

et al. 2014

J. Stat. Mech.

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We examine in detail the method introduced by Sanchez-Castro, Bedell, and Wiegers (SBW) to solve Landau's linearized kinetic equation, and compare it with the well-known standard method introduced by Abrikosov and Khalatnikov (AK). The SBW approach, hardly known, differs from AK in the way that moments are taken with respect to the angular functions of the Fourier transformed kinetic equation. We compare the SBW and AK solutions for zero-sound and firstsound propagation speeds and attenuation both analytically in the zero and full polarization limits, and numerically at arbitrary polarization using Landau parameters appropriate for thin 3 He films.We find that the lesser known method not only yields results in close agreement with the standard method, but in most cases does so with far less analytic and computational effort.

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Recent Progress in Thin 3He–4He Films

Cited by 3 publications

References 47 publications

Zero sound and first sound in thin arbitrarily polarized Fermi-liquid films

Zero sound and first sound in thin arbitrarily polarized Fermi-liquid films

Internal energy of the many-boson system with three- and four-particle direct correlations taken into account

Competing solutions of Landau’s kinetic equation for zero sound and first sound in thin arbitrarily polarized Fermi-liquid films

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