Russian Academy of Sciences

Landau Institute for Theoretical Physics

Seminars at the Landau Institute scientific council

Poverkhnostnye mikrochastitsy v zhidkom gelii. Kvantovyi zakon Arkhimeda

15 December, today in 11:30

А.М. Дюгаев

Issledovany otkloneniya ot zakona Arkhimeda dlya sfericheskikh chastits radiusa R0, vypolnennykh iz molekulyarnogo vodoroda u poverkhnosti zhidkogo He4. Klassicheskii zakon Arkhimeda imeet mesto, esli R0 bol’she kapillyarnoi dliny geliya Lk ≅ 500 µm. Pri etom velichina vozvysheniya chastitsy nad zhidkost’yu h+ ~ R0. V oblasti 30 < R0 < 500 µm sila Arkhimeda podavlyaetsya siloi poverkhnostnogo natyazheniya i h+~ R03⁄Lk2. Pri R0 < 30 µm chastitsa nakhoditsya pod poverkhnost’yu zhidkosti. Zdes’ sila Arkhimeda konkuriruet s siloi Kazimira, kotoraya ottalkivaet chastitsu ot poverkhnosti vglub’ zhidkosti. Rasstoyanie chastitsy do poverkhnosti h- ~ Rs5⁄3⁄R02⁄3, esli R0 > Rs. Zdes’ Rs – masshtab, nabrannyi, v osnovnom, iz mirovykh postoyannykh, Rs ≈ (ℏc/ϱg)1⁄5 ≈ 1µm. (ℏ - postoyannaya Planka, c - skorost’ sveta, g – uskorenie svobodnogo padeniya, ϱHe – plotnost’ geliya). Dlya ochen’ malen’kikh chastits ( R0 < Rs) rasstoyanie do poverkhnosti zhidkosti h- ne zavisit ot ikh razmera h- = Rs.

Medlennye ostsillyatsii magnitosoprotivleniya v vysokotemperaturnykh sverkhprovodnikakh YBCO: ikh chastota daet ploshchad’ karmanov poverkhnosti Fermi ili velichinu mezhsloevogo pereskoka elektronov

15 December, today in 11:30

P.D. Grigor’ev

Nablyudaemye magnitnykh kvantovye ostsillyatsii (MKO) v vysokotemperaturnykh sverkhprovodnikakh YBCO (YBa2Cu3O6 +x i YBa2Cu4O8) imeyut dovol’no neobychnyi sostav garmonik. Preobrazovanie Fur’e etikh MKO soderzhit tri blizkikh ravnoudalennykh pika pri dostatochno nizkikh chastotakh ~530T i 530+-90T, chto sootvetstvuet okolo 2% zony Brillyuena, prichem tsentral’nyi pik imeet amplitudu v ~2 raza vyshe, chem dva pika s kazhdoi iz storon. Obshcheprinyatoe ob’yasnenie takikh kvantovykh ostsillyatsii predpolagaet perestroiku iskhodnoi bol’shoi poverkhnosti Fermi iz-za fluktuiruyushchei volny zaryadovoi plotnosti (VZP). Odnako takoe ob’yasnenie imeet ryad sushchestvennykh nedostatkov. Naprimer, ono predpolagaet takzhe nabor drugikh blizkikh chastot MKO, kotorye ne nablyudayutsya eksperimental’no. Krome etogo, v etoi modeli nablyudaemye chastoty MKO dolzhny sil’no zaviset’ ot urovnya dopirovaniya, chto takzhe ne nablyudaetsya v eksperimente. My predlagaem al’ternativnuyu interpretatsiyu nablyudaemykh magnitnykh ostsillyatsii v YBCO, kotoraya dovol’no estestvennym obrazom ob’yasnyaet nablyudaemuyu kartinu bez dopolnitel’nykh podgonochnykh parametrov. Eta predlagaemaya model’ MKO uchityvaet dvukhsloinuyu kristallicheskuyu strukturu YBCO i vklyuchaet sootvetstvuyushchee rasshcheplenie elektronnogo spektra i dispersiyu elektronov perpendikulyarno provodyashchim sloyam. Pri etom osnovnaya nablyudaemaya chastota ~530T sootvetstvuet velichine bisloinogo rasshchepleniya, a ne malomu karmanu poverkhnosti Fermi (PF), vyzvannomu ee perestroikoi iz-za VZP. Takie "medlennye" magnitnye ostsillyatsii poyavlyayutsya dazhe bez perestroiki PF i pochti ne zavisyat ot urovnya dopirovaniya. Krome togo, v otlichie ot obychnykh MKO, eti "medlennye" ostsillyatsii ne podavlyayutsya dlinnovolnovoi prostranstvennoi neodnorodnost’yu obraztsa, tipichnoi dlya VTSP kristallov i privodyashchei k razmytiyu urovnya Fermi vdol’ obraztsa. Poetomu oni legche nablyudayutsya v eksperimente. Predlozhennaya interpretatsiya pozvolyaet razreshit’ «protivorechie» dannykh ARPES i MKO, a takzhe ob’yasnyaet nekotorye drugie osobennosti nablyudaemykh MKO v YBCO, kotorye dovol’no slozhno ob’yasnit’ stsenariem perestroiki PF vyzvannoi VZP.

Exact solutions for nonlinear development of Kelvin-Helmholtz instability for counterflow of superfluid and normal components of Helium II

22 December in 11:30

Pavel M. Lushnikov and Nikolay M. Zubarev

A relative motion of the normal and superfluid components of Helium II results in Kelvin-Helmholtz instability (KHI) at their common free surface. We found the exact solutions for the nonlinear stage of the development of that instability. Contrary to the usual KHI of the interface between two fluids, the dynamics of Helium II free surface allows decoupling of the governing equations with their reduction to the Laplace growth equation which has the infinite number of exact solutions including the formation of sharp cusps at free surface in a finite time.

Seminars are held on Fridays in the conference hall of Landau Institute for Theoretical Physics in Chernogolovka, beginning at 11:30.

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