# In Print

## Povtornoe poyavlenie anomal’nykh voln v optike.

16 February in 11:30

P.G. Grinevich, P.M. Santini

Ya khotel by rasskazat’ o nashei rabote s eksperimentatorami iz Rimskogo universiteta o nablyudenii povtornoi generatsii anomal’noi volny v opticheskom kristalle.

## Manufacturing of holes in supported films: transition from beam dependent to shock dependent radius of hole as absorbed energy increases

9 February in 11:30

N. Inogamov, V. Shepelev, P. Danilov, A. Kuchmizhak

Thin films on supporting substrates are important class of laser targets for surface nanomodification for, e.g., plasmonic or sensoric applications. There are many papers devoted to this problem. But all of them are concentrated on dynamics of a film, paying small attention to substrate. In those papers the substrate is just an object absorbing the first shock. Here we present another point of view directed namely onto dynamics of a substrate. We consider (i) generation of a shock wave (SW) in a supporting substrate, (this si generation by impact of a film/support contact on supporting condensed medium); (ii) transition from 1D to 2D propagation of SW; (iii) we analyze lateral propagation of the SW along a film/support contact; and (iv) we calculate pressure in the compressed layer behind the SW decaying with time. This positive pressure acting from substrate to the film accelerates the film in direction to vacuum. Above some threshold, velocity of accelerated film is enough to separate the film from support. In the cases with large energy absorbed by a film, the circle of separation is significantly wider than the circle of high heating around the focal laser spot on film surface. Absorbed laser heat exponentially decays around an irradiated spot $F = Fc\, exp(-r^2/RL^2)$, where RL is radius of laser Gaussian beam. While the law of decay for the 2D SW in substrate is the power law. Therefore in the mentioned cases of powerful laser action, the edge of a separation circle is driven by SW in support.
Illustrative materials are posted on youtube:

Video 1
This movie shows the map of evolution of density field. The gold film is the narrow horizontal strip, "vacuum" is above, supporting substrate is below the strip

Video 2
This is the pressure map. We see two shocks: one above and second below the film. Don't pay attention to the shock above, i.e. to shock in "vacuum", because in our simulation we cannot use real vacuum rho=0, p=0. Therefore we use low density media in place of vacuum. Pay attention to the left and right wings of crescent type shock propagating down. These wings pass along the film. Shock pressure in the wings accelerate the film up thus separating it from the silica substrate.

doc

## Differential Poisson's ratio of a crystalline two-dimensional membrane

26 January in 11:30

I.S. Burmistrov

We compute analytically the differential Poisson's ratio of a suspended two-dimensional crystalline membrane embedded into a space of large dimensionality $d \gg 1$. We demonstrate that, in the regime of anomalous Hooke's law, the differential Poisson's ratio approaches a universal value determined solely by the spatial dimensionality $d_c$, with a power-law expansion $\nu = -1/3 + 0.016/d_c + O(1/d_c^2)$, where $d_c=d-2$. Thus, the value $-1/3$ predicted in previous literature holds only in the limit $d_c\to \infty$.

## Mesoscopic Stoner instability: Suppression by tunneling to a reservoir

19 January in 11:30

I.S. Burmistrov

We derive the generalized Ambegaokar-Eckern-Schon action which governs the dynamics of the charge and spin degrees of freedom for the quantum dot described by the universal Hamiltonian and tunnel coupled to a reservoir. Contrary to previous works, we derive this dissipative action without the following assumptions (i) the absolute value of the spin is not a ected by the tunneling coupling to a reservoir and (ii) the spin rotates slowly such that the adiabatic approximation holds. We use the derived dissipative action for analysis of stability of the mesoscopic Stoner phenomenon with respect to the electron tunneling to a reservoir. We nd that at nite temperature the electron tunneling suppresses the mesoscopic Stoner instability at tunneling conductance which depends on temperature. At zero temperature we predict the existence of the quantum phase transition between the mesoscopic Stoner phase and the paramagnetic phase.

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

22 December 2017 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.

## Poverkhnostnye mikrochastitsy v zhidkom gelii. Kvantovyi zakon Arkhimeda

15 December 2017 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.

## Effektivizatsiya konechnozonnykh formul, opisyvayushchikh modulyatsionnuyu nestabil’nost’ v Nelineinom uravnenii Shridingera - sluchai N neustoichivykh mod.

8 December 2017 in 11:30

P.G. Grinevich, P.M. Santini

Dlya sluchaya proizvol’nogo chisla neustoichivykh mod my yavno s tochnost’yu do popravok vysshego poryadka vychislyaem vse velichiny, vkhodyashchie v konechnozonnye resheniya, chto privodit k otvetu v elementarnykh funktsiyakh (raznomu dlya raznykh oblastei x,t-ploskosti).

## Helical edge transport in the presence of anisotropic magnetic impurity

17 November 2017 in 11:30

P. D. Kurilovich, V. D. Kurilovich, I. S. Burmistrov, M. Goldstein

We consider the effects of electron scattering on a quantum magnetic impurity on the current-voltage characteristics of the helical edge of a two-dimensional topological insulator. We compute the backscattering contribution to the current along the edge for a general form of the exchange interaction matrix and arbitrary value of the magnetic impurity spin. We find that the differential conductance might be a non-monotonous function of the voltage with several extrema. Effects of magnetic anisotropy for the impurity are considered.

## Explicit computation of the Calabi-Yau moduli space geometry

10 November 2017 in 11:30

K. Aleshkin, A. Belavin

Knowledge of the CY moduli space geometry is crucial to determine Low energy Lagranzhian in superstring compactifications. For hypersurfaces in projective spaces explicit computations were done only in a few cases. In the talk I will explain a recently proposed method, which allows to perform explicit computations easily and in the more general cases. I'l show how to apply this method to computation the 101-dimensional moduli space of Quintic threefold .

## Cooper pair splitting in ballistic ferromagnetic SQUIDs

27 October 2017 in 11:30

P.L. Stroganov, Ya.V. Fominov

We consider ballistic SQUIDs with spin filtering inside half-metallic ferromagnetic arms. A singlet Cooper pair cannot pass through an arm in this case, so the Josephson current is entirely due to the Cooper pair splitting, with two electrons going to different interferometer arms. In order to elucidate the mechanisms of Josephson transport due to split Cooper pairs, we assume the arms to be single-channel wires in the short-junction limit. Different geometries of the system (determined by the length of the arms and the phases acquired by quasiparticles during splitting between the arms) lead to qualitatively different behavior of the SQUID characteristics (the Andreev levels, the current-phase relation, and the critical Josephson current) as a function of two control parameters, the external magnetic flux and misorientation of the two spin filters. The current-phase relation can change its amplitude and shape, in particular, turning to a pi-junction form or acquiring additional zero crossings. The critical current can become a nonmonotonic function of the misorientation of the spin filters and the magnetic flux (on half of period). Periodicity with respect to the magnetic flux is doubled, in comparison to conventional SQUIDs.