# In Print

## World population and climate variations

11 May in 11:30

Alexey Byalko

Few sets of the world population data are analyzed from 1 AD to 2015 together with temperature variations of the North Hemisphere from 1 AD to 1979. Possible data errors are evaluated. Hyperbolical behavior of the world population was evaluated by approximation of its inverse function. The population index is introduced as the relative difference between inverse numerical data and its parabolic approximation. The index occurs to be a bounded and an average zero function with the nearly uniform error level. He describes relative variations of the world population in the past. The population index is compared with North Hemisphere temperature variations. However, the population response to temperature variations occurred with a significant delay of about 100 years. Possible reasons for such a correlation are discussed against the background of known historical events and analyzed by the Hurst method. The historical analysis and the found climate—population correlations give a principal possibility to forecast the world population behavior approximately up to year 2080.

## Eukaryotic cell polarity and protein sorting

27 April in 11:30

Andrea Gamba, Politecnico di Torino

I will review some of the biophysical processes that allow eukaryotic cells to break their native symmetry and polarize in order to provide adequate responses to signals and properly adapt to the environment. An essential part of the process is the incessant spatial reorganization of membrane-bound proteins due to the action of reinforcing biochemical feedback loops that contrast the homogenizing effect of diffusion. A second component is the coupling of protein and lipid dynamics: protein crowding induces the bending of lipid membranes and the nucleation of small lipid vesicles enriched in specific molecular factors destined to be targeted to appropriate destinations. This mechanism leads to an incessant distillation process controlled by the strength of protein-protein interactions. A phenomenological theory of the process can be developed, predicting the existence of an optimal distillation regime characterized by simple scaling laws. Experiments suggest that living cells work close to this optimal regime, likely as the result of evolutionary pressure.

## Dielectric response of Anderson and pseudogapped insulators

27 April in 11:30

__M.V. Feigel'man__, D.A. Ivanov, E. Cuevas

Using a combination of analytic and numerical methods, we study the polarizability of a (non-interacting) Anderson insulator in one, two, and three dimensions and demonstrate that, in a wide range of parameters, it scales proportionally to the square of the localization length, contrary to earlier claims based on the effective-medium approximation. We further analyze the effect of electron-electron interactions on the dielectric constant in quasi-1D, quasi-2D and 3D materials with large localization length, including both Coulomb repulsion and phonon-mediated attraction. The phonon-mediated attraction (in the pseudogapped state on the insulating side of the Superconductor-Insulator Transition) produces a correction to the dielectric constant, which may be detected from a linear response of a dielectric constant to an external magnetic field.

## Some Aspects of Diquarks as seen by String Theory

20 April in 11:30

Oleg Andreev

I will discuss a few aspects of diquarks in QCD from the viewpoint of a 5-dimensional effective string theory.

## Magnetic oscillations of in-plane conductivity in quasi-two-dimensional metals

13 April in 11:30

Pavel Grigor’ev

We develop the theory of transverse magnetoresistance in layered quasi-two-dimensional metals. Using the Kubo formula and harmonic expansion we calculate intralayer conductivity in a magnetic field perpendicular to conducting layers. The analytical expressions for the amplitudes and phases of magnetic quantum oscillations (MQO) and of the so-called slow oscillations (SlO) are derived and applied to analyze their behavior as a function of several parameters: magnetic field strength, interlayer transfer integral and the Landau-level width. Both the MQO and SlO of intralayer and interlayer conductivity have approximately opposite phase in weak magnetic field and the same phase in strong field. The amplitude of SlO of intralayer conductivity changes sign at $\omega_c\tau\approx\sqrt{3}$. There are several other qualitative differences between magnetic oscillations of in-plane and out-of-plane conductivity. The results obtained are useful to analyze experimental data on magnetoresistance oscillations in various strongly anisotropic quasi-2D metals.

## Long-lived quantum vortex knots

6 April in 11:30

V.P. Ruban

In the bulk of a superfluid, besides well-known and experimentally observed quantum vortex rings, theoretically there can exist (developing in time) also solitary topologically non-trivial excitations as vortex knots [1-3]. The simplest of them are torus knots ${\cal T}_{p,q}$, where $p$ and $q$ are co-prime integers, while parameters of torus are the toroidal (large) radius $R_0$ and the poloidal (small) radius $r_0$, both sizes being large in comparison with a width of quantum vortex core $\xi$. It was believed on the basis of previously obtained numerical results that such knots are unstable and they reconnect during just a few typical times, traveling a distance of several $R_0$ (the lifetime is somewhat longer for smaller ratios $B_0=r_0/R_0$). The mentioned results were obtained for not too large ratios $R_0/\xi\lesssim 20$, and with a very coarse step (about 0.1) on parameter $B_0$. In this work it was numerically found that actually the situation is much more complicated and interesting. The dynamics of trefoil knot ${\cal T}_{2,3}$ was accurately simulated within a regularized Biot-Savart law using a small step on $B_0$. At fixed values of parameter $\Lambda=\log(R_0/\xi)$, the dependence of knot lifetime on parameter $B_0$ turned out to be drastically non-monotonic on sufficiently small $B_0\lesssim 0.2$. Moreover, at $\Lambda\gtrsim 3$ quasi-stability bands appear, where vortex knot remains nearly unchanged for many dozens and even hundreds of typical times [4]. Qualitatively similar results take place also for ${\cal T}_{3,2}$ [4], for some other knots (${\cal T}_{2,5}$, ${\cal T}_{2,7}$, ${\cal T}_{3,4}$, ${\cal T}_{3,5}$, ${\cal T}_{3,7}$), and for unknots ${\cal U}_{2,1}$ [5]. These observations essentially enrich our knowledge about dynamics of vortex filaments. References: [1] D. Proment, M. Onorato, and C. F. Barenghi, "Vortex knots in a Bose-Einstein condensate", Phys. Rev. E 85, 036306 (2012). [2] D. Proment, M. Onorato, and C. F. Barenghi, "Torus quantum vortex knots in the Gross-Pitaevskii model for Bose-Einstein condensates", J. Phys.: Conf. Ser. 544, 012022, (2014). [3] D. Kleckner, L. H. Kauffman, and W. T. M. Irvine, "How superfluid vortex knots untie", Nature Physics 12, 650 (2016). [4] Ruban V.P., "Dolgozhivushchie kvantovye vikhrevye uzly", Pis’ma v ZhETF, 107 (5), 325-328 (2018). [5] V. P. Ruban, unpublished.

## Dynamic phase transition in rare events statistics of 1D KPZ problem

30 March in 11:30

Alex Kamenev (University of Minnesota)

I will review the concept of non-equilibrium phase transitions in rare events statistics as well as a recent dramatic progress in studies of 1D KPZ. The focus of my talk is on the reflection symmetry breaking phase transition recently found stationary KPZ problem: https://arxiv.org/abs/1606.08738

## Chiral magnetic crystals

23 March in 11:30

Markus Garst (TU Dresden)

The weak Dzyaloshinskii-Moriya interaction in chiral cubic magnets like MnSi, FeGe or Cu_{2}OSeO_{3} twists the magnetization on long length scales resulting in spatially periodic magnetic textures — magnetic crystals. There exist especially magnetic crystals with a one- and two-dimensional periodicity corresponding to the magnetic helix and the topologically non-trivial skyrmion lattice, respectively. In this talk, we provide an overview of their properties. In particular, we discuss the crystallization process of these magnetic crystals that is characterized by strongly correlated chiral paramagnons that drive the transition first-order [1,2]. This fluctuation-induced first-order transition is well described by a theory put forward by Brazovskii. We will introduce the magnon band structure and their non-reciprocal properties in the presence of a magnetic field [3,4]. For the skyrmion lattice, this band structure is topological and characterized by finite Chern numbers that can be attributed to the formation of magnon Landau levels due to an emergent orbital magnetic field [5,6,7]. Finally, we will discuss domain walls of helimagnets that share similarities with grain boundaries consisting of disclination and dislocation defects of the helimagnetic order [8].
References:
[1] M. Janoschek et al. Phys. Rev. B 87, 134407 (2013).
[2] A. Bauer, M. Garst and C. Pfleiderer, Phys. Rev. Lett. 110, 177207 (2013).
[3] M. Kugler et al. Phys. Rev. Lett. 115, 097203 (2015)
[4] T. Weber et al. arXiv:1708.02098
[5] C. Schütte and M. Garst, Phys. Rev. B 90, 094423 (2014).
[6] T. Schwarze, J. Waizner, M. Garst, A. Bauer, I. Stasinopoulos, H. Berger, C. Pfleiderer, and D. Grundler, Nat. Mater. 14, 478 (2015).
[7] M. Garst J. Waizner, and D. Grundler, J. Phys. D: Appl. Phys. 50, 293002 (2017)
[8] P. Schoenherr et al. Nat. Phys. in press, arXiv:1704.06288

## Universality in statistics of Stokes flow over no-slip wall with random roughness

16 March in 11:30

__V. Parfenyev__, S. Belan, and V. Lebedev

Stochastic roughness is widespread feature of natural surfaces and is an inherent by-product of most fabrication techniques. In view of rapid development of microfluidics, the important question is how this inevitable evil affects the low-Reynolds flows which are common for micro-devices. Moreover, one could potentially turn the flaw into a virtue and control the flow properties by means of specially "tuned" random roughness. We investigate theoretically the statistics of fluctuations in fluid velocity produced by the waviness irregularities at the surface of a no-slip wall. Particular emphasis is laid on the issue of the universality of our findings.

## Spinovoe ekho v nakopitel’nykh kol’tsakh

2 March in 11:30

__N. Nikolaev__, F. Ratmann, F. Saleev

Sinkhrotronnye (prodol’nye) kolebaniya v banchirovannykh nakoplennykh puchkakh privodyat k razbrosu chastot pretsessii spina v nakopitele. Pri usrednenii po ansamblyu chastits eto privodit k zatukhanii vynuzhdennykh rezonansnym radiochastotnym rotatorom spina kolebanii polyarizatsii chastits. Budet pokazano, chto pri slaboi, no konechnoi otstroike chastoty rotatora (my rassmotrim radiochastotnyi fil’tr Vina) ot chastoty svobodnoi pretsessii spina v uderzhivayushchem magnitnom pole nakopitelya, voznikaet rezhim svoeobraznogo spinovogo ekha: ogibayushchaya vynuzhdennykh kolebanii ubyvaet vnachale po stepennomu zakonu, zatem amplituda polnost’yu vosstanavlivaetsya, i protsess povtoryaetsya periodicheski. Eto kur’yoznoe nablyudenie mozhet imet’ prakticheskoe prilozhenie k poiskam rezonansnogo vrashcheniya EDM zaryazhennykh chastits v nakopitelyakh.

## Matritsy Kartana v teorii tsepochek Toda-Darbu

2 March in 11:30

__A. Shabat__, V. Adler

Obsuzhdaetsya vzaimno odnoznachnoe sootvetstvie polinomial’nykh pervykh integralov gamil’tonovykh sistem s eksponentsial’nym vzaimodeistviem i “giper-integralov” dvumerizovannoi tsepochki Tody. Ustanovleny formuly pereschyota sootvetstvuyushchikh mnogochlenov i nekotorye obshchie svoistva ikh algebraicheskoi struktury.

## 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.

## 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 $d_c\to \infty$.