# In Print

## Quantum Many-Body Physics of Qubits

22 June in 11:30

L. Glazman (Yale University)

The ongoing development of superconducting qubits has brought some basic questions of many-body physics to the research forefront, and in some cases helped solving them. I will address two effects in quantum condensed matter highlighted by the development of a fluxonium qubit. The first one is the so-called cosine-phi problem stemming from the seminal paper of Brian Josephson: the predicted there phase dependence of the dissipative current across a Josephson junction was observed in a fluxonium, after nearly 50 years of unsuccessful attempts by other techniques. The second one is the dynamics of a weakly-pinned charge density wave: we predict that the dynamics may be revealed in measurements of microwave reflection off a superinductor, which is a key element of the fluxonium.

## Lazernoe vozdeistvie na veshchestvo: sovremennoe sostoyanie

15 June in 11:30

Anisimov S.I., Inogamov N.A., Petrov Yu.P., Khokhlov V.A.

V doklade aktsentiruetsya vnimanie na sravnenii rezhimov oblucheniya s raznoi dlitel’nost’yu impul’sa. V odnom sluchae eto ul’trakorotkie lazernye impul’sy (UkLI), v drugom subnanosekundnye. Ul’trakorotkimi nazyvayut impul’sy prodolzhitel’nost’yu poryadka pikosekund i koroche, t.e. i 2 ps, i 10 fs - eto UkLI. Rech’ idet o vozdeistvii na metall cherez prozrachnuyu sredu. Prozrachnaya sreda mozhet byt’ tverdoi, a mozhet byt’ zhidkoi. Ponyatno, chto energetika takogo vozdeistviya ogranichena, poskol’ku neobkhodimo izbegat’ razvitogo opticheskogo proboya prozrachnoi sredy - takoi proboi otsekaet lazernoe izluchenie ot metallicheskoi misheni. Zadacha imeet vazhnye prilozheniya v fizike lazernoi ablyatsii v zhidkost’, ablyatsii, soprovozhdayushcheisya generatsiei nanochastits i formirovaniem kolloidov. Eto burno rastushchee nauchno-tekhnologicheskoe napravlenie, ob’edinyayushchee fiziku lazernogo vozdeistviya i khimiyu protsessov mezhdu produktami ablyatsii i zhidkost’yu, predstavlennuyu rastvorami solei ili organiki. Vo vtoroi chasti doklada daetsya obzor rezul’tatov, poluchennykh za poslednie dva goda. Razlichnye razdely raboty vypolneny v sootvetstvii s goszadaniem i po grantam RNF (14-19-01599) i RFFI (16-02-00864, 16-08-01181).

## Dynamics of Poles in 2D Hydrodynamics with Free Surface: New Constants of Motion

8 June in 11:30

A. I. Dyachenko, S. A. Dyachenko, P. M. Lushnikov and V. E. Zakharov

We consider Euler equations for potential flow of ideal incompressible fluid with a free surface and infinite depth in two dimensional geometry. We admit a presence of gravity forces and surface tension. A time-dependent conformal mapping z(w,t) of the lower complex half-plane of the variable w into the area filled with fluid is performed with the real line of w mapped into the free fluid's surface. We study the dynamics of singularities of both z(w,t) and the complex fluid potential Pi(w,t) in the upper complex half-plane of w. We show the existence of solutions with an arbitrary finite number N of simple complex poles in z_w(w,t) and Pi_w(w,t) which are the derivatives of z(w,t) and Pi(w,t) over w. These poles are often coupled with branch points located at other points of the upper half-plane of w. We find that the residues of the simple poles of z_w(w,t) are new, previously unknown constants of motion, provided surface tension is zero. All these constants of motion commute with each other in the sense of underlying Hamiltonian dynamics. In absence of both gravity and surface tension, the residues of simple poles of Pi_w(w,t) are also the constants of motion. For nonzero gravity and zero surface tension, the residues of poles of any order of Pi_w(w,t) are the trivial linear functions of time. Nonzero surface tension allows residues of poles of even order to be compatible with the fluid dynamics. We also found solutions with N higher order poles. In all above cases the number of independent real integrals of motion is 4N for zero gravity and 4N-1 for nonzero gravity. We suggest that the existence of these nontrivial constants of motion provides an argument in support of the conjecture of complete integrability of free surface hydrodynamics in deep water.

## Spetsial’naya geometriya v strunnykh kompaktifikatsiyakh i kiral’nye algebry

1 June in 11:30

Konstantin Aleshkin

V doklade ya planiruyu izlozhit’ nedavnie uspekhi v vychislenii geometrii prostranstv moduleimnogoobrazii Kalabi-Yau, neobkhodimykh dlya opisaniya nizkoenergetichnogo predela teorii strun. Sovmestno s A. Belavinym nami byli polucheny obshchie formuly dlya normalizatsii konstant svyazi nizkoenergetichnoi teorii (spetsial’naya geometriya). A imenno, ispol’zuya svyaz’ s kiral’nymi algebrami, my napisali yavnye formuly v vide ryadov dlya spetsial’noi geometrii dlya klassov mnogoobrazii Kalabi-Yau tipa Ferma.

## Razmernost’ fraktal’nogo interfeisa v prostranstvennoi zadache dilemmy uznika.

25 May in 11:30

L.N. Shchur

V poslednie dvadtsat’ let polucheno mnogo rezul’tatov po klassifikatsii kriticheskogo povedeniya dvumernykh sistem na osnove kriticheskogo povedeniya interfeisov. Nezavisimo ot razvitiya etoi nauki (Evolyutsiya Shrama-Levnera), poyavilis’ utverzhdeniya, osnovannye na chislennom modelirovanii, o tom, chto protekanie v nekotorykh statisticheskikh sistemakh demonstriruet svoistva, tipichnye dlya fazovogo perekhoda pervogo roda. My issledovali geometricheskie svoistva interfeisov v zadache, kotoraya osnovana na klassicheskoi zadache iz teorii igr, zadache dilemmy uznika. V issleduemoi nami modeli igroki raspolagayutsya v uzlakh kvadratnoi reshetki. Kazhdyi igrok na kazhdom shage po vremeni mozhet menyat’ svoyu strategiyu v zavisimosti ot ego okruzheniya. V opredelennom diapazone parametra podscheta vybora strategii takaya deterministicheskaya dinamika privodit k kvazi-statsionarnomu rezhimu, s chetko vyrazhennoi strukturoi. Struktura sostoit iz dvukh tipov klasterov, ravnoi chislu vozmozhnykh strategii. Eti klastery imeyut konechnuyu massu, to est’ ikh razmernost’ ravna dvum. V sluchae perekhoda pervogo roda, dlina granitsy klastera rastet lineino s razmerom sistemy. V sluchae perekhoda vtorogo roda, dlina granitsy rastet bystree lineinoi, no medlennee, chem ploshchad’. V nashem sluchae, okazalos’, chto asimptoticheski razmernost’ interfeisa rastet kvadratichno. Eto dovol’no neozhidannyi rezul’tat. Izvestno, chto regulyarnye fraktaly mogut imet’ razmernost’ 2. Dlya sluchainykh fraktalov takoi sluchai ranee byl neizvesten.

## 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 Cu2OSeO3 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