# Seminars

Regular seminars are held on Thursdays in the Kapitza Institute in Moscow and on Fridays at the scientific council of the Landau Institute in Chernogolovka.

Departments of the institute hold their own seminars; the topic are determined by the scientific orientation of the related department.

Seminars information is also sent via e-mail. If you want to receive seminar announcements, please subscribe.

## A Josephson relation for e/3 and e/5 fractionally charged anyons

23 May, tomorrow in 11:30 in Kapitza Institute

D. Christian Glattli (Nanoelectronics Group, Service de Physique de l’Etat Condensé, CEA Saclay, France)

Anyons occur in two-dimensional electron systems as excitations with fractional charge in the topologically ordered states of the fractional quantum Hall effect (FQHE). Their dynamics are of utmost importance for topological quantum phases and possible decoherence-free quantum information approaches, but observing these dynamics experimentally is challenging. Here, we report on a dynamical property of anyons: the long-predicted [1] Josephson relation f

_{J}= e*V/h for charges e* = e/3 and e/5, where e is the charge of the electron and h is Planck’s constant [2]. The relation manifests itself as marked signatures in the dependence of photo-assisted shot noise (PASN) [3-4] on voltage V when irradiating contacts at microwaves frequency f_{J}[4]. The validation of FQHE PASN models indicates a path toward realizing time-resolved anyon sources based on levitons. The method may be of interest to provide a demonstration of anyonic statistics, a pre-requisite for topological quantum computing. [1] X. G. Wen, Edge transport properties of the fractional quantum Hall states and weak-impurity scattering of a one-dimensional charge-density wave, Phys. Rev. B 44, 5708–5719 (1991). [2] M. Kapfer, P. Roulleau, M. Santin, I. Farrer, D. A. Ritchie, and D. C. Glattli, A Josephson relation for fractionally charged anyons, Science 363, 846–849 (2019). [3] G. B. Lesovik and L. S. Levitov, Noise in an ac biased junction: Nonstationary Aharonov-Bohm effect, Phys. Rev. Lett. 72, 538–541 (1994). [4] C. de C. Chamon, D. E. Freed, and X. G. Wen, Tunneling and quantum noise in one-dimensional Luttinger liquids, Phys. Rev. B 51, 2363–2379 (1995).## Minimal excitations states: From time resolved single particle fermionic states for Electron Quantum Optics to Digital communication and music.

24 May, the day after tomorrow in 11:30 at scientific council

D. Christian Glattli (Nanoelectronics Group, Service de Physique de l’Etat Condensé, CEA Saclay, France)

In the 90’s, an impressive series of works by theoreticians from the Landau Institute on electrons shot noise in quantum conductors [1] and on the statistics of transfer of electrons [2] has leaded to the emergence of the beautiful concept of minimal excitation states [3-5]. These minimal excitation states can be generated by applying voltage pulses on the contact of a conductor to inject short single electron pulses. These states show minimal noise and provide a convenient and clean single electron source for electron optics whose aim is to perform quantum optics tasks with electrons instead of photons. The minimal excitations states, now called levitons, have been produced in recent experiments [6] and have triggered a large number of theoretical works. They have enabled Hong Ou Mandel like experiments [6] with electrons and single electron quantum Tomography [7]. Extension to fractionally charged anyons is possible.

At the root of the minimal excitation property is a specific single side band modulation of the electron wave by the Lorentzian voltage pulse. This property can be applied to classical electromagnetic or acoustic waves for applications in digital communication [8] or in music sound synthesis.

[1] G. B. Lesovik, JETP Letters, 49 (9), 592-594 (1989).

[2] L.S. Levitov, G.B. Lesovik, Charge-transport statistics in quantum conductors, JETP Lett., 55 (9), 555-559 (1992).

[3] A. Ivanov, H.W. Lee, L.S. Levitov, Coherent states of alternating current, Phys. Rev. B 56(11), 6839-6850 (1997); cond-mat/9501040

[4] L.S. Levitov, H. Lee, G.B. Lesovik, Electron Counting Statistics and Coherent States of Electric Current, J. Math. Phys., 37(10), 4845-4866 (1996); cond-mat/9607137.

[5] J. Keeling, I. Klich, and L. S. Levitov, Minimal Excitation States of Electrons in One-Dimensional Wires, Phys. Rev. Lett. 97, 116403 (2006).

[6] Minimal-excitation states for electron quantum optics using levitons, J. Dubois, T. Jullien, F. Portier, P. Roche, A. Cavanna, Y. Jin, W. Wegscheider, P. Roulleau & D. C. Glattli, Nature, 502, 659–663 (2013).

[7] Quantum tomography of an electron, T. Jullien, P. Roulleau, B. Roche, A. Cavanna, Y. Jin & D. C. Glattli, Nature, 514, 603–607 (2014).

[8] Power Spectrum Density of Single Side Band CPM Using Lorenztian Frequency Pulses, Haïfa Farès, D. Christian Glattli, Yves Louet, Jacques Palicot, Preden Roulleau, and Christophe Moy, IEEE Wireless Communications Letters, 6 (6), 786-789, (2017).

At the root of the minimal excitation property is a specific single side band modulation of the electron wave by the Lorentzian voltage pulse. This property can be applied to classical electromagnetic or acoustic waves for applications in digital communication [8] or in music sound synthesis.

[1] G. B. Lesovik, JETP Letters, 49 (9), 592-594 (1989).

[2] L.S. Levitov, G.B. Lesovik, Charge-transport statistics in quantum conductors, JETP Lett., 55 (9), 555-559 (1992).

[3] A. Ivanov, H.W. Lee, L.S. Levitov, Coherent states of alternating current, Phys. Rev. B 56(11), 6839-6850 (1997); cond-mat/9501040

[4] L.S. Levitov, H. Lee, G.B. Lesovik, Electron Counting Statistics and Coherent States of Electric Current, J. Math. Phys., 37(10), 4845-4866 (1996); cond-mat/9607137.

[5] J. Keeling, I. Klich, and L. S. Levitov, Minimal Excitation States of Electrons in One-Dimensional Wires, Phys. Rev. Lett. 97, 116403 (2006).

[6] Minimal-excitation states for electron quantum optics using levitons, J. Dubois, T. Jullien, F. Portier, P. Roche, A. Cavanna, Y. Jin, W. Wegscheider, P. Roulleau & D. C. Glattli, Nature, 502, 659–663 (2013).

[7] Quantum tomography of an electron, T. Jullien, P. Roulleau, B. Roche, A. Cavanna, Y. Jin & D. C. Glattli, Nature, 514, 603–607 (2014).

[8] Power Spectrum Density of Single Side Band CPM Using Lorenztian Frequency Pulses, Haïfa Farès, D. Christian Glattli, Yves Louet, Jacques Palicot, Preden Roulleau, and Christophe Moy, IEEE Wireless Communications Letters, 6 (6), 786-789, (2017).

## Sud’ba oskolkov obrazovaniya Luny: geofizicheskie sledstviya Gigantskogo stolknoveniya

30 May in 11:30 in Kapitza Institute

__A.V. Byalko__, M.I. Kuz’min (Institut geokhimii SO RAN)

Naibolee veroyatnyi stsenarii obrazovaniya Luny daetsya raschetami Gigantskogo stolknoveniya (GS) ProtoZemli s protoplanetoi, po masse, blizkoi Marsu. Iskhodya iz vozrasta zemnykh i lunnykh tsirkonov, GS proizoshlo 4.4—4.5 mlrd. let nazad, na 160—170 mln let pozzhe vzryva Sverkhnovoi, zadavshego izotopnyi sostav Solnechnoi sistemy (SS).
Pri GS na beskonechnost’ ukhodyat gazy i silikatnye oskolki s obshchei massoi poryadka 55-70% massy Luny. Odnako beskonechnost’ ubegayushchikh chastits est’ beskonechnost’ v zemnoi sisteme otscheta, v SS eti oskolki vykhodyat na konechnye orbity s periodami kak men’she, tak i bol’she goda. Vazhneishaya osobennost’ ikh orbit v tom, chto vse oni prokhodyat cherez uzkuyu oblast’ zemnoi orbity, gde proiskhodilo GS. Tam formiruetsya gazopylevoi struinyi potok, s zatukhayushchei intensivnost’yu on sushchestvuet menee milliona let.
Chislennymi resheniyami zadachi trekh tel rasschitany mnogochislennye traektorii oskolkov. Otseneny veroyatnosti ikh stolknovenii s Zemlei i Lunoi v zavisimosti ot vremeni posle GS, a takzhe popadaniya v treugol’nye tochki Lagranzha L4 i L5.
Vazhneishim geofizicheskim sledstviem stolknoveniya oskolkov s Zemlei yavlyaetsya obrazovanie zemnoi atmosfery v techenie pervykh soten let posle GS iz gazov, skondensirovavshikhsya na oskolkakh. Okean obrazovalsya iz atmosfernogo vodyanogo para posle okhlazhdeniya poverkhnosti nizhe kriticheskoi temperatury vody.

## Formation and decay of eddy currents generated by crossed surface waves

31 May in 11:30 at scientific council

__Parfenyev V.M.__, Filatov S.V., Brazhnikov M.Yu., Vergeles S.S., Levchenko A.A.

The mass-transport induced by crossed surface waves consists of the Stokes and Euler contributions which are very different in nature. The first contribution is a generalization of Stokes drift for a plane wave in ideal fluid and the second contribution arises due to the fluid viscosity and it is excited by a force applied in the viscous sublayer near the fluid surface. We study the formation and decay of the induced mass-transport theoretically and experimentally and demonstrate that both contributions have different time scales for typical experimental conditions. The evolution of the Euler contribution is described by a diffusion equation, where the fluid kinematic viscosity plays the role of the diffusion coefficient, while the Stokes contribution evolves faster, feeling the additional damping near the system boundaries. The difference becomes more pronounced if the fluid surface is contaminated. We model the effect of contamination by a thin insoluble liquid film presented on the fluid surface with the compression modulus being the only non-zero rheological parameter of the film. Then the Euler contribution into the mass-transport becomes parametrically larger and the evolution of the Stokes contribution becomes parametrically faster. The parameter is the same in both cases and it is equal to the quality factor of surfaces waves, which is modified by the presence of a surface film. We infer the value of the compression modulus of the film by fitting the results of transient measurements of eddy currents and demonstrate that the obtained value leads to the correct ratio of amplitudes of horizontal and vertical velocities of the wave motion and is in reasonable agreement with the measured dissipation rate of surface waves.

## Bernoulli Experiment under Restart

31 May in 11:30 at scientific council

S. Belan

It is known that restart of the stochastic process can significantly reduce the expected time required to its completion. This effect is widely implemented to speed up the randomized search algorithms and can potentially be used to increase the rate of chemical reactions. However, complex stochastic processes often exhibit several possible scenarios of completion which are not equally desirable in terms of efficiency. In this talk I will discuss how restart affects the splitting probabilities of a Bernoulli-like stochastic process, i.e., of a process which can end with one of two outcomes. Special attention will be paid to the class of problems, where a carefully tuned restart rate maximizes the chances to obtain the desired outcome. Importantly, the analysis revealed universality displayed by the optimally restarted processes.

## Termal’nyi effekt Kholla kak topologicheskii invaraint

7 June in 11:30 at scientific council

Lev Spodyneiko

## Parallel SPH modeling using dynamic domain decomposition and load balancing displacement of Voronoi subdomains

14 June in 11:30 at scientific council

__Maria S. Egorova__, Sergey A. Dyachkov, Anatoliy N. Parshikov, Vasily V. Zhakhovsky

A highly adaptive load balancing algorithm for parallel simulations using particle methods, such as molecular dynamics and smoothed particle hydrodynamics (SPH), is developed. Our algorithm is based on the dynamic spatial decomposition of simulated material samples between Voronoi subdomains, where each subdomain with all its particles is handled by a single computational process which is typically run on a single CPU core of a multiprocessor computing cluster. The algorithm displaces the positions of neighbor Voronoi subdomains in accordance with the local load imbalance between the corresponding processes. It results in particle transfers from heavy-loaded processes to less-loaded ones. Iteration of the algorithm puts into alignment the processor loads. Convergence to a well-balanced decomposition from imbalanced one is improved by the usage of multi-body terms in the balancing displacements. The high adaptability of the balancing algorithm to simulation conditions is illustrated by SPH modeling of the dynamic behavior of materials under extreme conditions, which are characterized by large pressure and velocity gradients, as a result of which the spatial distribution of particles varies greatly in time. The higher parallel efficiency of our algorithm in such conditions is demonstrated by comparison with the corresponding static decomposition of the computational domain. Our algorithm shows almost perfect strong scalability in tests using from tens to several thousand processes.

Publications: arXiv:1805.05128v2 [physics.comp-ph] ; Computer Physics Communications, Volume 234, January 2019, Pages 112-125

Publications: arXiv:1805.05128v2 [physics.comp-ph] ; Computer Physics Communications, Volume 234, January 2019, Pages 112-125

## Dvukh-zhidkostnye yavleniya v zhidkostyakh Lattinzhera

21 June in 11:30 at scientific council

Anton Andreev