F. Smirnov and A. Zamolodchikov in the paper published in 2016 showed that a special class of irrelevant perturbations (current-current perturbations) in integrable models of quantum field theory leads to appearance of CDD factors in the scattering matrices, i.e. scalar factors corresponding to non-uniqueness of solution to the Yang-Baxter equation for S matrices. They considered the sine-Gordon model and analogous models that only contain odd-spin integrals of motion. We find CDD factors (in the first order in the perturbation theory) for the current-current perturbations on the example of models that contain even-spin integrals of motion as well, the complex sinh-Gordon model and the scaling Z_N symmetric Ising model. Thus we generalize the Smirnov-Zamolodchikov formula to the case of several particles with diagonal scattering. We also obtain the CDD factors for Lorentz non-invariant perturbations of this type. Technically we use the representation by free fields for form factors, developed by us earlier.

Naibolee veroyatnyi stsenarii obrazovaniya Luny daetsya raschetami Gigantskogo stolknoveniya (GS) ProtoZemli s protoplanetoi, po masse, blizkoi Marsu [1, 2]. 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. Rassmotreny geofizicheskie sledstviya etikh stolknovenii.

1.Canup R.M. & Asphaug E. Origin of the Moon in a giant impact near the end of the Earth's formation, Nature, 412, 208–212 (2001).
2.Canup R.M. Simulations of a late lunar-forming impact, Icarus 168, 433–456 (2004).

Conventional Anderson localization is due to destructive interference of matter waves described by local random Hamiltonians. Correlations in random diagonal elements of such a Hamiltonian are known to favor delocalization. Recently systems with non-local Hamiltonians become experimentally accessible. We consider two families of such random matrix Hamiltonians with correlations in the long-range hopping terms and demonstrate that localization is enhanced and the wave function ergodicity is progressively degrading as the correlations become stronger. We review the localization/delocalization criteria of Mott and Anderson and show that the former is the sufficient criterion of weak ergodicity and the latter is the sufficient criterion of localization. The fact that these two criteria are not complimentary is the reason why the non-ergodic extended (multifractal) states may exist when neither the Mott, nor the Anderson criterion is fulfilled.
We suggest a new class of random matrix models (Toeplitz RMT) with translation-invariant hopping integrals and identify the character of eigenfunction and eigenvalue statistics in them. We formulate the principles of level statistics if the type of eigenfunction statistics is known both in the coordinate and in the momentum basis and demonstrate that for the Toeplitz RMT the ergodic delocalization in the coordinate space may coexist with the Poisson level statistics.
Finally, we suggest a matrix-inversion trick that allows to identify uniquely the type of eigenfunction statistics and prove the absence of delocalized states in the bulk of spectrum of long-range Hamiltonians with deterministic (fully correlated) hopping.

I consider the problem of reconstructing a source vector from its encrypted image corrupted by an additive Gaussian noise. Assuming encryption to be given by a random Gaussian mapping, the reconstruction problem in the framework of the Least Square Scheme turns out to be equivalent to finding the configuration of minimal energy in a certain version of spherical spin glass model. As a measure of the quality of the signal reconstruction one can use the mean overlap between the original signal and its recovered image. Thi overlap is analysed in the framework of Parisi scheme of Replica Symmetry Breaking. If the mapping is quadratic, there exists a threshold in the noise-to-signal ratio beyond which the reconstruction is impossible. The behaviour close to the threshold is controlled by the replica symmetry breaking mechanism and is characterized by a nontrivial exponent 3/4.

Pokazano, chto topologicheskoe sverkhtekuchee sostoyanie s p-sparivaniem (p_x + i p_y) mozhet byt’ realizovano v dvumernoi opticheskoi reshetke fermionnykh polyarnykh molekul. Dlya sistem s odnosloinoi i dvukhsloinoi geometriei vychislennye temperatury fazovykh perekhodov v sverkhtekuchee sostoyanie okazalis’ eksperimental’no dostizhimymi, poryadka desyatkov nanokel’vinov. [A.K. Fedorov, S.I. Matveenko, V. I. Yudson, G.V. Shlyapnikov , "Novel p-wave superfluids of fermionic polar molecules", Sci. Rep. 6, 27448; (2016).]
Issledovana chislenno i analiticheski fazovaya diagramma dvusloinoi sistemy fermionnykh polyarnykh molekul s disbalansom molekulyarnykh plotnostei v sloyakh. Dlya disbalansa (effektivnogo magnitnogo polya), prevyshayushchego kriticheskoe znachenie, sistema perekhodit pri dostatochno nizkikh temperaturakh iz sostoyaniya odnorodnoi sverkhtekuchei zhidkosti v sostoyaniya Larkina-Ovchinnikova-Ful’de-Ferrella s periodicheskoi strukturoi parametra poryadka. V otlichie ot sluchaya kontaktnogo vzaimodeistviya s singletnym sparivaniem, dipol’-dipol’noe vzaimodeistvie generiruet nenulevuyu tripletnuyu sostavlyayushchuyu parametra poryadka. [Hao Lee, S. I. Matveenko, Daw-Wei Wang, G. V. Shlyapnikov, "Fulde-Ferrell-Larkin-Ovchinnikov state in bilayer dipolar systems", Phys.Rev. A, 96, 061602(R) (2017)].
Issledovana odnomernoi model’ dvukhkomponentnogo fermionnogo gaza s sil’nym kontaktnym ottalkivaniem chastits s protivopolozhnym spinom i nelokal’nym prityazheniem fermionov s odinakovym spinom. Model’ mozhet byt’ eksperimental’no realizovana v sisteme kholodnykh atomov. Pri etom parametry vzaimodeistviya mogut izmenyat’sya v shirokom diapazone s pomoshch’yu vneshnego magnitnogo polya. Ispol’zuya metody bozonizatsii i renormgruppy, naideno osnovnoe sostoyanie sistemy v zavisimosti ot parametrov vzaimodeistviya. Pokazano, chto pri kriticheskom znachenii nelokal’nogo vzaimodeistviya proiskhodit fazovyi perekhod pervogo roda v sostoyanie s nenulevoi namagnichennost’yu. [D. V. Kurlov, S. I. Matveenko, V. Gritsev, G. V. Shlyapnikov, "One-dimensional two-component fermions with contact even-wave repulsion and SU(2) breaking near-resonant odd-wave attraction", Phys. Rev. A, (prinyata v pechat’)].

Doklad po teme predstavlyaemoi k zashchite kandidatskoi dissertatsii.

We use gauge/string duality to model a heavy quark-antiquark pair in a color singlet moving through a thermal plasma. In particular, we explore the effect of velocity on the string tension and Debye screening mass. Then we apply the results to the analysis of heavy quarkonium bound states. With some assumptions, we estimate the characteristic size of quarkonium and its dissociation temperature.