arXiv subjects

A. Morozov

Publications and source records attributed to A. Morozov.

At least 109 records · Page 6Linked to original sources

arXiv2021

Virasoro versus superintegrability. Gaussian Hermitian model

Relation between the Virasoro constraints and KP integrability (determinant formulas) for matrix models is a lasting mystery. We elaborate on the claim that the situation is improved when integrability is enhanced to super-integrability, i.e. to explicit formulas for Gaussian averages of characters. In this case, the Virasoro constraints are equivalent to simple recursive formulas, which have appropriate combinations of characters as their solutions. Moreover, one can easily separate dependence on the size of matrix, and deduce superintegrability from the Virasoro constraints. We describe one of the ways to do so for the Gaussian Hermitian matrix model. The result is a spectacularly elegant reformulation of Virasoro constraints as identities for the Schur functions evaluated at appropriate loci in the space of time-variables.

hep-th↗

arXiv2021

Khovanov polynomials for satellites and asymptotic adjoint polynomials

We compute explicitly the Khovanov polynomials (using the computer program from katlas.org) for the two simplest families of the satellite knots, which are the twisted Whitehead doubles and the two-strand cables. We find that a quantum group decomposition for the HOMFLY polynomial of a satellite knot can be extended to the Khovanov polynomial, whose quantum group properties are not manifest. Namely, the Khovanov polynomial of a twisted Whitehead double or two-strand cable (the two simplest satellite families) can be presented as a naively deformed linear combination of the pattern and companion invariants. For a given companion, the satellite polynomial "smoothly" depends on the pattern but for the "jump" at one critical point defined by the s-invariant of the companion knot. A similar phenomenon is known for the knot Floer homology and tau-invariant for the same kind of satellites.

hep-th↗

arXiv2021

Towards high-rate RPC-based thermal neutron detectors using low-resistivity electrodes

We present experimental results on the counting rate measurements for several single-gap $^{10}$B lined resistive plate chambers ($^{10}$B-RPCs) with anodes made from standard float glass, low resistivity glass and ceramic. The measurements were performed at the V17 monochromatic neutron beamline (3.35 Ȧ) at the Helmholtz-Zentrum Berlin. For the $^{10}$B-RPCs with 0.28 mm thick float glass a maximum counting rate density of about $8\times 10^{3}$ $Hz/cm^{2}$ was obtained. In the case of low resistivity glass and ceramic, the counting rate density did not deviate from linear dependence on the neutron flux up to the maximum flux available at this beamline and exceeded a value of $3\times 10^{4}$ $Hz/cm^{2}$.

physics.ins-det↗

arXiv2021

Duality in elliptic Ruijsenaars system and elliptic symmetric functions

We demonstrate that the symmetric elliptic polynomials $E_λ(x)$ originally discovered in the study of generalized Noumi-Shiraishi functions are eigenfunctions of the elliptic Ruijsenaars-Schneider (eRS) Hamiltonians that act on the mother function variable $y_i$ (substitute of the Young-diagram variable $λ$). This means they are eigenfunctions of the dual eRS system. At the same time, their orthogonal complements in the Schur scalar product, $P_R(x)$ are eigenfunctions of the elliptic reduction of the Koroteev-Shakirov (KS) Hamiltonians. This means that these latter are related to the dual eRS Hamiltonians by a somewhat mysterious orthogonality transformation, which is well defined only on the full space of time variables, while the coordinates $x_i$ appear only after the Miwa transform. This observation explains the difficulties with getting the apparently self-dual Hamiltonians from the double elliptic version of the KS Hamiltonians.

hep-th↗

arXiv2021

Superintegrability and Kontsevich-Hermitian relation

We analyze the well-known equivalence between the quadratic Kontsevich-Penner and Hermitian matrix models from the point of view of superintegrability relations, i.e. explicit formulas for character averages. This is not that trivial on the Kontsevich side and seems important for further studies of various deformations of Kontsevich models. In particular, the Brezin-Hikami extension of the above equivalence becomes straightforward.

hep-th↗

arXiv2021

Cut-and-join structure and integrability for spin Hurwitz numbers

Spin Hurwitz numbers are related to characters of the Sergeev group, which are the expansion coefficients of the Q Schur functions, depending on odd times and on a subset of all Young diagrams. These characters involve two dual subsets: the odd partitions (OP) and the strict partitions (SP). The Q Schur functions Q_R with R\in SP are common eigenfunctions of cut-and-join operators W_Δwith Δ\in OP. The eigenvalues of these operators are the generalized Sergeev characters, their algebra is isomorphic to the algebra of Q Schur functions. Similarly to the case of the ordinary Hurwitz numbers, the generating function of spin Hurwitz numbers is a τ-function of an integrable hierarchy, that is, of the BKP type. At last, we discuss relations of the Sergeev characters with matrix models.

hep-th↗

arXiv2021

Superintegrability of Kontsevich matrix model

Many eigenvalue matrix models possess a peculiar basis of observables which have explicitly calculable averages. This explicit calculability is a stronger feature than ordinary integrability, just like the cases of quadratic and Coulomb potentials are distinguished among other central potentials, and we call it superintegrability. Aa a peculiarity of matrix models, the relevant basis is formed by the Schur polynomials (characters) and their generalizations, and superintegrability looks like a property $ \,\sim character$. This is already known to happen in the most important cases of Hermitian, unitary, and complex matrix models. Here we add two more examples of principal importance, where the model depends on external fields: a special version of the complex model and the cubic Kontsevich model. In the former case, straightforward is a generalization to the complex tensor model. In the latter case, the relevant characters are the celebrated $Q$ Schur functions appearing in the description of spin Hurwitz numbers and other related contexts.

hep-th↗

arXiv2021

Generalized Q-functions for GKM

Recently we explained that the classical $Q$ Schur functions stand behind various well-known properties of the cubic Kontsevich model, and the next step is to ask what happens in this approach to the generalized Kontsevich model (GKM) with monomial potential $X^{n+1}$. We propose to use the Hall-Littlewood polynomials at the parameter equal to the $n$-th root of unity as a generalization of the $Q$ Schur functions from $n=2$ to arbitrary $n>2$. They are associated with $n$-strict Young diagrams and are independent of time-variables $p_{kn}$ with numbers divisible by $n$. These are exactly the properties possessed by the generalized Kontsevich model (GKM), thus its partition function can be expanded in such functions $Q^{(n)}$. However, the coefficients of this expansion remain to be properly identified. At this moment, we have not found any "superintegrability" property $ \,\sim character$, which expressed these coefficients through the values of $Q$ at delta-loci in the $n=2$ case. This is not a big surprise, because for $n>2$ our suggested $Q$ functions are not looking associated with characters.

hep-th↗

arXiv2021

Distal edge determination precision for a multi-slat promptgamma camera: a comprehensive simulation and optimization of the detection system

Multi-slat prompt-gamma camera is a promising tool for range monitoring during proton therapy. We report the results of a comprehensive simulation study analyzing the precision which is possible to reach with this camera in determination of the position of the distal edge of the Bragg peak. For the first time we include simulation of optical photons. The proton beam (single pencil beam, 130 MeV, 10 ns bunch period, total of 10^8 protons) is interacting with a polymethyl methacrylate (PMMA) phantom, which is a cylinder of 200 mm in diameter and length. The prompt gamma rays generated in the phantom are collimated with a multi-slat collimator and detected using a combination of yttrium aluminum perovskite (YAP) scintillators, installed in the collimator apertures, and light sensors. Two scintillator packing schemes, with one and with two scintillator plates per aperture, are considered. The collimator configuration (the septal thickness, aperture and height), resulting in the best precision, is determined using two methods of detector optimization. Precision of 2.1 mm (full width at half maximum) in the edge position determination is demonstrated.

physics.med-ph↗

arXiv2020

Electrostatic inactivation of RNA viruses at air-water and liquid-liquid interfaces

Understanding the interactions between viruses and surfaces or interfaces is important, as they provide the principles underpinning the cleaning and disinfection of contaminated surfaces. Yet, the physics of such interactions is currently poorly understood. For instance, there are longstanding experimental observations suggesting that the presence of air-water interfaces can generically inactivate and kill viruses, yet the mechanism underlying this phenomenon remains unknown. Here we use theory and simulations to show that electrostatics provides one such mechanism, and that this is very general. Thus, we predict that the free energy of an RNA virus should increase by several thousands of $k_BT$ as the virion breaches an air-water interface. We also show that the fate of a virus approaching a generic liquid-liquid interface depends strongly on the detailed balance between interfacial and electrostatic forces, which can be tuned, for instance, by choosing different media to contact a virus-laden respiratory droplet. We propose that these results can be used to design effective strategies for surface disinfection. Intriguingly, tunability requires electrostatic and interfacial forces to scale similarly with viral size, which naturally occurs when charges are arranged in a double-shell distribution as in RNA viruses like influenza and all coronaviruses.

cond-mat.soft↗

arXiv2020

Are Maxwell knots integrable?

We review properties of the null-field solutions of source-free Maxwell equations. We focus on the electric and magnetic field lines, especially on limit cycles, which actually can be knotted and/or linked at every given moment. We analyse the fact that the Poynting vector induces self-consistent time evolution of these lines and demonstrate that the Abelian link invariant is integral of motion. The same is expected to be true also for the non-Abelian invariants (like Jones and HOMFLY-PT polynomials or Vassiliev invariants), and many integrals of motion can imply that the Poynting evolution is actually integrable. We also consider particular examples of the field lines for the particular family of finite energy source-free "knot" solutions, attempting to understand when the field lines are closed -- and can be discussed in terms of knots and links. Based on computer simulations we conjecture that Ranada's solution, where every pair of lines forms a Hopf link, is rather exceptional. In general, only particular lines (a set of measure zero) are limit cycles and represent closed lines forming knots/links, while all the rest are twisting around them and remain unclosed. Still, conservation laws of Poynting evolution and associated integrable structure should persist.

hep-th↗

arXiv2020

Elliptic $q,t$ matrix models

The Gaussian matrix model is known to deform to the $q,t$-matrix model. We consider further deformation to the elliptic $q,t$ matrix model by properly deforming the Gaussian density as well as the Vandermonde factor. Properties of an associated basis of symmetric functions that provide the matrix model property $ \sim {\rm char}$ in the deformed elliptic case are discussed.

hep-th↗

arXiv2020

Towards elliptic deformation of $q,t$-matrix models

As a necessary step in constructing elliptic matrix models, which preserve the superintegrability property $ \sim {\rm char}$, we suggest an elliptic deformation of the peculiar loci $p_k^{Δ_n}$, which play an important role in precise formulation of this property. The suggestion is to define the $p_k^{Δ_n}$-loci as elliptic functions with the right asymptotics at $τ\to i\infty$. If this hypothesis is correct, one can move to substituting the Schur and Macdonald functions in the role of characters by the elliptic GNS and study their behavior at the deformed topological and $Δ$ loci.

hep-th↗

arXiv2020

Algebra of quantum ${\cal C}$-polynomials

Knot polynomials colored with symmetric representations of $SL_q(N)$ satisfy difference equations as functions of representation parameter, which look like quantization of classical ${\cal A}$-polynomials. However, they are quite difficult to derive and investigate. Much simpler should be the equations for coefficients of differential expansion nicknamed quantum ${\cal C}$-polynomials. It turns out that, for each knot, one can actually derive two difference equations of a finite order for these coefficients, those with shifts in spin $n$ of the representation and in $A=q^N$. Thus, the ${\cal C}$-polynomials are much richer and form an entire ring. We demonstrate this with the examples of various defect zero knots, mostly discussing the entire twist family.

hep-th↗

arXiv2020

Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function

As a development of arXiv:1912.12897, we note that the ordinary Shiraishi functions have an insufficient number of parameters to describe generic eigenfunctions of double elliptic system (Dell). The lacking parameter can be provided by substituting elliptic instead of the ordinary Gamma functions in the coefficients of the series. These new functions (ELS-functions) are conjectured to be functions governed by compactified DIM networks which can simultaneously play the three roles: solutions to non-stationary Dell equations, Dell conformal blocks with the degenerate field (surface operator) insertion, and the corresponding instanton sums in $6d$ SUSY gauge theories with adjoint matter. We describe the basics of the corresponding construction and make further conjectures about the various limits and dualities which need to be checked to make a precise statement about the Dell description by double-periodic network models with DIM symmetry. We also demonstrate that the ELS-functions provide symmetric polynomials, which are an elliptic generalization of Macdonald ones, and compute the generation function of the elliptic genera of the affine Laumon spaces. In the particular $U(1)$ case, we find an explicit plethystic formula for the $6d$ partition function, which is a non-trivial elliptic generalization of the $(q,t)$ Nekrasov-Okounkov formula from $5d$.

hep-th↗

arXiv2020

Distinguishing Mutant Knots

Knot theory is actively studied both by physicists and mathematicians as it provides a connecting centerpiece for many physical and mathematical theories. One of the challenging problems in knot theory is distinguishing mutant knots. Mutant knots are not distinguished by colored HOMFLY-PT polynomials for knots colored by either symmetric and or antisymmetric representations of $SU(N)$. Some of the mutant knots can be distinguished by the simplest non-symmetric representation $[2,1]$. However there is a class of mutant knots which require more complex representations like $[4,2]$. In this paper we calculate polynomials and differences for the mutant knot polynomials in representations $[3,1]$ and $[4,2]$ and study their properties.

hep-th↗

arXiv2020

Perspectives of differential expansion

We outline the current status of the differential expansion (DE) of colored knot polynomials i.e. of their $Z$--$F$ decomposition into representation-- and knot--dependent parts. Its existence is a theorem for HOMFLY-PT polynomials in symmetric and antisymmetric representations, but everything beyond is still hypothetical -- and quite difficult to explore and interpret. However, DE remains one of the main sources of knowledge and calculational means in modern knot theory. We concentrate on the following subjects: applicability of DE to non-trivial knots, its modifications for knots with non-vanishing defects and DE for non-rectangular representations. An essential novelty is the analysis of a more-naive ${\cal Z}$--${F_{Tw}}$ decomposition with the twist-knot $F$-factors and non-standard ${\cal Z}$-factors and a discovery of still another triangular and universal transformation $V$, which converts $\cal{Z}$ to the standard $Z$-factors $V^{-1}\cdot {\cal Z}= Z$ and allows to calculate $F$ as $F = V\cdot F_{Tw}$.

hep-th↗

arXiv2020

Multilayer $^{10}B$-RPC neutron imaging detector

Resistive plate chambers (RPC) lined with $^{10}B_{4}$C neutron converters is a promising cost effective technology for position-sensitive thermal neutron detection capable to outperform $^{3}$He-based detectors in terms of spatial resolution and timing. However, as for the other types of gaseous detectors with a single layer of $^{10}B_{4}$C at normal beam incidence, the detection efficiency to thermal neutrons of a single-gap $^{10}B$-RPC is only about 6%. Aiming to overcome this limitation, we introduce a multi-layer $^{10}B$-RPCs detector with a stack of ten double-gap hybrid RPCs. A description of the detector design and the results of its characterization performed at the TREFF neutron beamline at the FRM II neutron facility are presented. The results demonstrate that the detection efficiency exceeds 60% for neutrons with a wavelength of 4.7 Å and the spatial resolution (FWHM) is about 0.25 mm and 0.35 mm in the X and Y direction, respectively.

physics.ins-det↗