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A. Morozov

Publications and source records attributed to A. Morozov.

At least 91 records · Page 5Linked to original sources
arXiv2022

Polynomial representations of classical Lie algebras and flag varieties

Recently we have started a program to describe the action of Lie algebras associated with Dynkin-type diagrams on generic Verma modules in terms of polynomial vector fields. In this paper we explain that the results for the classical ABCD series of Lie algebras coincide with the more conventional approach, based on the knowledge of the entire algebra, not only the simple roots. We apply the coset description, starting with a large representation and then reducing it with the help of the algebra, commuting with the original one. The irreducible representations are then obtained by gauge fixing this residual symmetry.

hep-th↗
arXiv2022

The Splendors and Miseries of Heavisidisation

Machine Learning (ML) is applicable to scientific problems, i.e. to those which have a well defined answer, only if this answer can be brought to a peculiar form ${\cal G}: X\longrightarrow Z$ with ${\cal G}(\vec x)$ expressed as a combination of iterated Heaviside functions. At present it is far from obvious, if and when such representations exist, what are the obstacles and, if they are absent, what are the ways to convert the known formulas into this form. This gives rise to a program of reformulation of ordinary science in such terms -- which sounds like a strong enhancement of the constructive mathematics approach, only this time it concerns all natural sciences. We describe the first steps on this long way.

hep-th↗
arXiv2022

Machine learning of the well known things

Machine learning (ML) in its current form implies that an answer to any problem can be well approximated by a function of a very peculiar form: a specially adjusted iteration of Heavyside theta-functions. It is natural to ask if the answers to the questions, which we already know, can be naturally represented in this form. We provide elementary, still non-evident examples that this is indeed possible, and suggest to look for a systematic reformulation of existing knowledge in a ML-consistent way. Success or a failure of these attempts can shed light on a variety of problems, both scientific and epistemological.

hep-th↗
arXiv2022

Evolution properties of the knot's defect

The defect of differential (cyclotomic) expansion for colored HOMFLY-PT polynomials is conjectured to be invariant under any antiparallel evolution and change linearly with the evolution in any parallel direction. In other words, each ${\cal R}$-matrix can be substituted by an entire 2-strand braid in two different ways: the defect remains intact when the braid is antiparallel and changes by half of the added length when the braid is parallel.

hep-th↗
arXiv2022

Measurement of lepton-jet correlation in deep-inelastic scattering with the H1 detector using machine learning for unfolding

The first measurement of lepton-jet momentum imbalance and azimuthal correlation in lepton-proton scattering at high momentum transfer is presented. These data, taken with the H1 detector at HERA, are corrected for detector effects using an unbinned machine learning algorithm OmniFold, which considers eight observables simultaneously in this first application. The unfolded cross sections are compared to calculations performed within the context of collinear or transverse-momentum-dependent (TMD) factorization in Quantum Chromodynamics (QCD) as well as Monte Carlo event generators. The measurement probes a wide range of QCD phenomena, including TMD parton distribution functions and their evolution with energy in so far unexplored kinematic regions.

hep-ex↗
arXiv2022

Superintegrability summary

We enumerate generalizations of the superintegrability property $ \ \sim {\rm character}$ and illuminate possible general structures behind them. We collect variations of original formulas available up to date and emphasize the remaining difference between the cases of Hermitian and complex matrices, bosonic and fermionic ones. Especially important is that the story is in no way restricted to Gaussian potentials.

hep-th↗
arXiv2021

Matrix model partition function by a single constraint

In the recent study of Virasoro action on characters, we discovered that it gets especially simple for peculiar linear combinations of the Virasoro operators: particular harmonics of $\hat w$-operators. In this letter, we demonstrate that even more is true: a {\it single} $w$-constraint is sufficient to uniquely specify the partition functions provided one assumes that it is a power series in time-variables. This substitutes the previous specifications in terms of {\it two} requirements: either a string equation imposed on the KP/Toda $τ$-function or a pair of Virasoro generators. This mysterious {\it single}-entry definition holds for a variety of theories, including Hermitian and complex matrix models, and also matrix models with external matrix: the unitary and cubic Kontsevich models. In these cases, it is equivalent to W-representation and is closely related to {\it super}\,integrability. However, a similar single equation that completely determines the partition function exists also in the case of the generalized Kontsevich model (GKM) with the potential of higher degree, when the constraint algebra is a larger $W$-algebra, and neither W-representation nor superintegrability are understood well enough.

hep-th↗
arXiv2021

Natanzon-Orlov model and refined superintegrability

We reconsider the simple matrix model description of Hurwitz numbers proposed by S. Natanzon and A. Orlov, which uses the superintegrability property of the complex matrix model, and discuss a way of its possible supersymmetric extension to approach spin Hurwitz numbers.

hep-th↗
arXiv2021

Concept of a fast neutron detector based on 10B-RPCs

We propose an alternative approach for the detection of fast neutrons in the energy range from 10-4 to 5 MeV based on 10B-RPCs (hybrid double-gap Resistive Plate Chambers with 10B4C neutron converters) surrounded by a polyethylene moderator. The detection efficiency as a function of the neutron energy is obtained in Monte Carlo simulations performed with the Geant4 toolkit for several detector configurations. The thickness of the neutron converter is optimized for the maximum efficiency. The results show that for this type of detector it is possible to obtain an average detection efficiency larger than 50% with a weak dependence on the neutron energy. The dark count rate and gamma sensitivity are also discussed.

physics.ins-det↗
arXiv2021

From superintegrability to tridiagonal representation of $β$-ensembles

The wonderful formulas by I.Dumitriu and A.Edelman rewrite $β$-ensemble, with eigenvalue integrals containing Vandermonde factors in the power $2β$, through integrals over tridiagonal matrices, where $β$-dependent are the powers of individual matrix elements, not their differences. These potentially useful formulas are usually deduced from rather complicated and non-transparent combinatorics and are not as widely known as they deserve. We explain that the superintegrability property, i.e. a simple expression of the Gaussian averages of arbitrary Jack polynomials through the same Jack polynomials, is immediately consistent with this tridiagonal representation, which may serve as a clue to its simple and transparent interpretation. For a formal non-perturbative proof, we use the Virasoro constraints, which themselves acquire an interesting structure in the tridiagonal realization. We also attract attention to the surprising spontaneous breakdown of discrete invariance by the tridiagonal measure, which may signal a new interesting anomaly at the elementary level of the basic eigenvalue matrix model.

hep-th↗
arXiv2021

A new kind of anomaly: on W-constraints for GKM

We look for the origins of the single equation, which is a peculiar combination of W-constrains, which provides the non-abelian W-representation for generalized Kontsevich model (GKM), i.e. is enough to fix the partition function unambiguously. Namely we compare it with the scalar projection of the matrix Ward identity. It turns out that, though similar, the two equations do not coincide, moreover, the latter one is non-polynomial in time-variables. This discrepancy disappears for the cubic model if partition function is reduced to depend on odd times (belong to KdV sub-hierarchy of KP), but in general such reduction is not enough. We consider the failure of such direct interpretation of the "single equation" as a new kind of anomaly, which should be explained and eliminated in the future analysis of GKM.

hep-th↗
arXiv2021

Superintegrability of matrix Student's distribution

For ordinary matrix models, the eigenvalue probability density decays rapidly as one goes to infinity, in other words, has "short tails". This ensures that all the multiple trace correlators (multipoint moments) are convergent and well-defined. Still, many critical phenomena are associated with an enhanced probability of seemingly rare effects, and one expects that they are better described by the "long tail" models. In absence of the exponential fall-off, the integrals for high moments diverge, and this could imply a loss of (super)integrability properties pertinent to matrix and eigenvalue models and, presumably, to the non-perturbative (exact) treatment of more general quantum systems. In this paper, we explain that this danger to modern understanding could be exaggerated. We consider a simple family of long-tail matrix models, which preserve the crucial feature of superintegrability: exact factorized expressions for a full set of basic averages. It turns out that superintegrability can survive after an appropriate (natural and obvious) analytical continuation even in the presence of divergencies, which opens new perspectives for the study of the long-tail matrix models.

hep-th↗
arXiv2021

Statistical position reconstruction for RPC-based thermal neutron detectors

Multilayer position-sensitive 10B-RPC thermal neutron detectors offer an attractive combination of sub-millimeter spatial resolution and high (>50%) detection efficiency. Here we describe a new position reconstruction method based on a statistical approach. Using experimental data, we compare the performance of this method with that of the centroid reconstruction. Both methods result in a similar image linearity/uniformity and spatial resolution. However, the statistical method allows to improve the image quality at the detector periphery, offers more flexible event filtering and allows to develop automatic quality monitoring procedures for early detection of situations when a change in the detector operation conditions starts to affect reconstruction quality.

physics.ins-det↗
arXiv2021

Non-Abelian W-representation for GKM

$W$-representation is a miraculous possibility to define a non-perturbative (exact) partition function as an exponential action of somehow integrated Ward identities on unity. It is well known for numerous eigenvalue matrix models when the relevant operators are of a kind of $W$-operators: for the Hermitian matrix model with the Virasoro constraints, it is a $W_3$-like operator, and so on. We extend this statement to the monomial generalized Kontsevich models (GKM), where the new feature is the appearance of an ordered P-exponential for the set of non-commuting operators of different gradings.

hep-th↗
arXiv2021

Determination of the strong coupling constant $α_s(M_Z)$ in next-to-next-to-leading order QCD using H1 jet cross section measurements

The strong coupling constant $α_s(M_Z)$ is determined from inclusive jet and dijet cross sections in neutral-current deep-inelastic $ep$ scattering (DIS) measured at HERA by the H1 collaboration using next-to-next-to-leading order (NNLO) QCD predictions. The dependence of the NNLO predictions and of the resulting value of $α_s(M_Z)$ at the $Z$-boson mass $m_Z$ are studied as a function of the choice of the renormalisation and factorisation scales. Using inclusive jet and dijet data together, the strong coupling constant is determined to be $α_s(M_Z)=0.1166\,(19)_{\rm exp}\,(24)_{\rm th}$. Complementary, $α_s(M_Z)$ is determined together with parton distribution functions of the proton (PDFs) from jet and inclusive DIS data measured by the H1 experiment. The value $α_s(M_Z)=0.1147\,(25)_{\rm tot}$ obtained is consistent with the determination from jet data alone. The impact of the jet data on the PDFs is studied. The running of the strong coupling is tested at different values of the renormalisation scale and the results are found to be in agreement with expectations.

hep-ex↗
arXiv2021

Unperturbed inverse kinematics nucleon knockout measurements with a 48 GeV/c carbon beam

From superconductors to atomic nuclei, strongly-interacting many-body systems are ubiquitous in nature. Measuring the microscopic structure of such systems is a formidable challenge, often met by particle knockout scattering experiments. While such measurements are fundamental for mapping the structure of atomic nuclei, their interpretation is often challenged by quantum mechanical initial- and final-state interactions (ISI/FSI) of the incoming and scattered particles. Here we overcome this fundamental limitation by measuring the quasi-free scattering of 48 GeV/c 12C ions from hydrogen. The distribution of single protons is studied by detecting two protons at large angles in coincidence with an intact 11B nucleus. The 11B detection is shown to select the transparent part of the reaction and exclude the otherwise large ISI/FSI that would break the 11B apart. By further detecting residual 10B and 10Be nuclei, we also identified short-range correlated (SRC) nucleon-nucleon pairs, and provide direct experimental evidence for the separation of the pair wave-function from that of the residual many-body nuclear system. All measured reactions are well described by theoretical calculations that do not contain ISI/FSI distortions. Our results thus showcase a new ability to study the short-distance structure of short-lived radioactive atomic nuclei at the forthcoming FAIR and FRIB facilities. These studies will be pivotal for developing a ground-breaking microscopic understanding of the structure and properties of nuclei far from stability and the formation of visible matter in the universe.

nucl-ex↗
arXiv2021

Irreducible representations of simple Lie algebras by differential operators

We describe a systematic method to construct arbitrary highest-weight modules, including arbitrary finite-dimensional representations, for any finite dimensional simple Lie algebra $\mathfrak{g}$. The Lie algebra generators are represented as first order differential operators in $\frac{1}{2} \left(\dim \mathfrak{g} - \text{rank} \, \mathfrak{g}\right) $ variables. All rising generators ${\bf e}$ are universal in the sense that they do not depend on representation, the weights enter (in a very simple way) only in the expressions for the lowering operators ${\bf f}$. We present explicit formulas of this kind for the simple root generators of all classical Lie algebras.

hep-th↗