arXiv subjects

Igor Lobanov

Publications and source records attributed to Igor Lobanov.

10 recordsLinked to original sources

arXiv2026

Pixel-Translation-Equivariant Quantum Convolutional Neural Networks via Fourier Multiplexers

Convolutional neural networks owe much of their success to hard-coding translation equivariance. Quantum convolutional neural networks (QCNNs) have been proposed as near-term quantum analogues, but the relevant notion of translation depends on the data encoding. For address/amplitude encodings such as FRQI, a pixel shift acts as modular addition on an index register, whereas many MERA-inspired QCNNs are equivariant only under cyclic permutations of physical qubits. We formalize this mismatch and construct QCNN layers that commute exactly with the pixel cyclic shift (PCS) symmetry induced by the encoding. Our main technical result is a constructive characterization of all PCS-equivariant unitaries: conjugation by the quantum Fourier transform (QFT) diagonalizes translations, so any PCS-equivariant layer is a Fourier-mode multiplexer followed by an inverse QFT (IQFT). Building on this characterization, we introduce a deep PCS-QCNN with measurement-induced pooling, deferred conditioning, and inter-layer QFT cancellation. We also analyze trainability at random initialization and prove a lower bound on the expected squared gradient norm that remains constant in a depth-scaling regime, ruling out a depth-induced barren plateau in that sense.

quant-ph↗

arXiv2025

Magneto-Moir\'e Excitons in Twisted Bilayer CrSBr

Moir\'e superlattices in van der Waals materials have revolutionized the study of electronic and excitonic systems by creating periodic electrostatic potentials. Extending this concept to magnetic materials promises new pathways in merging spintronics with photonics. While moir\'e magnetism has been revealed with near-field probes and nonlinear optical techniques, the coupling of these magnetic textures to optical excitations - magneto-moir\'e excitons - remains unexplored. Here, we report the observation of magneto-moir\'e excitons in twisted bilayer CrSBr, correlated with moir\'e spin textures that emerge below a critical twist angle of ~2{\deg}. The nanoscale moir\'e spin texture imprints distinct signatures onto the optical spectrum, shifting the exciton energy via a periodic magnetic exchange field. First-principles calculations corroborate that these signatures arise from one-dimensional spin textures governed by the balance of exchange interactions and domain wall energy. Our results demonstrate that moir\'e magnetism can be used to engineer nanoscale excitonic energy landscapes, providing a new platform for magneto-optical sensing, quantum transduction, and control of non-collinear magnetism and topology through light.

cond-mat.mes-hall↗

arXiv2024

Multem 3: An updated and revised version of the program for transmission and band calculations of photonic crystals

We present here Multem 3, an updated and revised version of Multem 2, which syntax has been upgraded to Fortran 2018, with the source code being divided into modules. Multem 3 is equipped with LAPACK, the state-of-the art Faddeeva complex error function routine, and the Bessel function package AMOS. The amendments significantly improve both the speed, convergence, and precision of Multem 2. Increased stability allows to freely increase the cut-off value LMAX on the number of spherical vector wave functions and the cut-off value RMAX controlling the maximal length of reciprocal vectors taken into consideration. An immediate bonus is that Multem 3 can be reliably used to describe bound states in the continuum (BICs). To ensure convergence of the layer coupling scheme, it appears that appreciably larger values of convergence paramaters LMAX and RMAX are required than those reported in numerous published work in the past using Multem 2. We hope that Multem 3 will become a reliable and fast alternative to generic commercial software, such as COMSOL Multiphysics, CST Microwave Studio, or Ansys HFSS, and that it will become the code of choice for various optimization tasks for a large number of research groups. The improvements concern the core part of Multem 2, which is common to the extensions of Multem 2 for acoustic and elastic multiple scattering and to the original layer-Kohn-Korringa-Rostocker (LKKR) code. Therefore, the enhancements presented here can be readily applied to the above codes as well.

physics.comp-ph↗

arXiv2023

Skyrmion dynamics in moiré magnets

We consider a twisted magnetic bilayer subject to the perpendicular electric field. The interplay of induced Dzyaloshinskii - Moriya interaction and spatially varying moiré exchange potential results in complex non-collinear magnetic phases in these structures. We numerically demonstrate the coexistence of intralayer skyrmions and bound interlayer skyrmion pairs and show that they are characterized by distinct dynamics under the action of external in-plane electric field. Specifically we demonstrate the railing behaviour of skyrmions along the domain walls which could find applications in spintronic devices based on van der Waals magnets.

cond-mat.mes-hall↗

arXiv2023

Lifetime, collapse and escape paths for hopfions in bulk magnets with competing exchange interactions

The lifetimes of magnetic hopfions on a discrete lattice with competing exchange interactions are calculated within the framework of the transition state theory for magnetic degrees of freedom. Three sets of discrete model parameters corresponding to the same continuous micromagnetic model are considered. Minimal energy paths for hopfion collapses were found on the multidimensional energy surface of the system. The activation energies of the collapse processes have been calculated. It turned out that the activation energy differs significantly for the three considered values of the parameters, which indicates the importance of lattice effects, when the hopfion radius equals several lattice constants. Along with the collapse, the hopfion escape process through the sample boundary is studied. It is shown that this process does not require an activation energy. The lifetimes of hopfions are found and it is shown that they can exist only at temperatures of a few kelvins and practically cannot be generated due to thermal fluctuations.

cond-mat.mtrl-sci↗

arXiv2009

A remark on Schatten-von Neumann properties of resolvent differences of generalized Robin Laplacians on bounded domains

In this note we investigate the asymptotic behaviour of the $s$-numbers of the resolvent difference of two generalized self-adjoint, maximal dissipative or maximal accumulative Robin Laplacians on a bounded domain $Ω$ with smooth boundary $\partialΩ$. For this we apply the recently introduced abstract notion of quasi boundary triples and Weyl functions from extension theory of symmetric operators together with Krein type resolvent formulae and well-known eigenvalue asymptotics of the Laplace-Beltrami operator on $\partialΩ$. It will be shown that the resolvent difference of two generalized Robin Laplacians belongs to the Schatten-von Neumann class of any order $p$ for which $p>(dimΩ-1)/3$. Moreover, we also give a simple sufficient condition for the resolvent difference of two generalized Robin Laplacians to belong to a Schatten-von Neumann class of arbitrary small order. Our results extend and complement classical theorems due to M.Sh.Birman on Schatten-von Neumann properties of the resolvent differences of Dirichlet, Neumann and self-adjoint Robin Laplacians.

math.SP↗

arXiv2009

Lower bound on the spectrum of the Schrödinger operator in the plane with delta-potential supported by a curve

We consider the Schrödinger operator in the plane with delta-potential supported by a curve. For the cases of an infinite curve and a finite loop we give estimates on the lower bound of the spectrum expressed explicitly through the strength of the interaction and a parameter which characterizes geometry of the curve. Going further we cut the curve into finite number of pieces and estimate the bottom of the spectrum using the parameters for the pieces. As an application of the elaborated theory we consider a curve with a finite number of cusps and "leaky" quantum graphs.

math.SP↗

arXiv2007

Schrödinger operators on armchair nanotubes. I

We consider the Schrödinger operator with a periodic potential on quasi-1D models of armchair single-wall nanotubes. The spectrum of this operator consists of an absolutely continuous part (intervals separated by gaps) plus an infinite number of eigenvalues with infinite multiplicity. We describe all eigenfunctions with the same eigenvalue. We define a Lyapunov function, which is analytic on some Riemann surface. On each sheet, the Lyapunov function has the same properties as in the scalar case, but it has branch points, which we call resonances. In example we show the existence of real and complex resonances for some specific potentials.

math-ph↗

arXiv2006

Schrödinger operators on zigzag graphs

We consider the Schrödinger operator on zigzag graphs with a periodic potential. The spectrum of this operator consists of an absolutely continuous part (intervals separated by gaps) plus an infinite number of eigenvalues with infinite multiplicity. We describe all compactly supported eigenfunctions with the same eigenvalue. We define a Lyapunov function, which is analytic on some Riemann surface. On each sheet, the Lyapunov function has the same properties as in the scalar case, but it has branch points, which we call resonances. We prove that all resonances are real. We determine the asymptotics of the periodic and anti-periodic spectrum and of the resonances at high energy. We show that there exist two types of gaps: i) stable gaps, where the endpoints are periodic and anti-periodic eigenvalues, ii) unstable (resonance) gaps, where the endpoints are resonances (i.e., real branch points of the Lyapunov function). We obtain the following results from the inverse spectral theory: 1) we describe all finite gap potentials, 2) the mapping: potential -- all eigenvalues is a real analytic isomorphism for some class of potentials. We apply all these results to quasi-1D models of zigzag single-well carbon nanotubes.

math.SP↗

arXiv2006

Zigzag periodic nanotube in magnetic field

We consider the magnetic Schrödinger operator on the so-called zigzag periodic metric graph (a quasi 1D continuous model of zigzag nanotubes) with a periodic potential. The magnetic field (with the amplitude $B\in R$) is uniform and it is parallel to the axis of the nanotube. The spectrum of this operator consists of an absolutely continuous part (spectral bands separated by gaps) plus an infinite number of eigenvalues with infinite multiplicity. We describe all compactly supported eigenfunctions with the same eigenvalue. We define a Lyapunov function, which is analytic on some Riemann surface. On each sheet, the Lyapunov function has the same properties as in the scalar case, but it has branch points, which we call resonances. We prove that all resonances are real. We determine the asymptotics of the periodic and anti-periodic spectrum and of the resonances at high energy. We show that endpoints of the gaps are periodic or anti-periodic eigenvalues or resonances (real branch points of the Lyapunov function). We describe the spectrum as functions of $B$. For example, if $B\to B_{k,m}=\frac{4(\fracπ{2}-\frac{πk}{N}+πm)}{\sqrt 3 \cos \fracπ{2N}}, k=1,2,..,N, m\in Z$, then some spectral band shrinkes into a flat band i.e., an eigenvalue of infinite multiplicity.

math.SP↗