arXiv subjects

Mikhail V. Dolgopolov

Publications and source records attributed to Mikhail V. Dolgopolov.

4 recordsLinked to original sources

arXiv2026

Effective atom-dimer bands of three-body lattice systems at strong coupling: exact critical mass ratios and a statistics-quasimomentum duality

We study three particles on the square lattice with contact interactions of infinite strength, for all total quasimomenta, for three statistics: three identical bosons, two identical fermions plus a third particle, and two identical bosons plus a third particle. Previous work treated only the trimer and zero quasimomentum. Here the atom-dimer sector is analyzed on the whole Brillouin zone. A Feshbach-Schur reduction onto the infinitely degenerate eigenvalue 1 of the pair-contact operator gives explicit effective Hamiltonians with proved first-order error. The threshold problem reduces to a 4x4 Hermitian matrix criterion built from the two-point resistances of the square lattice, and hence to a quartic polynomial. This yields the complete atom-dimer zone and the critical mass ratio on the Brillouin zone, with bound between 1 and pi/(pi-2), and closed forms at all symmetry points. We prove: the zones in closed form; the critical mass ratio with exact value pi/(pi-2) at zero quasimomentum, reproducing a numerical value; at most two atom-dimer states for every quasimomentum and mass ratio; the onset laws, an essential singularity on the zone boundary and a linear-over-logarithm onset in the pure p-wave; two exact dualities showing that a change of statistics is equivalent to a shift of quasimomentum by pi; and the global range of the second fermionic threshold. The onset laws admit a renormalization-group reading: the inverse lattice Green function is a marginal s-wave coupling, binding energies arise by dimensional transmutation with lattice scale 16, and the zone boundary is of marginal (BCS/Kondo) type rather than of Berezinskii-Kosterlitz-Thouless type. All constants are verified independently by lattice quadrature, computer algebra, exact diagonalisation, and infinite-lattice solvers.

math-ph↗

arXiv2026

Graphene-Assisted Electrostatic Screening of Resonant Transport in MR-DWELL Dosimeters with Tunable Sensitivity--Radiation Tolerance Trade-off: A Reduced-Order Benchmark and Self-Consistent Perspective

We propose a Multi-Resonant Double-barrier Quantum-dot-in-a-Well (MR-DWELL) dosimeter with a tunable trade-off between sensitivity and radiation tolerance, realized through graphene-assisted electrostatic screening. The sensing mechanism relies on radiation-induced trapped charge that shifts and broadens resonant tunneling states in the DWELL heterostructure. The~dimensionless capacitance ratio $η=C_Q/C_{\mathrm{geo}}$ is introduced as the universal design parameter: it~controls the screening factor $S=η/(1+η)$ and thereby the trade-off between sensitivity and radiation hardness. For $η=2.09$ the effective low-dose shift coefficient is reduced threefold (from $0.14$~to $0.045~\mathrm{meV/mGy}$), while the screened architecture retains $\sim\!83\%$ of the peak tunneling current and a peak-to-valley ratio $\sim\!10$ after $1~\mathrm{MGy}$, thereby preserving the dosimetric sensitivity required for practical readout. The~second-derivative spectroscopy $d^2I/dV^2$ is identified as a robust experimental readout. A~reduced-order Landauer model calibrated against literature data is employed for the screening physics, while a self-consistent NEGF-Poisson-trap framework is formulated for future quantitative validation. Explicit design rules for three operating regimes (high sensitivity, balanced, maximum hardness) are provided, together with a three-population trap model that conceptually enables dose-rate discrimination in the FLASH radiotherapy regime. A~comparative analysis of model vintages and their methodological foundations is included to guide interpretation of numerical predictions.

math-ph↗

arXiv2026

Disentangling Measurement Protocol from Material Physics in Isotypic and Anisotypic SiC/Si Heterojunctions: A Metrology-Driven Study for Betavoltaic Energy Conversion

We compare isotypic (n-SiC/n-Si) and anisotypic (n-SiC/p-Si) heterojunctions using Kelvin probe force microscopy, scanning tunnelling spectroscopy, precision electrical measurements with a Keithley 2450 SourceMeter, and a 0.1 farad supercapacitor charge-storage test. Two-wire probing shows an enhanced low-bias current in the isotypic structures; four-wire Kelvin sensing removes the voltage-drop contribution of external leads and contacts and collapses this current to a much lower bulk and interface limited level. The high density of interface states detected by KPFM and STS, up to five times ten to the twelfth per square centimetre per electronvolt in dislocation-rich regions, provides a plausible origin for the enhanced local response. Anisotypic junctions exhibit a genuine diode-like current-voltage characteristic and an open-circuit voltage of about 1.2 volts under beta irradiation. In the capacitor test with the patented charge-pump converter, the anisotypic structure reaches 0.25 volts versus 0.05 volts for the isotypic one after 30 minutes, giving an energy ratio of about 25. We formulate a measurement-interpretation framework based on four-wire Kelvin sensing, generator polarity with cathode to LO, and high-impedance output-off state. Our results show that anisotypic SiC/Si heterojunctions are the preferred platform for betavoltaic conversion when measured correctly.

math-ph↗

arXiv2011

Some aspects of the $m$-adic analysis and its applications to $m$-adic stochastic processes

In this paper we consider a generalization of analysis on $p$-adic numbers field to the $m$ case of $m$-adic numbers ring. The basic statements, theorems and formulas of $p$-adic analysis can be used for the case of $m$-adic analysis without changing. We discuss basic properties of $m$-adic numbers and consider some properties of $m$-adic integration and $m$-adic Fourier analysis. The class of infinitely divisible $m$-adic distributions and the class of $m$-adic stochastic Levi processes were introduced. The special class of $m$-adic CTRW process and fractional-time $m$-adic random walk as the diffusive limit of it is considered. We found the asymptotic behavior of the probability measure of initial distribution support for fractional-time $m$-adic random walk.

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