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Alexander Petrov

Publications and source records attributed to Alexander Petrov.

At least 19 recordsLinked to original sources
arXiv2026

Formality for rigid-analytic spaces satisfying the weight-monodromy conjecture

We prove that \'etale and de Rham cohomology algebras of a smooth proper rigid-analytic space over a finite extension of $\mathbf{Q}_p$ are formal if the rigid-analytic space satisfies the weight-monodromy conjecture. This is achieved by showing that the underlying $E_\infty$-algebra of a monodromy-pure $E_\infty$-algebra in Weil--Deligne representations is formal. We give examples of smooth proper rigid-analytic surfaces whose cohomology algebras are not formal.

math.AG↗
arXiv2026

Electric field dependent g factors of RaOCH$_3$ molecule

The sensitivity of experiments searching for the electron electric dipole moment (eEDM) using the symmetric top molecules can be greatly enhanced by laser cooling. A detailed understanding of the Zeeman structure of the eEDM-sensitive levels is crucial for controlling systematic effects. We have developed a method for calculating the $g$-factors of $K$-doublet levels in symmetric top molecules and applied it to RaOCH$_3$. The electric-field-dependent $g$-factors of the first excited rotational level of RaOCH$_3$ are calculated. $K$-doublet levels with a small difference in $g$-factors are identified, and the main contributions to this difference are determined.

physics.atom-ph↗
arXiv2026

Quantum Scattering of Fullerene 12C60 with Rare Gas Atoms and its selection rules for rotational quenching

The discovery of the C60 fullerene opened new horizons to design carbon nanostructures with targeted electronic structure as well as transport and optical properties. For example, endohedral 12C60 molecules were proposed as candidates for functional quantum architectures to store and manipulate encased atomic and molecular qubits. Recent advances in cryogenic buffer-gas cooling and frequency-comb spectroscopy have enabled rovibrational quantum-state-resolved measurements of gas-phase 12C60, revealing rotational fine structure reflecting its high icosahedral symmetry. Here, we present a perturbative quantum description of the 12C60 molecule interacting with a buffer gas of 40Ar atoms at temperatures of order 100 K, including a detailed analysis of their electronic structure, their interaction anisotropies, and the collision-induced rotational quenching of 12C60 in its vibrational and electronic ground state. The role of the icosahedral symmetry on the collisional dynamics is emphasized leading to unusual selection rules. Finally, we compute the isotropic and anisotropic static and dynamic dipole polarizability of 12C60 in its absolute ground state in order to evaluate the long-range, van der Waals interaction between 12C60 and 40Ar.

physics.atom-ph↗
arXiv2025

Non-decomposability of the de Rham complex and non-semisimplicity of the Sen operator

We describe the obstruction to decomposing in degrees $\leq p$ the de Rham complex of a smooth variety over a perfect field $k$ of characteristic $p$ that lifts over $W_2(k)$, and show that there exist liftable smooth projective varieties of dimension $p+1$ whose Hodge-to-de Rham spectral sequence does not degenerate at the first page. We also describe the action of the Sen operator on the de Rham complex in degrees $\leq p$ and give examples of varieties with a non-semisimple Sen operator. Our methods rely on the commutative algebra structure on de Rham and Hodge-Tate cohomology, and are inspired by the properties of Steenrod operations on cohomology of cosimplicial commutative algebras. The example of a non-degenerate Hodge-to-de Rham spectral sequence relies on a non-vanishing result on cohomology of groups of Lie type. We give applications to other situations such as describing extensions in the canonical filtration on de Rham, Hodge, and étale cohomology of an abelian variety equipped with a group action. We also show that the de Rham complex of a smooth variety over $k$ is formal as an $E_{\infty}$-algebra if and only if the variety lifts to $W_2(k)$ together with its Frobenius endomorphism.

math.AG↗
arXiv2025

Energy dependent Chemical Interface Damping induced by 1-Decanethiol Self-Assembled Monolayer on Au(111)

The chemical interface damping (CID) effect increases the collision frequency of free electrons in metals by changes of the metal surface. We have now experimentally disentangled the two contributions to CID: induced roughness and direct charge transfer. The latter is an important area of research in photoelectrochemistry with potential applications in light-induced chemical reactions. We present a broadband investigation of the CID effect on Au(111) covered by a self-assembled monolayer of decanethiol. Spectroscopic ellipsometry measurements show a photon energy dependent increase of collision frequency. We observe a constant, photon energy independent contribution, which is attributed to induced roughness and a contribution that linearly increases with photon energy from about 1 eV upwards which we attribute to direct charge transfer. The onset of the charge transfer mechanism corresponds to occupied orbitals of thiols bound to the Au surface, as confirmed by density functional theory calculations.

cond-mat.mtrl-sci↗
arXiv2025

Impact of ligand (OH) deformation on LuOH$^+$ rovibrational spectra

Triatomic cation $^{175}$LuOH$^+$, featuring near-degenerate, opposite-parity $l$-doublets, offers enhanced sensitivity to $\mathcal{P}$- and $\mathcal{T}$-violating interactions. We present \emph{ab initio} calculations of its electronic structure and rovibrational structure beyond the rigid-ligand approximation by explicitly including OH-ligand deformation together with bending and stretching motions. Potential-energy surfaces are computed at the relativistic coupled cluster level of theory. The nuclear Schrödinger equation in Jacobi coordinates is solved by means of a coupled-channel expansion. Ligand deformation reduces the bending frequency by a few percent and increases the $l$-doubling constant $q$, while the stretching frequencies and rotational constants remain largely unchanged. For the first excited bending level, we predict $ΔE_{J=1}=2q \approx 24.9$--$26.4$ MHz. These results establish LuOH$^+$ as a viable platform for precision searches for $\mathcal{CP}$-violating physics via the electron electric dipole moment and the nuclear magnetic quadrupole moment.

physics.chem-ph↗
arXiv2025

Hyperfine structure and $K$-doubling in RaOCH$_3$ molecule

RaOCH$_3$ molecule is one of the most sensitive systems for the electron electric dipole moment ($e$EDM) searches. Its hyperfine and $K-$doubling structure in the external electric field is of key importance for preparing and interpreting the experiment. We propose the method for calculation the symmetric top molecules and applied it for RaOCH$_3$. Hyperfine structure, $K-$doubling and sensitivity of the molecule to $e$EDM in the external electric field were calculated.

physics.atom-ph↗
arXiv2025

Electric field dependent g factors of ThF$^+$

The g-factors for $J = 1$, $F=3/2$, $|M_F|=3/2$ hyperfine levels of the ground electronic state $^3Δ_1$ of the $^{232}$ThF$^+$ cation are calculated as functions of the external electric field. These calculations are necessary for the analysis of systematic effects in the experiment aimed at searching for the electron electric dipole moment.

physics.atom-ph↗
arXiv2025

Decomposition of de Rham complex for quasi-F-split varieties

Using the de Rham stack of Bhatt-Lurie and Drinfeld, we prove that de Rham complex of a smooth quasi-F-split variety over a perfect field of positive characteristic decomposes in all degrees. In particular, smooth proper quasi-F-split varieties have degenerate Hodge-to-de Rham spectral sequence, and satisfy Kodaira-Akizuki-Nakano vanishing. We apply this to prove that the Hodge-to-de Rham spectral sequence for the classifying stack of a reductive group over a field of positive characteristic degenerates.

math.AG↗
arXiv2024

On spectral sequences for semiabelian varieties over non-closed fields

We give a new, short proof of the formula for the first potentially non-zero differential of the Hochschild--Serre spectral sequence for semiabelian varieties over non-closed fields. We show that this differential is non-zero for the Jacobian of a curve when the image of the torsor of theta-characteristics under the Bockstein map is non-zero. An explicit example is a curve of genus 2 whose Albanese torsor is not divisible by 2. When the Albanese torsor is trivial, we show that the Hochschild--Serre spectral sequence for the Jacobian degenerates at the second page. We give a formula for the differential of the Hochschild--Serre spectral sequence for a torus which computes its Brauer group. Finally, we describe the differentials of the Hochschild--Serre spectral sequence for a smooth projective curve, generalising a lemma of Suslin.

math.AG↗
arXiv2024

Electric field dependent g factors of YbOH molecule

YbOH molecule is one of the most sensitive systems for the electron electric dipole moment ($e$EDM) searches. Zeeman splittings of the $e$EDM sensitive levels have significant implications to control and suppress important systematic effects due to stray magnetic field in experiments for $e$EDM searches. The electric-field-dependent g factors of the lowest rotational level of the first excited bending vibrational mode of $^{174}$YbOH are calculated. l-doublet levels with small g factors difference are found and main contributions to the difference are determined.

physics.atom-ph↗
arXiv2024

Chemical Interface Damping by Electrochemical Gold Oxidation

Chemical interface damping is a change in the effective collision frequency of conduction band electrons in metal originating from a chemical change of the metal interface. In this work, we present in-situ ellipsometric measurements that reveal the chemical interface damping effect from electrochemical oxidation of single crystal and polycrystalline gold films. We observe an increase in collision frequency of up to 21 meV for single-crystalline gold. To compare to results obtained with thiols and metal-oxides on gold nanoparticles, we normalize the collision frequency by the electron mean free path to the surface of the structure. We show that electrochemical gold oxidation provides a stronger effect on collision frequency than these coatings. Similar ellipsometric experiments have previously been conducted to investigate the optical properties of gold oxide, but without taking chemical interface damping into account. The change in reflection from oxidation of gold was solely attributed to the oxide coating. We also show that the chemical interface damping effect saturates at a larger effective oxide thickness, which is attributed to the stabilization of the gold-oxide interface.

cond-mat.mtrl-sci↗
arXiv2024

Size dependent photoemission study by electrochemical coarsening of nanoporous gold

The generation and utilization of hot charge carriers in plasmonic materials have emerged as a topic of significant importance, with profound implications across multiple disciplines, including optoelectronics, photovoltaics, photocatalysis, and sensing. In this study, we investigate the hot electron transfer from nanoporous gold (npAu) in dependence of the structure size, utilizing both the nanoscale feature size and the interconnected nature of this material. We employ photoelectron injection from nanoporous gold into the electrolyte under UV illumination as a test electron transfer process. Nanoporous gold thin films with sub-10 nm initial ligament diameter are stepwise coarsened by potential cycles in a photoelectrochemical setup, thereby allowing us to precisely probe the influence of ligament diameter on the photocurrent response. The resulting ligament diameter variations are confirmed by scanning electron microscopy (SEM) analysis. As the ligament diameter increased from 8 to 16 nm, there was a corresponding decrease in quantum efficiency proportional to the inverse ligament diameter squared. Such dependency is expected for electrons excited by surface collisions. For the small ligament diameter of 10 nm we estimate an emission efficiency of excited 6sp electrons as 3.14%, reaching 23% for the surface excited electrons.

physics.optics↗
arXiv2023

Electronic matrix elements for parity doubling in YbOH molecule

YbOH molecule is one of the most sensitive systems for the electron electric dipole moment ($e$EDM) searches. The $e$EDM-induced energy shift is proportional to polarization ($P$) of the molecule. In Ref. [A. Petrov and A. Zakharova, Phys. Rev. A 105, L050801 (2022)] was shown that the value of l-doubling and spin-rotation splitting directly influences the maximum value of $P$. Recently in Ref. [Jadbabaie, Y. Takahashi, N. H. Pilgram, C. J. Conn, Y. Zeng, C. Zhang, and N. R. Hutzler, New Journal of Physics 25, 073014 (2023)] the corresponding energy levels was determined experimentally. We introduced electronic matrix elements in Hund's case $c$ coupling scheme to reproduce experimental energy levels and calculated $P$ as function of external electric field.

physics.atom-ph↗
arXiv2023

Magnetic quadrupole moment of $^{175}$Lu and parity-violating polarization degree of levels in $^{175}$LuOH$^+$

The calculation of the parity-violating polarizations in the external electric field, which are associated with the electron electric dipole moment ($e$EDM) and magnetic quadrupole moment (MQM) of the $^{175}$Lu nucleus, as well as the determination of the rovibrational structure for the $^{175}$LuOH$^+$ cation, is performed. Beyond the bending of the molecule, the slight effect of the stretching of the distance between Lu and OH is taken into account. This study is required for the preparation of the experiment and for the extraction of the $e$EDM and MQM values of $^{175}$Lu from future measurements.

physics.atom-ph↗
arXiv2023

Quantum Control of Atom-Ion Charge Exchange via Light-induced Conical Intersections

Conical intersections are crossing points or lines between two or more adiabatic electronic potential energy surfaces in the multi-dimensional coordinate space of colliding atoms and molecules. Conical intersections and corresponding non-adiabatic coupling can greatly affect molecular dynamics and chemical properties. In this paper, we predict significant or measurable non-adiabatic effects in an ultracold atom-ion charge-exchange reaction in the presence of laser-induced conical intersections (LICIs). We investigate the fundamental physics of these LICIs on molecular reactivity under unique conditions: those of relatively low laser intensity of $10^8$ W/cm$^2$ and ultracold temperatures below 1 mK. We predict irregular interference effects in the charge-exchange rate coefficients between K and Ca$^+$ as functions of laser frequency. These irregularities occur in our system due to the presence of two LICIs. To further elucidate the role of the LICIs on the reaction dynamics, we compare these rate coefficients with those computed for a system where the CIs have been ``removed''. In the laser frequency window, where conical interactions are present, the difference in rate coefficients can be as large as $10^{-9}$ cm$^3$/s.

physics.atom-ph↗