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Alexander Petrov

Publications and source records attributed to Alexander Petrov.

At least 37 records · Page 2Linked to original sources
arXiv2022

$\mathcal{P}$,$\mathcal{T}$-odd energy shifts of the $^{173}$YbOH

The energy shift in molecular spectra due to interaction of nuclear magnetic quadrupole moment ($M$) with electrons is equal to $δE_M = MW_M P_{ M}$, where $W_M$ is a constant determined by the electronic structure of the molecule and $P_{ M}$ is a dimensionless constant. We extended the method for calculation of parity nonconservation effects in triatomic molecules developed in Ref. [A. Petrov and A. Zakharova, Phys. Rev. A ${\bf 105}$, L050801 (2022)] to the case of $P_{ M}$ constant and applied it to $^{173}$YbOH in the first excited $v=1$ bending mode. Results of our calculations are required for the extraction of the $M$ value from the YbOH experiment.

physics.atom-ph↗
arXiv2022

Impact of the ligand deformation on the $\mathcal{P}$,$\mathcal{T}$-violation effects in the YbOH molecule

The ytterbium monohydroxide is a promising molecule for a new physics searches. It is well known that levels of the opposite parity, separated by the energy split, so-called $l$-doublets, define the experimental electric field strength required for the molecule polarization. In addition, in our previous paper [Phys.Rev. A 105, L050801 (2022)] we have shown that the value of $l$-doubling directly influences the sensitivity of linear triatomic molecules to the $\mathcal{P}$,$\mathcal{T}$-odd effects. In our work [The JCP 155, 164301 (2021)] we have calculated the value of $l$-doubling for the YbOH molecule with approximation of fixed O-H bond length. Accounting the importance of this property, in the present study we consider the additional degree of freedom corresponding to the ligand (OH) deformation.

physics.atom-ph↗
arXiv2022

Sensitivity of the YbOH molecule to $\mathcal{P}$,$\mathcal{T}$-odd effects in the external electric field

Electron electric dipole moment (eEDM) search using lasercoolable triatomics like YbOH is one of the most sensitive probes for physics beyond the Standard Model. The eEDM-induced energy shift is proportional to polarization ($P$) of the molecule. Similarly to diatomics with $Ω-$doubling structure it was assumed that for triatomics with $l-$doubling structure, related to the vibrational angular momentum, $P$ can easily be saturated to almost 100\% value with moderate external electric field. We developed the method for calculation of properties of triatomic molecules and applied it to calculation of $P$ of $^{174}$YbOH in the first excited $v=1$ bending mode. Calculations showed that the most of the levels reach less than 50\% efficiency. We showed that this fact is related to the Hund's case $b$ coupling scheme of YbOH. As coupling scheme (for $Ω=1/2$ molecules) approaches $a$ (or $c$) case polarization increases up to 100\% value. Results of our calculations should be used for correct extracting of eEDM value from YbOH experiment and similar calculations are required for other molecules.

physics.atom-ph↗
arXiv2021

Rovibrational structure of the Ytterbium monohydroxide molecule and the $\mathcal{P}$,$\mathcal{T}$-violation searches

The spectrum of triatomic molecules with close rovibrational opposite parity levels is sensitive to the $\mathcal{P}$,$\mathcal{T}$-odd effects. This makes them a convenient platform for the experimental search of a new physics. Among the promising candidates one may distinguish the YbOH as a non-radioactive compound with a heavy atom. The energy gap between levels of opposite parity, $l$-doubling, is of a great interest as it determines the electric field strength required for the full polarization of the molecule. Likewise, the influence of the bending and stretching modes on the sensitivities to the $\mathcal{P}$,$\mathcal{T}$-violation requires a thorough investigation since the measurement would be performed on the excited vibrational states. This motivates us to obtain the rovibrational nuclear wavefunctions, taking into account the anharmonicity of the potential. As a result, we get the values of the $E_{\rm eff}$ and $E_s$ for the lowest excited vibrational state and determine the $l$-doubling

physics.atom-ph↗
arXiv2021

Geometrically irreducible $p$-adic local systems are de Rham up to a twist

We prove that any geometrically irreducible $\overline{\mathbb{Q}}_p$-local system on a smooth algebraic variety over a $p$-adic field $K$ becomes de Rham after a twist by a character of the Galois group of $K$. In particular, for any geometrically irreducible $\overline{\mathbb{Q}}_p$-local system on a smooth variety over a number field the associated projective representation of the fundamental group automatically satisfies the assumptions of the relative Fontaine-Mazur conjecture. The proof uses $p$-adic Simpson and Riemann-Hilbert correspondences of Diao-Lan-Liu-Zhu and the Sen operator on the decompletions of those developed by Shimizu. Along the way, we observe that a $p$-adic local system on a smooth geometrically connected algebraic variety over $K$ is Hodge-Tate if its stalk at one closed point is a Hodge-Tate Galois representation. Moreover, we prove a version of the main theorem for local systems with arbitrary geometric monodromy, which allows us to conclude that the Galois action on the pro-algebraic completion of the fundamental group is de Rham.

math.AG↗
arXiv2021

Relativistic aspects of orbital and magnetic anisotropies in the chemical bonding and structure of lanthanide molecules

The electronic structure of magnetic lanthanide atoms is fascinating from a fundamental perspective. They have electrons in a submerged open 4f shell lying beneath a filled 6s shell with strong relativistic correlations leading to a large magnetic moment and large electronic orbital angular momentum. This large angular momentum leads to strong anisotropies, i. e. orientation dependencies, in their mutual interactions. The long-ranged molecular anisotropies are crucial for proposals to use ultracold lanthanide atoms in spin-based quantum computers, the realization of exotic states in correlated matter, and the simulation of orbitronics found in magnetic technologies. Short-ranged interactions and bond formation among these atomic species have thus far not been well characterized. Efficient relativistic computations are required. Here, for the first time we theoretically determine the electronic and ro-vibrational states of heavy homonuclear lanthanide Er2 and Tm2 molecules by applying state-of-the-art relativistic methods. In spite of the complexity of their internal structure, we were able to obtain reliable spin-orbit and correlation-induced splittings between the 91 Er2 and 36 Tm2 electronic potentials dissociating to two ground-state atoms. A tensor analysis allows us to expand the potentials between the atoms in terms of a sum of seven spin-spin tensor operators simplifying future research. The strengths of the tensor operators as functions of atom separation are presented and relationships among the strengths, derived from the dispersive long-range interactions, are explained. Finally, low-lying spectroscopically relevant ro-vibrational energy levels are computed with coupled-channels calculations and analyzed.

quant-ph↗
arXiv2021

Conserved Currents and Superpotentials in Teleparallel Equivalent of General Relativity

We study the Teleparallel Equivalent of General Relativity (TEGR) with Lagrangian that includes the flat (inertial) spin connection and that is evidently invariant with respect to local Lorentz rotations. Applying directly the Noether theorem, we construct new expressions for conserved currents and related superpotentials. They are covariant both under coordinate transformations and local Lorentz rotations, and allow us to construct well defined conserved charges, unlike earlier approaches. The advantage is achieved by an explicit presence of a displacement vector in the new expressions that can be interpreted as a Killing vector, as a proper vector of an observer, etc. The new expressions are used to introduce a principle for definition of an inertial spin connection that is undetermined one in the TEGR from the start. Theoretical results are applied to calculate mass for the Schwarzschild black hole and densities of conserved quantities for freely falling observers both in Friedmann-Lemaitre-Robertson-Walker world of all the three signs of curvature and in (anti-)de Sitter space.

gr-qc↗
arXiv2020

$\mathcal{P}$,$\mathcal{T}$-odd effects for RaOH molecule in the excited vibrational state

Triatomic molecule RaOH combines the advantages of laser-coolability and the spectrum with close opposite-parity doublets. This makes it a promising candidate for experimental study of the $\mathcal{P}$,$\mathcal{T}$-violation. Previous studies concentrated on the calculations for different geometries without the averaging over the rovibrational wave function and stressed the possibility that the dependence of the $\mathcal{P}$, $\mathcal{T}$ parameters on the bond angle may significantly alter the observed value. We obtain the rovibrational wave functions of RaOH in the ground electronic state and excited vibrational state using the close-coupled equations derived from the adiabatic Hamiltonian. The potential surface is constructed based on the two-component relativistic CCSD(T) computation employing the generalized relativistic effective core potential (GRECP) for the Radium atom. The averaged values of the parameters $E_{\rm eff}$ and $E_s$ describing the sensitivity of the system to the electron electric dipole moment and the scalar-pseudoscalar nucleon-electron interaction are calculated and the value of $l$-doubling is obtained.

physics.atom-ph↗
arXiv2020

Effects of Conical Intersections on Hyperfine Quenching of Hydroxyl OH in collision with an ultracold Sr atom

The effect of conical intersections (CIs) on electronic relaxation, transitions from excited states to ground states, is well studied, but their influence on hyperfine quenching in a reactant molecule is not known. Here, we report on ultracold collision dynamics of the hydroxyl free-radical OH with Sr atoms leading to quenching of OH hyperfine states. Our quantum-mechanical calculations of this process reveal that quenching is efficient due to anomalous molecular dynamics in the vicinity of the conical intersection at collinear geometry. We observe wide scattering resonance features in both elastic and inelastic rate coefficients at collision energies below k x 10 mK. They are identified as either p- or d-wave shape resonances. We also describe the electronic potentials relevant for these non-reactive collisions, their diabatization procedure, as well as the non-adiabatic coupling between the diabatic potentials near the CIs.

physics.chem-ph↗
arXiv2020

Photon-mediated charge-exchange reactions between 39K atoms and 40Ca+ ions in a hybrid trap

We present experimental evidence of charge exchange between laser-cooled potassium $^{39}$K atoms and calcium $^{40}$Ca$^+$ ions in a hybrid atom-ion trap and give quantitative theoretical explanations for the observations. The $^{39}$K atoms and $^{40}$Ca$^+$ ions are held in a magneto-optical (MOT) and a linear Paul trap, respectively. Fluorescence detection and high resolution time of flight mass spectra for both species are used to determine the remaining number of $^{40}$Ca$^+$ ions, the increasing number of $^{39}$K$^+$ ions, and $^{39}$K number density as functions of time. Simultaneous trap operation is guaranteed by alternating periods of MOT and $^{40}$Ca$^+$ cooling lights, thus avoiding direct ionization of $^{39}$K by the $^{40}$Ca$^+$ cooling light. We show that the K-Ca$^+$ charge-exchange rate coefficient increases linearly from zero with $^{39}$K number density and, surprisingly, the fraction of $^{40}$Ca$^+$ ions in the 4p\,$^2$P$_{1/2}$ electronically-excited state. Combined with our theoretical analysis, we conclude that these data can only be explained by a process that starts with a potassium atom in its electronic ground state and a calcium ion in its excited 4p\,$^2$P$_{1/2}$ state producing ground-state $^{39}$K$^+$ ions and metastable, neutral Ca\,(3d4p$^3$P$_1$) atoms, releasing only 150 cm$^{-1}$ equivalent relative kinetic energy. Charge-exchange between either ground- or excited-state $^{39}$K and ground-state $^{40}$Ca$^+$ is negligibly small as no energetically-favorable product states are available. Our experimental and theoretical rate coefficients of $9\times10^{-10}$ cm$^3$/s are in agreement given the uncertainty budgets.

physics.atom-ph↗
arXiv2020

Some Aspects of a Software Reliability Problem

Obviously, the dynamism of software reliability research has speeded up significantly in the last period, and we can state the fact that its intensity is approaching, and in some cases is ahead of the information systems hardware reliability research intensity. Reliability of software is much more important than its other characteristics, such as runtime, and although the absolute reliability of modern software is apparently unattainable, there is still no generally accepted measure of reliability of computer programs. The article analyzes the reasons for the situation and offers an approach to solving the problem. The article touches upon the issue of general characteristics of information systems software life cycle. Considered software application reliability questions and use of fail-safe ensuring programming. Also presented basic types of so-called virus programs that lead to abnormal functioning of information systems. Much attention is given to presenting some known models used for software debugging and operating. So, this review paper consists of four sections: information systems software process creation, reliability of information systems software, using of fail-safe programs and estimation of software reliability according the results of adjusting and normal operation.

cs.SE↗
arXiv2019

Emulating optical cycling centers in polyatomic molecules

An optical cycling center (OCC) is a recently coined term to indicate two electronic states within a complex quantum object that can repeatedly experience optical laser excitation and spontaneous decay, while being well isolated from its environment. Here we present a quantitative understanding of electronic, vibrational, and rotational excitations of the polyatomic SrOH molecule, which possesses a localized OCC near its Sr atom. In particular, we describe the vibrationally-dependent trends in the Franck-Condon factors of the bending and stretching modes of the molecular electronic states coupled in the optical transition. These simulations required us to perform electronic structure calculations of the multi-dimensional potential energy surfaces of both ground and excited states, the determination of vibrational and bending modes, and corresponding Franck-Condon factors. We also discuss the extent to which the optical cycling center has diagonal Franck-Condon factors.

physics.chem-ph↗
arXiv2019

Excitation-assisted nonadiabatic charge-transfer reaction in a mixed atom-ion system

An important physical process unique to neutral-ion systems is the charge-transfer (CT) reaction. Here, we present measurements of and models for CT processes between co-trapped ultracold Ca atoms and Yb ions under well-controlled conditions. The theoretical analysis reveals the existence of three reaction mechanisms when lasers from a magneto-optical trap (MOT) and an additional catalyst laser are present. Besides the direct CT involving existent excited Ca population in the MOT, the second pathway is controlled by MOT-induced CT, whereas the third one mostly involves the additional red-detuned laser.

physics.chem-ph↗
arXiv2018

Ptychographic characterization of polymer compound refractive lenses manufactured by additive technology

The recent success in the development of high precision printing techniques allows one to manufacture free-standing polymer structures of high quality. Two-photon polymerization lithography is a mask-less technique with down to 100 μm resolution that provides full geometric freedom. It has recently been applied to the nanofabrication of X-ray compound refractive lenses (CRLs). In this article we report on the characterization of two sets of CRLs of different design produced by two-photon polymerization induced lithography.

physics.optics↗
arXiv2018

Emission enhancement in dielectric nanocomposites

We consider emitting nanoparticles in dielectric nanocomposites with varying refractive index contrast and geometry. For that we develop a simple and universal method to calculate the emission enhancement in nanocomposites that employs solely the calculation of the effective refractive index and electric field distributions from three quasistatic calculations with orthogonal polarizations. The method is exemplified for dilute nanocomposites without electromagnetic interaction between emitting particles as well as for dense nanocomposites with strong particle interaction. We show that the radiative decay in dielectric nanocomposites is greatly affected by the shape and arrangement of its constituents and give guidelines for larger enhancement.

physics.optics↗
arXiv2017

The Gauss-Manin connection on the periodic cyclic homology

It is expected that the periodic cyclic homology of a DG algebra over the field of complex numbers (and, more generally, the periodic cyclic homology of a DG category) carries a lot of additional structure similar to the mixed Hodge structure on the de Rham cohomology of algebraic varieties. Whereas a construction of such a structure seems to be out of reach at the moment its counterpart in finite characteristic is much better understood thanks to recent groundbreaking works of Kaledin. In particular, it is proven by Kaledin that under some assumptions on a DG algebra $A$ over a perfect field $k$ of characteristic $p$, a lifting of $A$ over the ring of second Witt vectors $W_2(k)$ specifies the structure of a Fontaine-Laffaille module on the periodic cyclic homology of $A$. The purpose of this paper is to develop a relative version of Kaledin's theory for DG algebras over a base $k$-algebra $R$ incorporating in the picture the Gauss-Manin connection on the relative periodic cyclic homology constructed by Getzler. Our main result asserts that, under some assumptions on $A$, the Gauss-Manin connection on its periodic cyclic homology can be recovered from the Hochschild homology of $A$ equipped with the action of the Kodaira-Spencer operator as the inverse Cartier transform (in the sense of Ogus-Vologodsky). As an application, we prove, using the reduction modulo $p$ technique, that, for a smooth and proper DG algebra over a complex punctured disk, the monodromy of the Gauss-Manin connection on its periodic cyclic homology is quasi-unipotent.

math.AG↗
arXiv2017

Pendular trapping conditions for ultracold polar molecules enforced by external electric fields

We theoretically investigate trapping conditions for ultracold polar molecules in optical lattices, when external magnetic and electric fields are simultaneously applied. Our results are based on an accurate electronic-structure calculation of the polar $^{23}$Na$^{40}$K polar molecule in its absolute ground state combined with a calculation of its rovibrational-hyperfine motion. We find that an electric field strength of $5.26(15)$ kV/cm and an angle of $54.7^\circ$ between this field and the polarization of the optical laser lead to a trapping design for $^{23}$Na$^{40}$K molecules where decoherences due laser-intensity fluctuations and fluctuations in the direction of its polarization are kept to a minimum. One standard deviation systematic and statistical uncertainties are given in parenthesis. Under such conditions pairs of hyperfine-rotational states of $v=0$ molecules, used to induce tunable dipole-dipole interactions between them, experience ultrastable, matching trapping forces.

quant-ph↗