arXiv subjects
Publications and source records attributed to Mikhail Volkov.
We investigate identities satisfied by monoids of triangular matrices over fields and over additively idempotent semirings with 0 and 1, and exhibit several new instances in which these identities admit no finite axiomatization.
We introduce a complete set of combinatorial data that encode the category $2\mathfrak{Cob}$ of all $2$-cobordisms. As an application, we show that the local monoids of $2\mathfrak{Cob}$ do not have finitely axiomatizable equational theories. As yet another application, we construct a von-Neumann-regular extension of this category. Similar results are provided for the topological annular category and various quotients of the latter, like the affine Temperley--Lieb category.
We construct a faithful representation of the semiring of all order-preserving decreasing transformations of a chain with $n+1$ elements by Boolean upper triangular $n\times n$-matrices.
Attosecond transient absorption spectroscopy (ATAS) has emerged as a powerful technique within the field of attosecond science, combining extremely high temporal and excellent spectral resolution. So far, ATAS has been implemented in pump-probe experiments where an attosecond extreme-ultraviolet (XUV) pump or probe pulse was combined with a near-infrared (NIR) pulse in the femtosecond range, with the attosecond time resolution deriving from sub-cycle NIR-driven dynamics. Investigations of ultrafast electron dynamics in atoms, molecules and solids, with potential impact across physics, chemistry, and biology, would benefit significantly from the ability to perform all-attosecond transient absorption spectroscopy (AATAS). Here we demonstrate time-resolved AATAS using a table-top high-harmonic generation (HHG) source. The method is applied to investigate previously unresolved electronic coherences in Xe, revealing oscillatory valence hole motion with a 3-femtosecond period. In addition, systematic investigations of electron dynamics in Kr, Ar, and Ne are presented. Our work shows that, thanks to its broad bandwidth, high stability and easy accessibility, HHG is an ideal source for AATAS, offering the potential for replication in numerous laboratories.
The pseudovariety $\mathbf{DS}$ consists of all finite monoids whose regular $D$-classes form subsemigroups. We exhibit a uniform winning strategy for Synchronizer in the synchronization game on every synchronizing automaton whose transition monoid lies in $\mathbf{DS}$, and we prove that $\mathbf{DS}$ is the largest pseudovariety with this property.
Optical frequency combs and their spectra of evenly spaced discrete laser lines are essential to modern time and frequency metrology. Recent advances in integrated photonic waveguides enable efficient nonlinear broadening of an initially narrowband frequency comb to multi-octave bandwidth. Here, we study the nonlinear dynamics in the generation of such ultra-broadband spectra where different harmonics of the comb can overlap. We show that a set of interleaved combs with different offset frequencies extending across the entire spectrum can emerge, which transform into a single evenly spaced ultra-broadband frequency comb when the initial comb is offset-free.
This memorial article for Mark Sapir provides a brief overview of his life and career. Among his many contributions we highlight two of his most celebrated achievements: his groundbreaking solutions to Burnside-type problems for semigroups and his innovative construction of S-machines. Additionally, reflections from his colleagues and friends offer a heartfelt tribute, blending professional insights with personal memories.
We exhibit a winning strategy for Synchronizer in the synchronization game on every synchronizing automaton in whose transition monoid the regular D-classes form subsemigroups
The need for ever-faster information processing requires extremely small devices operating at frequencies approaching the terahertz and petahertz regimes. For the diagnostics of such devices, researchers need a spatiotemporal tool that surpasses the device under test in speed and spatial resolution and therefore, such a tool cannot be provided by electronics itself. Here we show how ultrafast electron beam probe with terahertz-compressed electron pulses can directly sense local electro-magnetic fields in electronic devices with femtosecond, micrometre and millivolt resolution under normal operation conditions. We analyse the dynamical response of a coplanar waveguide circuit and reveal the impulse response, signal reflections, attenuation and waveguide dispersion directly in the time domain. The demonstrated measurement bandwidth reaches 10 THz and the sensitivity to electric fields is tens of millivolts or -20 dBm. Femtosecond time resolution and the potential to directly integrate our technique into existing electron-beam inspection devices in semiconductor industry makes our femtosecond electron beam probe a promising tool for research and development of next-generation electronics at unprecedented speed and size.
We exhibit new conditions under which a primitive automaton is synchronizing. In particular, we show that the primitivity of an automaton forces its synchronizability whenever the automaton has either a letter of defect 1 or a word of rank 2.
The ability to perform attosecond-pump attosecond-probe spectroscopy (APAPS) is a longstanding goal in ultrafast science. While first pioneering experiments demonstrated the feasibility of APAPS, the low repetition rates (10-120 Hz) and the large footprints of existing setups have so far hindered the widespread exploitation of APAPS. Here we demonstrate two-color APAPS using a commercial laser system at 1 kHz, straightforward post-compression in a hollow-core fiber and a compact high-harmonic generation (HHG) setup. The latter enables the generation of intense extreme-ultraviolet (XUV) pulses by using an out-of-focus HHG geometry and by exploiting a transient blueshift of the driving laser in the HHG medium. Near-isolated attosecond pulses are generated, as demonstrated by one-color and two-color XUV-pump XUV-probe experiments. Our concept allows selective pumping and probing on extremely short timescales and permits investigations of fundamental processes that are not accessible by other pump-probe techniques.
Shaping electron beams with the cycles of light provides femtosecond and attosecond time resolution in electron microscopy and enables fundamental quantum-coherent measurements. However, efficient light-electron control requires a prolonged interaction between the two beams for cascaded transfer of photon energy and momentum to the freely propagating electrons. Here we report the use of traveling evanescent terahertz waves to achieve velocity matching and thereby high acceleration gradients both in space and in time. With experiment and simulations, we demonstrate attosecond streaking, temporal pulse compression, acceleration and spatial focusing of sub-relativistic electron pulses with a single evanescent-wave element under the control of selected terahertz delays and phases. Based on these results, we propose to use a symmetric arrangement with two evanescent terahertz waves to generate isolated attosecond electron pulses in a beam with realistic parameters. These results establish subluminal terahertz waves as a promising tool for ultrafast electron pulse control.
MXenes are two-dimensional materials with a rich set of remarkable chemical and electromagnetic properties, the latter including saturable absorption and intense surface plasmon resonances. To fully harness the functionality of MXenes for applications in optics, electronics and sensing, it is important to understand the interaction of light with MXenes on atomic and femtosecond dimensions. Here, we use ultrafast electron diffraction and high-resolution electron microscopy to investigate the laser-induced structural dynamics of Ti3C2Tx nanosheets. We find an exceptionally fast lattice response with an electron-phonon coupling time of 230 femtoseconds. Repetitive femtosecond laser excitation transforms Ti3C2Tx through a structural transition into a metamaterial with deeply sub-wavelength nanoripples that are aligned with the laser polarization. By a further laser illumination, the material is reversibly photo-switchable between a flat and rippled morphology. The resulting nanostructured MXene metamaterial with directional nanoripples is expected to exhibit an anisotropic optical and electronic response as well as an enhanced chemical activity that can be switched on and off by light.
The 6-element Brandt monoid $B_2^1$ admits a unique addition under which it becomes an additively idempotent semiring. We show that this addition is a term operation of $B_2^1$ as an inverse semigroup. As a consequence, we exhibit an easy proof that the semiring identities of $B_2^1$ are not finitely based.
We approach the task of computing a carefully synchronizing word of optimum length for a given partial deterministic automaton, encoding the problem as an instance of SAT and invoking a SAT solver. Our experiments demonstrate that this approach gives satisfactory results for automata with up to 100 states even if very modest computational resources are used. We compare our results with the ones obtained by the first author for exact synchronization, which is another version of synchronization studied in the literature, and draw some theoretical conclusions.
In the present study we have demonstrated epitaxial stabilization of the metastable magnetically-hard $\varepsilon$-Fe$_2$O$_3$ phase on top of a thin MgO(111) buffer layer grown onto the GaN (0001) surface. The primary purpose to introduce a 4\,nm-thick buffer layer of MgO in between Fe$_2$O$_3$ and GaN was to stop thermal migration of Ga into the iron oxide layer. Though such migration and successive formation of the orthorhombic GaFeO$_3$ was supposed earlier to be a potential trigger of the nucleation of the isostructural $\varepsilon$-Fe$_2$O$_3$, the present work demonstrates that the growth of single crystalline uniform films of epsilon ferrite by pulsed laser deposition is possible even on the MgO capped GaN. The structural properties of the 60\,nm thick Fe$_2$O$_3$ layer on MgO / GaN were probed by electron and x-ray diffraction, both suggesting that the growth of $\varepsilon$-Fe$_2$O$_3$ is preceded by formation of a thin layer of $γ$-Fe$_2$O$_3$. The presence of the magnetically hard epsilon ferrite was independently confirmed by temperature dependent magnetometry measurements. The depth-resolved x-ray and polarized neutron reflectometry reveal that the 10\,nm iron oxide layer at the interface has a lower density and a higher magnetization than the main volume of the $\varepsilon$-Fe$_2$O$_3$ film. The density and magnetic moment depth profiles derived from fitting the reflectometry data are in a good agreement with the presence of the magnetically degraded $γ$-Fe$_2$O$_3$ transition layer between MgO and $\varepsilon$-Fe$_2$O$_3$. The natural occurrence of the interface between magnetoelectric $\varepsilon$- and spin caloritronic $γ$- iron oxide phases can enable further opportunities to design novel all-oxide-on-semiconductor devices.
We use a semigroup-theoretic construction by Peter Higgins in order to produce, for each even $n$, an $n$-state and 3-letter synchronizing automaton with the following two features: 1) all its input letters act as idempotent selfmaps of rank $\dfrac{n}2$; 2) its reset threshold is asymptotically equal to $\dfrac{n^2}2$. In the revised version a few inaccuracies (spotted by the anonymous referees of the previous version) have been removed and several relevant references have been added.
Up to isomorphism, there exist two non-isomorphic two-element monoids. We show that the identities of the free product of every pair of such monoids admit no finite basis.