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We consider a Hamiltonian chain of rotators (in general nonlinear) in which the first rotator is damped. Being motivated by problems of nonequilibrium statistical mechanics of crystals, we construct a strict Lyapunov function that allows us to find a lower bound for the total energy dissipation rate when the energy and time are large. Our construction is explicit and its analysis is rather straightforward. We rely on a method going back to Matrosov, Malisoff and Mazenc, which we review in our paper. The method is rather universal and we show that it is applicable to a chain of oscillators as well., Comment: 22 pages

Recently, pre-trained foundation models have enabled significant advancements in multiple fields. In molecular machine learning, however, where datasets are often hand-curated, and hence typically small, the lack of datasets with labeled features, and codebases to manage those datasets, has hindered the development of foundation models. In this work, we present seven novel datasets categorized by size into three distinct categories: ToyMix, LargeMix and UltraLarge. These datasets push the boundaries in both the scale and the diversity of supervised labels for molecular learning. They cover nearly 100 million molecules and over 3000 sparsely defined tasks, totaling more than 13 billion individual labels of both quantum and biological nature. In comparison, our datasets contain 300 times more data points than the widely used OGB-LSC PCQM4Mv2 dataset, and 13 times more than the quantum-only QM1B dataset. In addition, to support the development of foundational models based on our proposed datasets, we present the Graphium graph machine learning library which simplifies the process of building and training molecular machine learning models for multi-task and multi-level molecular datasets. Finally, we present a range of baseline results as a starting point of multi-task and multi-level training on these datasets. Empirically, we observe that performance on low-resource biological datasets show improvement by also training on large amounts of quantum data. This indicates that there may be potential in multi-task and multi-level training of a foundation model and fine-tuning it to resource-constrained downstream tasks.

Radiofrequency-driven resonant spin rotators are routinely used as standard instruments in polarization experiments in particle and nuclear physics. Maintaining the continuous exact parametric spin-resonance condition of the equality of the spin rotator and the spin precession frequency during operation constitutes one of the challenges. We present a detailed analytic description of the impact of detuning the exact spin resonance on the vertical and the in-plane precessing components of the polarization. An important part of the formalism presented here is the consideration of experimentally relevant spin-decoherence effects. We discuss applications of the developed formalism to the interpretation of the experimental data on the novel pilot bunch approach to control the spin-resonance condition during the operation of the radiofrequency-driven Wien filter that is used as a spin rotator in the first direct deuteron electric dipole moment measurement at COSY. We emphasize the potential importance of the hitherto unexplored phase of the envelope of the horizontal polarization as an indicator of the stability of the radiofrequency-driven spin rotations in storage rings. The work presented here serves as a satellite publication to the work published concurrently on the proof of principle experiment about the so-called pilot bunch approach that was developed to provide co-magnetometry for the deuteron electric dipole moment experiment at COSY., Comment: 31 pages, 10 figures, 5 tables

In polarization experiments at storage rings, one of the challenges is to maintain the spin-resonance condition of a radio-frequency spin rotator with the spin-precessions of the orbiting particles. Time-dependent variations of the magnetic fields of ring elements lead to unwanted variations of the spin precession frequency. We report here on a solution to this problem by shielding (or masking) one of the bunches stored in the ring from the high-frequency fields of the spin rotator, so that the masked pilot bunch acts as a co-magnetometer for the other signal bunch, tracking fluctuations in the ring on a time scale of about one second. While the new method was developed primarily for searches of electric dipole moments of charged particles, it may have far-reaching implications for future spin physics facilities, such as the EIC and NICA., Comment: 5 pages, 3 figures + references + supplemental material (6 pages, 2 figures, 6 tables + references)

We find asymptotical expansions as $\nu \to 0$ for integrals of the form $\int_{\mathbb{R}^d} F(x) / \big(\omega(x)^2 + \nu^2\big)\, dx$, where sufficiently smooth functions $F$ and $\omega$ satisfy natural assumptions for their behaviour at infinity and all critical points of the function $\omega$ from the set $\{\omega(x) = 0\}$ are non-degenerate. These asymptotics play a crucial role when analysing stochastic models for non-linear waves systems. Our result generalizes that of [S. Kuksin, Russ. J. Math. Phys.'2017] where a similar asymptotics was found in a particular case when $\omega$ is a non-degenerate quadratic form of the signature $(d/2,d/2)$ with even $d$., Comment: 18 pages

Based on the notion that the local dark-matter field of axions or axion-like particles (ALPs) in our Galaxy induces oscillating couplings to the spins of nucleons and nuclei (via the electric dipole moment of the latter and/or the paramagnetic axion-wind effect), we establish the feasibility of a new method to search for ALPs in storage rings. Based on previous work that allows us to maintain the in-plane polarization of a stored deuteron beam for a few hundred seconds, we performed a first proof-of-principle experiment at the Cooler Synchrotron COSY to scan momenta near 970 MeV/c. This entailed a scan of the spin precession frequency. At resonance between the spin precession frequency of deuterons and the ALP-induced EDM oscillation frequency there will be an accumulation of the polarization component out of the ring plane. Since the axion frequency is unknown, the momentum of the beam and consequently the spin precession frequency were ramped to search for a vertical polarization change that would occur when the resonance is crossed. At COSY, four beam bunches with different polarization directions were used to make sure that no resonance was missed because of the unknown relative phase between the polarization precession and the axion/ALP field. A frequency window of 1.5-kHz width around the spin precession frequency of 121 kHz was scanned. We describe the experimental procedure and a test of the methodology with the help of a radiofrequency Wien filter located on the COSY ring. No ALP resonance was observed. As a consequence an upper limit of the oscillating EDM component of the deuteron as well as its axion coupling constants are provided., Comment: 27 pages, 24 figures, 7 tables, 104 references

In his paper from 1996 on quadratic forms Heath-Brown developed a version of the circle method to count points in the intersection of an unbounded quadric with a lattice of short period, if each point is given a weight, and approximated this quantity by the integral of the weight function against a measure on the quadric. The weight function is assumed to be $C_0^\infty$-smooth and vanish near the singularity of the quadric. In our work we allow the weight function to be finitely smooth, not vanish at the singularity and have an explicit decay at infinity. The paper uses only elementary results from the number theory and is available to readers without a number-theoretical background., Comment: To appear in Sbornik: Mathematics

We consider the damped/driven cubic NLS equation on the torus of a large period $L$ with a small nonlinearity of size $\lambda$, a properly scaled random forcing and dissipation. We examine its solutions under the subsequent limit when first $\lambda\to 0$ and then $L\to \infty$. The first limit, called the limit of discrete turbulence, is known to exist, and in this work we study the second limit $L\to\infty$ for solutions to the equations of discrete turbulence. Namely, we decompose the solutions to formal series in amplitude and study the second order truncation of this series. We prove that the energy spectrum of the truncated solutions becomes close to solutions of a damped/driven nonlinear wave kinetic equation. Kinetic nonlinearity of the latter is similar to that which usually appears in works on wave turbulence, but is different from it (in particular, it is non-autonomous). Apart from tools from analysis and stochastic analysis, our work uses two powerful results from the number theory.

In his paper from 1996 on quadratic forms Heath-Brown developed a version of circle method to count points in the intersection of an unbounded quadric with a lattice of short period, if each point is given a weight. The weight function is assumed to be $C_0^\infty$-smooth and to vanish near the singularity of the quadric. In out work we allow the weight function to be finitely smooth and not vanish near the singularity, and we give also an explicit dependence on the weight function.

We investigated coherent betatron oscillations of a deuteron beam in the storage ring COSY, excited by a detuned radio-frequency Wien filter. The beam oscillations were detected by conventional beam position monitors. With the currently available apparatus, we show that oscillation amplitudes down to \SI{1}{\micro \meter} can be detected. The interpretation of the response of the stored beam to the detuned radio-frequency Wien filter is based on simulations of the beam evolution in the lattice of the ring and realistic time-dependent 3D field maps of the Wien filter. Future measurements of the electric dipole moment of protons will, however, require control of the relative position of counter-propagating beams in the sub-picometer range. Since here the stored beam can be considered as a rarefied gas of uncorrelated particles, we moreover demonstrate that the amplitudes of the zero-point (ground state) betatron oscillations of individual particles are only a factor of about 10 larger than the Heisenberg uncertainty limit. As a consequence of this, we conclude that quantum mechanics does not preclude the control of the beam centroids to sub-picometer accuracy. The smallest Lorentz force exerted on a single particle that we have been able to determine is \SI{10}{aN}., Comment: 20 pages, 16 figures

A calorimetric polarimeter based on inorganic LYSO scintillators is described. It has been designed for use in a storage ring to search for electric dipole moments (EDM) of charged particles such as the proton and deuteron. Its development and first use was on the Cooler Synchrotron (COSY) at the Forschungszentrum J\"ulich with 0.97 GeV/c polarized deuterons, a particle and energy suitable for an EDM search. The search requires a polarimeter with high efficiency, large analyzing power, and stable operating characteristics. With typical beam momenta of about 1 GeV/c, the scattering of protons or deuterons from a carbon target into forward angles becomes a nearly optimal choice of an analyzing reaction. The polarimeter described here consists of 52 LYSO detector modules, arranged in 4 symmetric blocks (up, down, left, right) for energy determination behind plastic scintillators for particle identification via energy loss. The commissioning results of the current setup demonstrate that the polarimeter is ready to be employed in a first direct search for an EDM on the deuteron, which is planned at COSY in the next two years.

The J\"ulich Electric Dipole moment Investigation (JEDI) collaboration aims at a direct measurement of the Electric Dipole Moment (EDM) of protons and deuterons using a storage ring. The measurement is based on a polarization measurement. In order to reach highest accuracy, one has to know the exact trajectory through the magnets, especially the quadrupoles, to avoid the influence of magnetic fields on the polarization vector. In this paper, the development of a beam-based alignment technique is described that was developed and implemented at the COoler SYnchrotron (COSY) at Forschungszentrum J\"ulich. Well aligned quadrupoles permit one to absolutely calibrate the Beam Position Monitors (BPMs). The method is based on the fact that a particle beam, which does not pass through the center of a quadrupole, experiences a deflection. The precision reached by the method is approximately 40 micro meter. Some consequences for the design of a new high precision storage ring for EDM mesasurements are discussed., Comment: Submitted to "Journal of Instrumentation (JINST)"

New high precision total and differential cross sections are reported for the $dp\to {}^3\textrm{He}\,\eta$ reaction close to threshold. The measurements were performed using the magnetic spectrometer ANKE, which is an internal fixed target facility at the COSY cooler synchrotron. The data were taken for deuteron beam momenta between $3.14641~\textrm{GeV}/c$ and $3.20416~\textrm{GeV}/c$, which corresponds to the range in excess energy $Q$ for this reaction between $1.14~\textrm{MeV}$ and $15.01~\textrm{MeV}$. The normalization was established through the measurement in parallel of deuteron-proton elastic scattering and this was checked through the study of the $dp\to {}^3\textrm{He}\,\pi^0$ reaction. The previously indicated possible change of sign of the slope of the differential cross sections near the production threshold, which could be explained by a rapid variation of the $s$- and $p$-wave interference term, is not confirmed by the new data. The energy dependence of the total cross section and the $90^{\circ}$ slope parameter are well explained by describing the final state interaction in terms of a complex Jost function and the results are significant in the discussion of $\eta$-mesic nuclei. In combination with recently published WASA-at-COSY data [P. Adlarson $et\, al.$, Phys. Lett. B 782, 297 (2018)], a smooth variation of the slope parameter is achieved up to an excess energy of $80.9~\textrm{MeV}$., Comment: 12 pages, 11 figures, preprint submitted to Physical Review C

A measurement of vector analyzing powers in elastic deuteron-carbon scattering has been performed at the Cooler Synchrotron COSY of Forschungszentrum J\"ulich, Germany. Seven kinetic beam energies between 170 and 380 MeV have been used. A vector-polarized beam from a polarized deuteron source was injected, accelerated to the final desired energy and stored in COSY. A thin needle-shaped diamond strip was used as a carbon target, onto which the beam was slowly steered. Elastically scattered deuterons were identified in the forward direction using various layers of scintillators and straw tubes. Where data exist in the literature (at 200 and 270 MeV), excellent agreement of the angular shape was found. The beam polarization of the presented data was deduced by fitting the absolute scale of the analyzing power to these references. Our results extend the world data set and are necessary for polarimetry of future electric dipole moment searches at storage rings. They will as well serve as an input for theoretical description of polarized hadron-hadron scattering.

A previous publication has shown that the in-plane polarization (IPP) component of a polarized 0.97-GeV/c deuteron beam in the COSY storage ring may acquire a polarization half-life in excess of 1000 s through a combination of beam bunching, electron cooling (prior to any spin manipulation), sextupole field adjustment, and a limitation of the beam intensity. This paper documents further tests pointing to additional gains in the IPP lifetime if cooling is active throughout the beam store., Comment: 11 pages, 6 figures Submitted to Physical Review Accelerators and Beams

The proposed method exploits charged particles confined as a storage ring beam (proton, deuteron, possibly $^3$He) to search for an intrinsic electric dipole moment (EDM) aligned along the particle spin axis. Statistical sensitivities could approach 10$^{-29}$ e$\cdot$cm. The challenge will be to reduce systematic errors to similar levels. The ring will be adjusted to preserve the spin polarisation, initially parallel to the particle velocity, for times in excess of 15 minutes. Large radial electric fields, acting through the EDM, will rotate the polarisation from the longitudinal to the vertical direction. The slow rise in the vertical polarisation component, detected through scattering from a target, signals the EDM. The project strategy is outlined. A stepwise plan is foreseen, starting with ongoing COSY activities that demonstrate technical feasibility. Achievements to date include reduced polarization measurement errors, long horizontal plane polarization lifetimes, and control of the polarization direction through feedback from scattering measurements. The project continues with a proof-of-capability measurement (precursor experiment; first direct deuteron EDM measurement), an intermediate prototype ring (proof-of-principle; demonstrator for key technologies), and finally a high-precision electric-field storage ring., Comment: 243 pages

In this note we present the main results of the papers \cite{DK, DK2}, dedicated to rigorous study of the limiting properties of the stochastic model for wave turbulence due to Zakharov-L'vov. Proofs of the assertions, stated below without reference, may be found in those works.

We consider the damped/driver (modified) cubic NLS equation on a large torus with a properly scaled forcing and dissipation, and decompose its solutions to formal series in the amplitude. We study the second order truncation of this series and prove that when the amplitude goes to zero and the torus' size goes to infinity the energy spectrum of the truncated solutions becomes close to a solution of the damped/driven wave kinetic equation. Next we discuss higher order truncations of the series.

In this paper we continue to study small amplitude solutions of the damped cubic NLS equation, driven by a random force (the study was initiated in our previous work [A.Dymov, S.Kuksin, Comm. Math. Phys.'2021] and continued in [A.Dymov, S.Kuksin, A.Maiocchi, S.Vladuts, arXiv:2104.11967]). We write solutions of the equation as formal series in the amplitude and discuss the behaviour of this series under the wave turbulence limit, when the amplitude goes to zero, while the space-period goes to infinity., Comment: 61 pages