I will make a few comments on heavy tetraquarks using the gauge/string duality. In particular, I describe the structure of the two low-lying Born-Oppenheimer potentials.

This talk presents results of a comprehensive study of the classical and quantum dynamics of spin 1/2 Dirac fermion particles with dipole moments under the action of arbitrary external fields (including gravitational, inertial, electromagnetic, axion ones). The gauge-theoretic framework of the general-relativistically covariant Dirac theory is used to describe in a consistent way the minimal and nonminimal couplings of fermions to external fields of different physical nature. The quantum and quasiclassical equations of motion are derived and a complete consistency of the quantum and classical spin dynamics is demonstrated. Applications range from astrophysics, to precision experiments with polarized particles in accelerators and storage rings, to the heavy-ion collisions.

Synchronization between the internal dynamics of the superconducting phase in a Josephson junction (JJ) and an external ac signal is a fundamental physical phenomenon, manifesting as constant-voltage Shapiro steps in the current-voltage characteristic. Mathematically, this phase-locking effect is captured by the Resistively Shunted Junction (RSJ) model, an important example of a nonlinear dynamical system. The standard RSJ model considers an overdamped JJ with a sinusoidal (single-harmonic) current-phase relation (CPR) in the current-driven regime with a monochromatic ac component. While this model predicts only integer Shapiro steps, the inclusion of higher Josephson harmonics is known to generate fractional Shapiro steps. In this paper, we show that only two Josephson harmonics in the CPR are sufficient to produce all possible fractional Shapiro steps within the RSJ framework. Using perturbative methods, we analyze amplitudes of these fractional steps. Furthermore, by introducing a phase shift between the two Josephson harmonics, we reveal an asymmetry between positive and negative fractional steps — a signature of the Josephson diode effect.

We develop a theoretical framework, using the slow variables method in the RSJ model, and perform numerical simulations to explain the peculiarities of the Josephson diode effect observed in an asymmetric SQUID with a superconducting nanobridge and an SNS junction in recent experiments by Vasiliy Stolyarov’s group at MIPT. For this case we predict the new (amplitude) mechanism of the diode effect which originates from the presence of a superconducting nanobridge exhibiting a multivalued current-phase relation (CPR). Theoretically, this mechanism manifests itself in the dependence of the amplitude of the first Josephson harmonic in the CPR of the SQUID on the current direction. We demonstrate that this mechanism accounts for the experimentally observed pronounced asymmetry of the Shapiro steps, which coexists with a relatively small asymmetry in the critical current. Additionally, we investigate how the diode efficiency (quantified via the Shapiro steps asymmetry) depends on both the magnetic flux through the superconducting loop and the power of the external microwave irradiation. Our theoretical predictions are found to be in good agreement with the experimental observations. This talk is based on the article Phys. Rev. B 112, 144504 (2025).