In a 2009 paper "Turbulence in Integrable Systems", Zakharov discussed weakly integrable systems which have an infinite, but not sufficient for the full integrability, number of invariants. An example is KP1 for which Zakharov wrote a kinetic equation describing wave turbulence, and which has an infinite number of invariants and thermodynamic equilibria. In the present talk, I will report on numerical simulations of this kinetic equation, in particular, a kinetic instability of a wavepacket, and relaxation to equilibrium characterised by a condensation into low-frequency waves.

Nonlocal phase-coherent transport via Majorana bound states, so-called teleportation, requires Coulomb blockade to suppress local Andreev reflection. We show that dissipation can replace the need for Coulomb blockade. We study a Kitaev chain coupled to a Markovian bath and identify a regime where the magnitude of nonlocal conductance contribution reach the local one. In this regime, the lowest-energy subspace is maximally mixed, reminiscent of a directly grounded nontrivial topological superconductor. Phase coherence is confirmed by Aharonov-Bohm oscillations. Our results establish dissipation as a tool for controlling quantum teleportation in Majorana systems.

We establish a correspondence between the free-field construction and the minimal-model construction of the Calabi–Yau sector of the four-dimensional heterotic string compactified on Berglund–Hübsch type Calabi–Yau manifolds and their orbifolds. For Fermat-type polynomials the Calabi–Yau vertex operators expressed in terms of free fields are shown to correspond to products of primary fields of ????=2 minimal models. Using this correspondence we verify modular invariance of the free-field construction and extend it to Berglund–Hübsch Calabi–Yau orbifolds, deriving the conditions on complete vertex operators that parallel those of the minimal-model construction [1]. [1] A. Belavin, D. Gepner, G. Makarov, Free-Field Construction of Heterotic String Compactified on Calabi–Yau Orbifolds via Correspondence with N=2 SCFT Minimal Models, Nucl. Phys. B 117668 (2026).

The Berry curvature effect in anomalous transport driven by statistical forces such as the gradient of temperature or chemical potential has been developed by Di Xiao et al in Phys. Rev. Lett. 97, 026603 (2006). This theory operates with spinless fermions. So, the Berry curvature, corresponding magnetic moment of wave packets and the magnetic field dependent density of states originate from the electron orbital degrees of freedom. We present an alternative derivation of the Berry curvature effect on charge, heat and as well on thermalelectric currents in altermagnets and noncentrosymmertric metals where the electron band dispersion possesses spin dependent band splitting.

The band spin splitting in the hexagonal altermagnet CrSb is established using the magnetic group formalism that allows to find the additional spin splitting missed in the frame of the exchange approximation.

Phys.Rev.B 114, 065130 (2026).

Altermagnets are substances with a momentum-dependent spin splitting of electron bands due to a specific crystal structure that is invariant under time reversal only in combination with rotations and reflections. The developed phenomenological approach allows to obtain a spectrum of electron bands in altermagnets corresponding to antiferromagnets with the same symmetry. We consider antiferromagnetic, weak ferromagnetic, and ferrimagnetic structures. The calculated Berry curvature of electron bands in the alterrmarnet with zero spontaneous magnetisation occurs an odd function of momentum whereas it is even in a weak ferromagnetic state. The Berry curvature in ferrimagnetic state is equal to zero.

In this work, we propose an algorithm for constructing orbifolds of Calabi-Yau manifolds of Berglund-Hubsch type. This approach allows us to obtain all mirror pairs for Calabi-Yau manifolds of this type. As an example, we considered one of the Fermat-type models, for which all its orbifolds and their mirror pairs were found, and also for each orbifold the number of generations of quarks and leptons was found, as well as the number of types of particles participating only in gravitational interaction, i.e. dark matter particles.