We study the spatial dependence of pair correlation functions of velocity field components in a rotating turbulent fluid on a background of a coherent geostrophic vortex. The statistics of the turbulent pulsations are determined by their dynamics, which is the dynamics of inertial waves affected by the differential rotation in the vortex and a weak viscous damping. We are interested in distances which are larger than the scale of the wave forcing but smaller than the radius of the coherent vortex. We establish the anisotropy of the velocity field correlation function at the distances. All the diagonal elements of the correlation function decay logarithmically in the streamwise direction and power-like in radial direction and the direction along the rotation axis. This laws are independent of the details of the forcing correlation function that indicate “coherency” of the flow. On the contrary, the cross-correlation function of the radial-azimuth velocity components, which turns into the Reynolds stress for zero distance, demonstrates strong dependence on the forcing correlation function and decays quickly at distances larger than the forcing scale.

Leon L. Ogorodnikov, Sergey S. Vergeles. “Long-range spatial velocity statistics in a rotating coherent turbulent vortex”, Physical Review Fluids, vol. 10, p. 124702 (2025)

The search for conditions supporting degenerate steady states in nonequilibrium topological superconductors is important for advancing dissipative quantum engineering, a field that has attracted significant research attention over the past decade. In this study, we address this problem by investigating topological superconductors hosting unpaired Majorana modes under the influence of environmental dissipative fields. Within the Gorini-Kossakowski-Sudarshan-Lindblad framework and the third quantization formalism, we establish a correspondence between equilibrium Majorana zero modes and non-equilibrium kinetic zero modes. We further derive a simple algebraic relation between the numbers of these excitations expressed in terms of hybridization between the single-particle wavefunctions and linear dissipative fields. Based on these findings, we propose a practical recipes how to stabilize degenerate steady states in topological superconductors through controlled dissipation engineering. To demonstrate their applicability, we implement our general framework in the BDI-class Kitaev chain with long-range hopping and pairing terms — a system known to host a robust edge-localized Majorana modes.

Within the quantum field-theoretical approach describing the evolution of a quadratic Liouvillian in the basis of Keldysh contour coherent states, we investigate the spectral and transport properties of a dissipative superconducting system coupled to normal Fermi reservoirs. We derive a generalization of the Meir-Wingreen formula and Onsager matrix for a superconducting system subject to an arbitrary number of fermionic baths. Following Kirchhoff's rule, we obtain an expression describing the dissipation-induced loss current and formulate modified quantum kinetic equations. For wide-band contacts locally coupled to individual sites, we find that each contact reduces the degeneracy multiplicity of the non-equilibrium steady state by one. These results are numerically verified through several cases of the extended Kitaev model at symmetric points with a single contact. Furthermore, in the linear response regime at low temperatures, we demonstrate that (non-)degenerate non-equilibrium steady states correspond to (non-)quantized conductance peaks. Revisiting a paradigmatic problem of resonant transport in the Majorana mode of the Kitaev model we demonstrate that the dissipation accounts for the zero-bias peak suppression and its asymmetry.