Universal Upper Bound for the Entropy of Superconducting Vortices and the Quantum Nernst Effect

We show that the entropy per quantum vortex per layer in superconductors in external magnetic fields is bounded by the universal value kBln2, which explains puzzling results of recent experiments on the Nernst effect.

Dynamical evolution and decay of multi-charged quantum vortex in a Bose–Einstein condensate

We report the observation of the twisted decay of quadruply charged vortices taking place in an atomic Bose–Einstein condensate. Supporting numerical simulations show that the singly-charged vortices, which result from the decay of a multi-charged vortex, twist around intertwined in the shape of helical Kelvin waves.

Universal upper bound for the entropy of superconducting vortices and the quantum Nernst effect

We show that the entropy per quantum vortex per layer in superconductors in external magnetic fields is bounded by the universal value kBln 2, which explains puzzling results of recent experiments on the Nernst effect. The observed plateau of the Nernst signal as a function of the magnetic field is correspondingly attributed to a manifestation of the integer quantum Nernst effect.

Approximation Theorems for the Schrödinger Equation and Quantum Vortex Reconnection

We prove the existence of smooth solutions to the Gross–Pitaevskii equation on $$\mathbb {R}^3$$ R 3 that feature arbitrarily complex quantum vortex reconnections. We can track the evolution of the vortices during the whole process. This permits to describe the reconnection events in detail and verify that this scenario exhibits the properties observed in experiments and numerics, such as the $$t^{1/2}$$ t 1 / 2 and change of parity laws. We are mostly interested in solutions tending to 1 at infinity, which have finite Ginzburg–Landau energy and physically correspond to the presence of a background chemical potential, but we also consider the cases of Schwartz initial data and of the Gross–Pitaevskii equation on the torus. In the proof, the Gross–Pitaevskii equation operates in a nearly linear regime, so the result applies to a wide range of nonlinear Schrödinger equations. Indeed, an essential ingredient in the proofs is the development of novel global approximation theorems for the Schrödinger equation on $$\mathbb {R}^n$$ R n . Specifically, we prove a qualitative approximation result that applies for solutions defined on very general spacetime sets and also a quantitative result for solutions on product sets in spacetime $$D\times \mathbb {R}$$ D × R . This hinges on frequency-dependent estimates for the Helmholtz–Yukawa equation that are of independent interest.