We overview the concept of dynamical phase transitions (DPTs) in isolated quantum
systems quenched out of equilibrium. We focus on non-equilibrium transitions characterized …

This article reviews theoretical and experimental developments for one-dimensional Fermi
gases. Specifically, the experimentally realized two-component delta-function interacting …

Topological Lifshitz transitions involve many types of topological structures in momentum
and frequency–momentum spaces, such as Fermi surfaces, Dirac lines, Dirac and Weyl …

We study the nonadiabatic dynamics of a two-dimensional p+ ip superfluid following an
instantaneous quantum quench of the BCS coupling constant. The model describes a …

We study the dynamic response of an s-wave BCS-BEC (atomic-molecular) condensate to
detuning quenches within the two-channel model beyond the weak-coupling BCS limit. At …

What distinguishes trivial superfluids from topological superfluids in interacting many-body
systems where the number of particles is conserved? Building on a class of integrable …

Topology in momentum space is the main characteristic of the ground state of a system at
zero temperature, the quantum vacuum. The gaplessness of fermions in bulk, on the surface …

We propose an extension of the numerical approach for integrable Richardson-Gaudin
models based on a new set of eigenvalue-based variables [A. Faribault, Phys. Rev. B 83 …

This chapter gives an overview of Richardson-Gaudin states which represent weakly
correlated pairs of electrons. They are parametrized by sets of numbers obtained from non …

Central spin models describe a variety of quantum systems in which a spin-1 2 qubit
interacts with a bath of surrounding spins, as realized in quantum dots and defect centers in …