The use of exactly solvable Richardson-Gaudin models to describe the physics of systems
with strong pair correlations is reviewed. The article begins with a brief discussion of …

We review and summarize recent theoretical and experimental work on electron spin
dynamics in quantum dots and related nanostructures due to hyperfine interaction with …

We introduce a generalized Gaudin Lie algebra and a complete set of mutually commuting
quantum invariants allowing the derivation of several families of exactly solvable …

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 …

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of
the energy spectra and form factors (operator matrix elements in the basis of Hamiltonian …

We solve the long-standing central spin problem for a general set of inhomogeneous bath
couplings and a large class of initial bath states. We compute the time evolution of the …

We determine the zero-temperature quantum phase diagram of apx+ ipy pairing model
based on the exactly solvable hyperbolic Richardson-Gaudin model. We present analytical …

We obtain analytically close forms of benchmark quantum dynamics of the collapse and
revival (CR), the reduced density matrix, Von Neumann entropy, and fidelity for the XXZ …

Superconducting pairing of electrons in nanoscale metallic particles with discrete energy
levels and a fixed number of electrons is described by the reduced Bardeen, Cooper, and …