Nonequilibrium Transport in Quantum Impurity Models (Bethe-Ansatz for open systems)

We develop an exact non-perturbative framework to compute steady-state properties of quantum-impurities subject to a finite bias. We show that the steady-state physics of these systems is captured by nonequilibrium scattering eigenstates which satisfy an appropriate Lippman-Schwinger equation. Introducing a generalization of the equilibrium Bethe-Ansatz - the Nonequilibrium Bethe-Ansatz (NEBA), we explicitly construct the scattering eigenstates for the Interacting Resonance Level model and derive exact, nonperturbative results for the steady-state properties of the system.Comment: 4 pages, 1 figur

Magneto-optic dynamics in a ferromagnetic nematic liquid crystal

We investigate dynamic magneto-optic effects in a ferromagnetic nematic liquid crystal experimentally and theoretically. Experimentally we measure the magnetization and the phase difference of the transmitted light when an external magnetic field is applied. As a model we study the coupled dynamics of the magnetization, M, and the director field, n, associated with the liquid crystalline orientational order. We demonstrate that the experimentally studied macroscopic dynamic behavior reveals the importance of a dynamic cross-coupling between M and n. The experimental data are used to extract the value of the dissipative cross-coupling coefficient. We also make concrete predictions about how reversible cross-coupling terms between the magnetization and the director could be detected experimentally by measurements of the transmitted light intensity as well as by analyzing the azimuthal angle of the magnetization and the director out of the plane spanned by the anchoring axis and the external magnetic field. We derive the eigenmodes of the coupled system and study their relaxation rates. We show that in the usual experimental set-up used for measuring the relaxation rates of the splay-bend or twist-bend eigenmodes of a nematic liquid crystal one expects for a ferromagnetic nematic liquid crystal a mixture of at least two eigenmodes.Comment: 20 pages, 23 figures, 42 reference

Exact solution of a non-Hermitian PT\mathscr{PT}-symmetric Heisenberg spin chain

We construct the exact solution of a non-Hermitian $\mathscr{PT}$-symmetric isotropic Heisenberg spin chain with integrable boundary fields. We find that the system exhibits two types of phases we refer to as $A$ and $B$ phases. In the $B$ type phase, the $\mathscr{PT}$- symmetry remains unbroken and it consists of eigenstates with only real energies, whereas the $A$ type phase contains a $\mathscr{PT}$-symmetry broken sector comprised of eigenstates with only complex energies and a sector of unbroken $\mathscr{PT}$-symmetry with eigenstates of real energies. The $\mathscr{PT}$-symmetry broken sector consists of pairs of eigenstates whose energies are complex conjugates of each other. The existence of two sectors in the $A$ type phase is associated with the exponentially localized bound states at the edges with complex energies which are described by boundary strings. We find that both $A$ and $B$ type phases can be further divided into sub-phases which exhibit different ground states. We also compute the bound state wavefunction in one magnon sector and find that as the imaginary value of the boundary parameter is increased, the exponentially localized wavefunction broadens thereby protruding more into the bulk, which indicates that exponentially localized bound states may not be stabilized for large imaginary values of the boundary parameter.Comment: 28 pages and 4 figure

Rise and fall of Yu-Shiba-Rusinov bound-states in charge conserving ss-wave one-dimensional superconductors

We re-examine the problem of a magnetic impurity coupled to a superconductor focusing on the role of quantum fluctuations. We study in detail, a system that consists of a one-dimensional charge conserving spin-singlet superconductor coupled to a boundary magnetic impurity. Our main finding is that quantum fluctuations lead to the destruction of Yu-Shiba-Rusinov (YSR) intra-gap bound-states in all but a narrow region of the phase diagram. We carry out our analysis in three stages, increasing the role of the quantum fluctuations at each stage. First we consider the limit of a classical impurity and study the bulk semiclassically, finding YSR states throughout the phase diagram, a situation similar to conventional BCS superconductors. In the second stage, we reintroduce quantum fluctuations in the bulk and find that the YSR state is suppressed over half of the phase diagram, existing only around the quantum critical point separating the unscreened and the partially screened phases. In the final stage we solve exactly the full interacting model with arbitrary coupling constants using Bethe Ansatz. We find that including both the quantum fluctuating bulk and quantum impurity destabilizes the YSR state over most of the phase diagram allowing it to exist only in a small region, the YSR regime, between a Kondo-screened and an unscreened regime. Within the YSR regime a first order phase transition occurs between a spin singlet and doublet ground state. We also find that for large enough impurity spin exchange interaction a renormalized Kondo-screened regime is established. In this regime, not found for BCS superconductors, there is no YSR state and a renormalized Kondo temperature scale is generated