These lecture notes from the 2019 Les Houches Summer School on Quantum Information Machines provides a pedagogical introduction to theory of non-reciprocal quantum interactions and devices. The goal is connect various approaches concepts, including Hamiltonians encoding synthetic gauge fields, scattering descriptions, master equations, non-Hermitian Hamiltonians. importance having both non-triv...

We derive the third subleading (N$^3$LO) corrections of quadratic-in-spin sectors via EFT spinning objects in post-Newtonian (PN) gravity. These consist contributions from $4$ for generic compact binaries, that enter at fifth PN order. One these is due to a new tidal interaction, unique with spin, and complements first interaction also enters this order simple point-mass sector. The evaluation ...

Integrable multistate or multiflavor/color models were recently introduced. They are generalizations of models corresponding to the defining representations of the Uq( ̂ sl(m)) quantum algebras. Here I show that a similar generalization is possible for all higher dimensional representations. The R-matrices and the Hamiltonians of these models are constructed by fusion. The sl(2) case is treated ...

First examples of quasi-exactly solvable models describing spin-orbital interaction are constructed. In contrast with other examples of matrix quasi-exactly solvable models discussed in the literature up to now, our models admit infinite (but still incomplete) sets of exact (algebraic) solutions. The hamiltonians of these models are hermitian operators of the form H = −∆ +V1(r)+ (s · l)V2(r)+ (...

We give a formulation of quantum ergodicity for Pauli Hamiltonians with arbitrary spin in terms of a Wigner-Weyl calculus. The corresponding classical phase space is the direct product of the phase space of the translational degrees of freedom and the two-sphere. On this product space we introduce a combination of the translational motion and classical spin precession. We prove quantum ergodici...

Interesting spin Hamiltonians can be realized with ultracold atoms in a two-component Mott insulator (2CMI) [Adv. Phys. 56, 243 (2007); Rev. Mod. Phys. 80, 885 (2008)]. It was recently demonstrated that the application of a magnetic field gradient to the 2CMI enables new techniques of thermometry [Phys. Rev. Lett. 103, 245301 (2009)] and adiabatic cooling [e-print arXiv:1006.4674]. Here we pres...