We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Using the Bethe ansatz and similarity transformations this yields new exact results. In a complementary approach we generalize previous work[1, 2] and present a new description of these and other processes and the related quantum chains ...

We consider the classical spin models where the Hamiltonians are small modifications of the Hamiltonians of Dyson's hierarchical models. Under some assumptions we investigate rigorously the neighbourhood of the critical point and find the critical indices. It follows that in the cases under consideration phenomenologicat Landau's theory of phase transitions is valid.

We investigate topological insulating states in both two and three dimensions with the harmonic potential and strong spin-orbit couplings breaking the inversion symmetry. Landau-level-like quantization appear with the full twoand three-dimensional rotational symmetry and time-reversal symmetry. Inside each band, states are labeled by their angular momenta over which energy dispersions are stron...

Abstract Molecular Hamiltonians are constituted by momentum operators (e.g. kinetic energy and interaction with electro-magnetic radiation), local potential operators (e.g. electron-electron coulomb, electron-nucleus and electron-external field interactions) and spin operators. In general the effect of transformations that generate states from a reference state is to destroy this form. Here it ...

Many solid-state NMR experiments exploit interference effects between time dependencies in the system Hamiltonian to design an effective time-independent Hamiltonian with the desired properties. Effective Hamiltonians can be designed such that they contain only selected parts of the full system Hamiltonian while all other parts are averaged to zero. A general theoretical description of such exp...

We describe nonlinear quantum atom–light interfaces and nonlinear quantum metrology in the collective continuous variable formalism. We develop a nonlinear effective Hamiltonian in terms of spin and polarization collective variables and show that model Hamiltonians of interest for nonlinear quantum metrology can be produced in 87Rb ensembles. With these Hamiltonians, metrologically relevant ato...

The spontaneous magnetization of a two-dimensional lattice model can be expressed in terms of the partition function W of a system with fixed boundary spins and an extra weight dependent on the value of a particular central spin. For the superintegrable case of the chiral Potts model with cylindrical boundary conditions, W can be expressed in terms of reduced hamiltonians H and a central spin o...