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## BCS model with asymmetric pair scattering: a non-Hermitian, exactly solvable Hamiltonian exhibiting generalised exclusion statistics

Jon Links, Amir Moghaddam, Yao-Zhong Zhang

We demonstrate the occurrence of free quasi-particle excitations obeying generalised exclusion statistics in a BCS model with asymmetric pair scattering. The results are derived from an exact solution of the Hamiltonian, which was obtained via the algebraic Bethe ansatz utilising the representation theory of an underlying Yangian algebra. The free quasi-particle excitations are associated to highest-weight states of the Yangian algebra, corresponding to a class of analytic solutions of the Bethe ansatz equations.

http://arxiv.org/abs/1304.5818
Exactly Solvable and Integrable Systems (nlin.SI); Superconductivity (cond-mat.supr-con); Mathematical Physics (math-ph)

## A ‘Dysonization’ Scheme for Identifying Particles and Quasi-Particles Using Non-Hermitian Quantum Mechanics

Katherine Jones-Smith

In 1956 Dyson analyzed the low-energy excitations of a ferromagnet using a Hamiltonian that was non-Hermitian with respect to the standard inner product. This allowed for a facile rendering of these excitations (known as spin waves) as weakly interacting bosonic quasi-particles. More than 50 years later, we have the full denouement of non-Hermitian quantum mechanics formalism at our disposal when considering Dyson’s work, both technically and contextually. Here we recast Dyson’s work on ferromagnets explicitly in terms of two inner products, with respect to which the Hamiltonian is always self-adjoint, if not manifestly “Hermitian”. Then we extend his scheme to doped antiferromagnets described by the t-J model, in hopes of shedding light on the physics of high-temperature superconductivity.

http://arxiv.org/abs/1304.5689
Quantum Physics (quant-ph)

## Vector Models in PT Quantum Mechanics

Katherine Jones-Smith, Rudolph Kalveks

We present two examples of non-Hermitian Hamiltonians which consist of an unperturbed part plus a perturbation that behaves like a vector, in the framework of PT quantum mechanics. The first example is a generalization of the recent work by Bender and Kalveks, wherein the E2 algebra was examined; here we consider the E3 algebra representing a particle on a sphere, and identify the critical value of coupling constant which marks the transition from real to imaginary eigenvalues. Next we analyze a model with SO(3) symmetry, and in the process extend the application of the Wigner-Eckart theorem to a non-Hermitian setting.

http://arxiv.org/abs/1304.5692
Quantum Physics (quant-ph)

## PT asymmetry in viscous fluids with balanced inflow and outflow

Huidan (Whitney)Yu, Xi Chen, Nan Chen, Yousheng Xu, Yogesh N. Joglekar

In recent years, open systems with equal loss and gain have been investigated via their symmetry properties under combined parity and time-reversal ($$\mathcal{PT}$$) operations. We numerically investigate $$\mathcal{PT}$$-symmetry properties of an incompressible, viscous fluid with “balanced” inflow-outflow configurations. We define configuration-dependent asymmetries in velocity, kinetic energy density, and vorticity fields, and find that all asymmetries scale quadratically with the Reynolds number. Our proposed configurations have asymmetries that are orders of magnitude smaller than the asymmetries that occur in traditional configurations at low Reynolds numbers. Our results show that $$\mathcal{PT}$$-symmetric fluid flow configurations, which are defined here for the first time, offer a hitherto unexplored avenue to tune fluid flow properties.

http://arxiv.org/abs/1304.5348

Fluid Dynamics (physics.flu-dyn); Quantum Physics (quant-ph)