Abstract
We discuss the phase diagram and properties of global vortices in the non-Hermitian parity-time-symmetric relativistic model possessing two interacting scalar complex fields. The phase diagram contains stable PT-symmetric regions and unstable PT-broken regions, which intertwine nontrivially with the U(1)-symmetric and U(1)-broken phases, thus forming rich patterns in the space of parameters of the model. The notion of the PT-symmetry breaking is generalized to the interacting theory. At finite quartic couplings, the non-Hermitian model possesses classical vortex solutions in the PT-symmetric regions characterized by broken U(1) symmetry. In the long-range limit of two-component Bose-Einstein condensates, the vortices from different condensates experience mutual dissipative dynamics unless their cores overlap precisely. For comparison, we also consider a close Hermitian analog of the system and demonstrate that the non-Hermitian two-component model possesses much richer dynamics than its Hermitian counterpart.
Highlights
Quantum-mechanical systems are traditionally described by Hermitian Hamiltonians which ensure the real-valuedness of the full energy spectrum and, the unitary evolution of the system as a whole
Non-Hermitian two-field models appear, for example, in the description of two-component out-of-equilibrium condensates in a non-Hermitian system of electron-hole pairs and photons in a semiconductor microcavity system. This open quantum many-body system resides in steady-state regimes characterized by a nontrivial phase diagram which contains an exceptional point that marks an endpoint of the first-order phase boundary [34] and exhibits anomalous critical phenomena [35]
We show that the simple extension of the model makes the analysis of the phase diagram very complicated
Summary
Quantum-mechanical systems are traditionally described by Hermitian Hamiltonians which ensure the real-valuedness of the full energy spectrum and, the unitary evolution of the system as a whole It turns out, that the Hermitian description can be extended with a large class of non-Hermitian terms which are invariant under combined parity-time (PT ) transformations. We work with vortex topological defects in a bosonic non-Hermitian model which involves a pair of scalar fields associated with interacting condensates. Non-Hermitian two-field models appear, for example, in the description of two-component out-of-equilibrium condensates in a non-Hermitian system of electron-hole pairs and photons in a semiconductor microcavity system This open quantum many-body system resides in steady-state regimes characterized by a nontrivial phase diagram which contains an exceptional point that marks an endpoint of the first-order phase boundary [34] and exhibits anomalous critical phenomena [35].
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