Abstract We study stability and collisions of quantum droplets (QDs) forming in a binary bosonic condensate trapped in parity-time ( )-symmetric optical lattices. It is found that the stability of QDs in the -symmetric system depends strongly on the values of the imaginary part W 0 of the -symmetric optical lattices, self-repulsion strength g , and the condensate norm N . As expected, the -symmetric QDs are entirely unstable in the broken -symmetric phase. However, the -symmetric QDs exhibit oscillatory stability with the increase of N and g in the unbroken -symmetric phase. Finally, collisions between -symmetric QDs are considered. The collisions of droplets with unequal norms are completely different from that in free space. Besides, a stable -symmetric QDs collides with an unstable ones tend to merge into breathers after the collision.
We investigate a two-level spin system based anti-parity-time (anti-
PT)-symmetric qubit and study its decoherence as well as entanglement entropy properties. We compare our findings with that of the corresponding
PT-symmetric and Hermitian qubits. First we consider the time-dependent Dyson map to find the exact analytical dynamics for a general non-Hermitian qubit system coupled with a bath, then we specialize it to the case of the anti-
PT-symmetric qubit. We find that the decoherence function for the anti-
PT-symmetric qubit decays slower than the
PT-symmetric and Hermitian qubits. For the entanglement entropy we find that for the anti-
PT-symmetric qubit it grows more slowly compared to the
PT-symmetric and Hermitian qubits. Similarly, we find that the corresponding variance and area of Fisher information is much higher compared to the
PT-symmetric and Hermitian qubits. These results demonstrate that anti-
PT-symmetric qubits may be better suited for quantum computing and quantum information processing applications than conventional Hermitian or even
PT-symmetric qubits.
By means of geometric quantization, we discuss the quantum-deformed-symmetric-top model. We show that the quantum-deformed symmetric top and the quantum-standard symmetric top obey the same Heisenberg equations of motion. The quantum-deformed-symmetric-top model possesses quantum group symmetry; thus the quantum group can be dynamical symmetries of the symmetric-top system. The energy levels and wave functions of stationary states of the quantum-deformed-symmetric-top model are obtained exactly by a quantum-group-theoretic approach. Using the exactly solved model, we investigate the rotational spectra of symmetric-top molecules and diatomic molecules when the moment of inertia about the line joining the nuclei is not exactly zero.