Spontaneous symmetry breaking in a split potential box

𝒫𝒯-symmetric and antisymmetric nonlinear states in a split potential box

We introduce a one-dimensional [Formula: see text]-symmetric system, which includes the cubic self-focusing, a double-well potential in the form of an infinitely deep potential box split in the middle by a delta-functional barrier of an effective height ε, and constant linear gain and loss, γ, in each half-box. The system may be readily realized in microwave photonics. Using numerical methods, we construct [Formula: see text]-symmetric and antisymmetric modes, which represent, respectively, the system's ground state and first excited state, and identify their stability. Their instability mainly leads to blowup, except for the case of ε=0, when an unstable symmetric mode transforms into a weakly oscillating breather, and an unstable antisymmetric mode relaxes into a stable symmetric one. At ε>0, the stability area is much larger for the [Formula: see text]-antisymmetric state than for its symmetric counterpart. The stability areas shrink with increase of the total power, P In the linear limit, which corresponds to [Formula: see text], the stability boundary is found in an analytical form. The stability area of the antisymmetric state originally expands with the growth of γ, and then disappears at a critical value of γThis article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.

Symmetry breaking, Josephson oscillation and self-trapping in a self-bound three-dimensional quantum ball

We study spontaneous symmetry breaking (SSB), Josephson oscillation, and self-trapping in a stable, mobile, three-dimensional matter-wave spherical quantum ball self-bound by attractive two-body and repulsive three-body interactions. The SSB is realized by a parity-symmetric (a) one-dimensional (1D) double-well potential or (b) a 1D Gaussian potential, both along the z axis and no potential along the x and y axes. In the presence of each of these potentials, the symmetric ground state dynamically evolves into a doubly-degenerate SSB ground state. If the SSB ground state in the double well, predominantly located in the first well (z > 0), is given a small displacement, the quantum ball oscillates with a self-trapping in the first well. For a medium displacement one encounters an asymmetric Josephson oscillation. The asymmetric oscillation is a consequence of SSB. The study is performed by a variational and a numerical solution of a non-linear mean-field model with 1D parity-symmetric perturbations.