Related papers: PT symmetry and spontaneous symmetry breaking in a…
We show that the spontaneous symmetry breaking can be defined also for finite systems based on the properly defined jump probability between the ground states in the 2d and 3d Ising models on a square and a cubic lattice respectively. Our…
We study a two-dimensional exactly solvable non-Hermitian $PT-$non-symmetric quantum model with real spectrum, which is not amenable to separation of variables, by supersymmetrical methods. Here we focus attention on the property of…
We investigate complex versions of the Korteweg-deVries equations and an Ito type nonlinear system with two coupled nonlinear fields. We systematically construct rational, trigonometric/hyperbolic, elliptic and soliton solutions for these…
We find that a broken PT-symmetry operator when interacts with suitable Hermitian operator, new system becomes completely un-broken PT symmetry. Further on varying the contribution of Hermiticity one can delay or control the broken…
The local reggeon field theory is studied perturbatively taking advantage of the PT symmetry in the Hamiltonian formulation. In the lowest non trivial order we show that the pomeron interactions renormalize the slope. In the same order we…
We show that a local non-Hermitian perturbation in a Hermitian lattice system generically induces scale-free localization for the continuous-spectrum eigenstates. When the perturbation lies at a finite distance to the boundary, the…
We investigate what determines the shape of a particle condensate in situations when it emerges as a result of spontaneous breaking of translational symmetry. We consider a model with particles hopping between sites of a one-dimensional…
We have calculated the ground state wave functions for a systems of multicomponent interacting fermions. We show that it describes the state with spontaneously broken chiral symmetry. In the limit of an infinitely strong interaction it…
The conditions leading to flat dispersionless frequency bands in truly one-dimensional parity-time ($\cal PT$) symmetric metamaterials comprising split-ring resonators (SRRs) arranged in a binary pattern are obtained analytically. In this…
Parity-time (PT) symmetry gives rise to unusual phenomena in many physical systems, presently attracting a lot of attention. One essential and non-trivial task is the fabrication and design of the PT-symmetric lattices in different systems.…
We address dissipative soliton formation in modulated PT-symmetric continuous waveguide arrays composed from waveguides with amplifying and absorbing sections, whose density gradually increases (due to decreasing waveguide separation)…
While Hermiticity of a time-independent Hamiltonian leads to unitary time evolution, in and of itself, the requirement of Hermiticity is only sufficient for unitary time evolution. In this paper we provide conditions that are both necessary…
Non-Hermiticity has recently emerged as a rapidly developing field due to its exotic characteristics related to open systems, where the dissipation plays a critical role. In the presence of balanced energy gain and loss with environment,…
A new proof is given for why the non-Hermitian, PT-Invariant cubic oscillator with imaginary coupling has real eigenvalues. The proof consists of two steps. In the first step, it is shown that for many PT-Invariant Hamiltonians, one can…
Integrability of a square billiard is spontaneously broken as it rotates about one of its corners. The system becomes quasi-integrable where the invariant tori are broken with respect to a certain parameter, $\lambda = 2E/\omega^{2}$ where…
We present a clear and mathematically simple procedure explaining spontaneous symmetry breaking in quantum mechanical systems. The procedure is applicable to a wide range of models and can be easily used to explain the existence of a…
We analyse some PT-symmetric oscillators with $T_{d}$ symmetry that depend on a potential parameter $g$. We calculate the eigenvalues and eigenfunctions for each irreducible representation and for a range of values of $g$. Pairs of…
The non-Hermitian PT-symmetric quantum-mechanical Hamiltonian $H=p^2+x^2(ix)^\epsilon$ has real, positive, and discrete eigenvalues for all $\epsilon\geq 0$. These eigenvalues are analytic continuations of the harmonic-oscillator…
A one dimensional, parity-time (${\cal PT}$)-symmetric magnetic metamaterial comprising split-ring resonators having both gain and loss is investigated. In the linear regime, the transition from the exact to the broken ${\cal PT}$-phase is…
High resolution eigenvalue spectra of several two- and three-dimensional superconducting microwave cavities have been measured in the frequency range below 20 GHz and analyzed using a statistical measure which is given by the distribution…