Related papers: Fragile PT-symmetry in a solvable model
In many PT symmetric models with real spectra, apparently, energy levels "merge and disappear" at a point of the spontaneous PT-symmetry breaking. We argue that such an oversimplified and discontinuous physical interpretation of this…
We briefly explain some simple arguments based on pseudo Hermiticity, supersymmetry and PT-symmetry which explain the reality of the spectrum of some non-Hermitian Hamiltonians. Subsequently we employ PT-symmetry as a guiding principle to…
We show that and how point interactions offer one of the most suitable guides towards a quantitative analysis of properties of certain specific non-Hermitian (usually called PT-symmetric) quantum-mechanical systems. A double-well model is…
A new version of an elementary PT-symmetric square well quantum model is proposed in which a certain Hermiticity-violating end-point interaction leaves the spectrum real in a large domain of couplings $\lambda\in (-1,1)$. Within this…
PT-symmetric systems can have a real spectrum even when their Hamiltonian is non-hermitian, but develop a complex spectrum when the degree of non-hermiticity increases. Here we utilize random-matrix theory to show that this spontaneous…
Closed expressions are derived for the pseudo-norm, norm and orthogonality relations for arbitrary bound states of the PT symmetric and the Hermitian Scarf II potential for the first time. The pseudo-norm is found to have indefinite sign in…
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 simplest purely imaginary and piecewise constant $\cal PT$-symmetric potential located inside a larger box is studied. Unless its strength exceeds a certain critical value, all the spectrum of its bound states remains real and discrete.…
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…
The appearances of complex eigenvalues in the spectra of PT-symmetric quantum-mechanical systems are usually associated with a spontaneous breaking of PT. In this letter we discuss a family of models for which this phenomenon is also linked…
Exact solvability of the discretized N-point version of the PT-symmetric square-well model is pointed out. Its wave functions are found proportional to the classical Tshebyshev polynomials of a complex argument. At all N a compact secular…
We study the spectrum in such a PT-symmetric square well of a diameter L where the "strength of the non-Hermiticity" is controlled by the two parameters, viz., by an imaginary coupling ig and by the distance d of its onset from the origin.…
Two alternative scenarios are shown possible in Quantum Mechanics working with non-Hermitian $PT-$symmetric form of observables. While, usually, people assume that $P$ is a self-adjoint indefinite metric in Hilbert space (and that their…
The impact of an anti-unitary symmetry on the spectrum of non-hermitean operators is studied. Wigner's normal form of an anti-unitary operator is shown to account for the spectral properties of non-hermitean, PT-symmetric Hamiltonians. Both…
It is believed that unbroken PT symmetry is sufficient to guarantee that the spectrum of a non-Hermitian Hamiltonian is real. We prove that this is not true. We study a Hamiltonian with complex spectrum for which PT symmetry is not…
The occurrence of parity-time reversal ($\mathcal{PT}$) symmetry breaking is discussed in a non-Hermitian spin chain. The Hermiticity of the model is broken by the presence of an alternating, imaginary, transverse magnetic field. A full…
Many indefinite-metric (often called pseudo-Hermitian or PT-symmetric) quantum models H prove "physical" (i.e., Hermitian with respect to an innovated, ad hoc scalar product) inside a characteristic domain of parameters D. This means that…
PT-symmetric quantum mechanics is an alternative formulation of quantum mechanics in which the mathematical axiom of Hermiticity (transpose and complex conjugate) is replaced by the physically transparent condition of space-time reflection…
Bound states generated by K coupled PT-symmetric square wells are studied in a series of models where the Hamiltonians are assumed $R-$pseudo-Hermitian and $R^2-$symmetric. Specific rotation-like generalized parities $R$ are considered such…
The original Calogero and Sutherland models describe N quantum particles on the line interacting pairwise through an inverse square and an inverse sinus-square potential. They are well known to be integrable and solvable. Here we extend the…