相关论文: Quantum Complex Henon-Heiles Potentials
Two-dimensional PT-symmetric quantum-mechanical systems with the complex cubic potential V_{12}=x^2+y^2+igxy^2 and the complex Henon-Heiles potential V_{HH}=x^2+y^2+ig(xy^2-x^3/3) are investigated. Using numerical and perturbative methods,…
Recently, a class of PT-invariant quantum mechanical models described by the non-Hermitian Hamiltonian $H=p^2+x^2(ix)^\epsilon$ was studied. It was found that the energy levels for this theory are real for all $\epsilon\geq0$. Here, the…
A simple approximate solution for the quantum-mechanical quartic oscillator $V= m^2 x^2+g x^4$ in the double-well regime $m^2<0$ at arbitrary $g \geq 0$ is presented. It is based on a combining of perturbation theory near true minima of the…
We construct Q-ball solutions from a model consisting of one massive scalar field $\xi$ and one massive complex scalar field $\phi$ interacting via the cubic couplings $g_1 \xi \phi^{*} \phi + g_2 \xi^3$, typical of Henon-Heiles-like…
One-dimensional PT-symmetric quantum-mechanical Hamiltonians having continuous spectra are studied. The Hamiltonians considered have the form $H=p^2+V(x)$, where $V(x)$ is odd in $x$, pure imaginary, and vanishes as $|x|\to\infty$. Five…
On the basis of extensive numerical studies it is argued that there are strong analogies between the probabilistic behavior of quantum systems defined by Hermitian Hamiltonians and the deterministic behavior of classical mechanical systems…
The optical properties of wide Quantum Wells are considered, taking into account the screened electron-hole interaction potential and parabolic confinement potentials, different for the electrons and for the holes. The role of the…
We consider a Parity-time (PT) invariant non-Hermitian quasi-exactly solvable (QES) potential which exhibits PT phase transition. We numerically study this potential in a complex plane classically to demonstrate different quantum effects.…
This paper demonstrates that complex PT-symmetric periodic potentials possess real band spectra. However, there are significant qualitative differences in the band structure for these potentials when compared with conventional real periodic…
The theory of electron holes is extended into the quantum regime. The Wigner--Poisson system is solved perturbatively based in lowest order on a weak, standing electron hole. Quantum corrections are shown to lower the potential amplitude…
We investigate the spectroscopy and decays of the charmonium and upsilon systems in a potential model consisting of a relativistic kinetic energy term, a linear confining term including its scalar and vector relativistic corrections and the…
A few 2+1-dimensional equations belonging to the KP and modified KP hierarchies are shown to be sufficient to provide a unified picture of all the integrable cases of the cubic and quartic H\'enon-Heiles Hamiltonians.
We show that the complex $\cal PT$-symmetric periodic potential $V(x) = - ({\rm i} \xi \sin 2x + N)^2$, where $\xi$ is real and $N$ is a positive integer, is quasi-exactly solvable. For odd values of $N \ge 3$, it may lead to exceptional…
A variational calculation of the energy levels of a class of PT-invariant quantum mechanical models described by the non-Hermitian Hamiltonian H= p^2 - (ix)^N with N positive and x complex is presented. Excellent agreement is obtained for…
A non-standard generalisation of the Bender potentials $x^2(\ii x^\ve)$ is suggested. The spectra are obtained numerically and some of their particular properties are discussed.
The fourth, missing example of an exactly solvable complex potential with PT symmetry V(x) = [V(-x)]^* defined on a bent contour and leading, at the real energies, to the Jacobi polynomial wave functions is found in a generalized Hulthen…
In a previous paper it was shown that a one-turning-point WKB approximation gives an accurate picture of the spectrum of certain non-Hermitian PT-symmetric Hamiltonians on a finite interval with Dirichlet boundary conditions. Potentials to…
The comparison of $K^+$ and $K^-$ spectra at low transverse momentum in light symmetric heavy ion reactions at energies around 2 AGeV allows for a direct experimental determination of the strength of the $K^+$ as well as of t he $K^-$…
Quark number susceptibilities as computed in lattice QCD are commonly believed to provide insights into the microscopic structure of QCD matter, in particular its degrees of freedom. We generalize a previously constructed partonic…
PT symmetric complex potential V(r) = - r^4 + i a r^3 + b r^2 + i c r + i d/r + e/r^2 is studied. Arbitrarily large multiplets of its closed bound-state solutions with real energies are shown obtainable quasi-exactly (i.e., with a certain…