相关论文: Experiments in PT-symmetric quantum mechanics
We apply the quantum Hamilton-Jacobi formalism, naturally defined in the complex domain, to a number of complex Hamiltonians, characterized by discrete parity and time reversal (PT) symmetries and obtain their eigenvalues and…
A condition to have a real spectrum for a non-Hermitian Hamiltonian is given. As special cases, it is shown that the condition is reduced to Hermiticity and PT symmetric conditions.
The overall principles of what is now widely known as PT-symmetric quantum mechanics are listed, explained and illustrated via a few examples. In particular, models based on an elementary local interaction V(x) are discussed as motivated by…
A review is given on the foundations and applications of non-Hermitian classical and quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra, including Jordan normal form, biorthogonality, exceptional…
Despite acute interest in the dynamics of non-Hermitian systems, there is a lack of consensus in the mathematical formulation of non-Hermitian quantum mechanics in the community. Different methodologies are used in the literature to study…
We describe recent progress in understanding the continuous symmetry properties of non-Hermitian, PT-symmetric quantum field theories. Focussing on a simple non-Hermitian theory composed of one complex scalar and one complex pseudoscalar,…
We investigate complex PT-symmetric potentials, associated with quasi-exactly solvable non-hermitian models involving polynomials and a class of rational functions. We also look for special solutions of intertwining relations of SUSY…
In the framework of quasi-Hermitian quantum mechanics it is shown that a weakening of the isotropy of the Hilbert-space geometry can help us to enlarge the domain of the parameters at which the evolution is unitary. The idea is tested using…
We generalize a recently proposed algebraic method in order to treat non-Hermitian Hamiltonians. The approach is applied to several quadratic Hamiltonians studied earlier by other authors. Instead of solving the Schr\"odinger equation we…
We study non-Hermitian quantum mechanics in the presence of a minimal length. In particular we obtain exact solutions of a non-Hermitian displaced harmonic oscillator and the Swanson model with minimal length uncertainty. The spectrum in…
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…
We review some recent results of the so-called quasi-hermitian quantum mechanics, with particular focus on the quantum dynamics both in the Schr\"odinger and in the Heisenberg representations. The role of Krein spaces is also discussed.
While the Hamiltonians used in standard quantum mechanics are Hermitian, it is also possible to extend the theory to non-Hermitian Hamiltonians. Particularly interesting are non-Hermitian Hamiltonians satisfying parity-time (PT) symmetry,…
We present two examples of non-Hermitian Hamiltonians which consist of an unperturbed part plus a perturbation that behaves like a vector, in the framework of PT quantum mechanics. The first example is a generalization of the recent work by…
Parallels between the concepts of symmetry, supersymmetry and (recently introduced) PT-symmetry are reviewed and discussed, with particular emphasis on the new insight in quantum theory which is rendered possible by their combined use.
The Hamiltonian for quantum electrodynamics becomes non-Hermitian if the unrenormalized electric charge $e$ is taken to be imaginary. However, if one also specifies that the potential $A^\mu$ in such a theory transforms as a pseudovector…
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…
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…
The author discusses a different kind of Hermitian quantum mechanics, called $J$-Hermitian quantum mechanics. He shows that $PT$-symmetric quantum mechanics is indeed $J$-Hermitian quantum mechanics, and that time evolution (in the Krein…
This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…