Related papers: Trapped Particles in $PT$ Symmetric Theories
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.
Recently developed methods for PT-symmetric models are applied to quantum-mechanical matrix models. We consider in detail the case of potentials of the form $V=-(g/N^{p/2-1})Tr(iM)^{p}$ and show how the calculation of all singlet wave…
In PT quantum mechanics a fundamental principle of quantum mechanics, that the Hamiltonian must be hermitian, is replaced by another set of requirements, including notably symmetry under PT, where P denotes parity and T denotes time…
We prove the reality of the perturbed eigenvalues of some PT symmetric Hamiltonians of physical interest by means of stability methods. In particular we study 2-dimensional generalized harmonic oscillators with polynomial perturbation and…
In the recent years a generalization $H=p^2 +x^2(ix)^\epsilon$ of the harmonic oscillator using a complex deformation was investigated, where \epsilon\ is a real parameter. Here, we will consider the most simple case: \epsilon even and x…
The recently-developed notion of 'parity-time (PT) symmetry' in optical systems with a controlled gain-loss interplay has spawned an intriguing way of achieving optical behaviors that are presently unattainable with standard arrangements.…
In our previous work, we proposed a mathematical framework for PT-symmetric quantum theory, and in particular constructed a Krein space in which PT-symmetric operators would naturally act. In this work, we explore and discuss various…
We construct an exactly solvable PT-symmetric example of Sturmian bound states which exist in the absence of any confining potential. Their origin is purely topological -- these states live on certain nontrivial contours of complex…
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…
Non-Hermitian, one-dimensional potentials which are also non-local, allow for scattering asymmetries, namely, asymmetric transmission or reflection responses to the incidence of a particle from left or right. The symmetries of the potential…
We consider passive Brownian particles trapped in an "imperfect" harmonic trap. The trap is imperfect because it is randomly turned off and on, and as a result, particles fail to equilibrate. Another way to think about this is to say that a…
The eigenvalue of the hermitic Hamiltonian is real undoubtedly. Actually, The reality can also be guaranteed by the $PT$-symmetry. The hermiticity and the $PT$-symmetric quantum theory both have requirements regarding the boundary…
We numerically investigate the quantum transport in a coupled kicked rotors with the $\mathcal{PT}$-symmetric potential. We find that the spontaneous $\mathcal{PT}$-symmetry breaking of wavefunctions emerges when the amplitude of the…
In quantum physics the free particle and the harmonically trapped particle are arguably the most important systems a physicist needs to know about. It is little known that, mathematically, they are one and the same. This knowledge helps us…
We point out that PT-symmetric potentials $V_{PT}(x)$ having imaginary asymptotic saturation: $V_{PT}(x=\pm \infty) =\pm i V_1, V_1 \in \Re$ are devoid of scattering states and spectral singularity. We show the existence of real (positive…
The Hermiticity axiom of quantum mechanics guarantees that the energy spectrum is real and the time evolution is unitary (probability-preserving). Nevertheless, non-Hermitian but $\mathcal{PT}$-symmetric Hamiltonians may also have real…
Quantum correlations, both spatial and temporal, are the central pillars of quantum mechanics. Over the last two decades, a big breakthrough in quantum physics is its complex extension to the non-Hermitian realm, and dizzying varieties of…
The physics of systems that cannot be described by a Hermitian Hamiltonian, has been attracting a great deal of attention in recent years, motivated by their nontrivial responses and by a plethora of applications for sensing, lasing, energy…
We study the one-dimensional Dirac equation with local PT-symmetric potentials whose discrete eigenfunctions and continuum asymptotic eigenfunctions are eigenfunctions of the PT operator, too: on these conditions the bound-state spectra are…
We study the supersymmetric partners of the harmonic oscillator with an infinite potential barrier at the origin and obtain the conditions under which it is possible to add levels to the energy spectrum of these systems. It is found that…