Related papers: Non-Hermitian Hamiltonian versus E=0 localized sta…
We discuss the coherent states for PT-/non-PT-Symmetric and non-Hermitian generalized Morse Potential obtained by using path integral formalism over the holomorphic coordinates. We transform the action of generalized Morse potential into…
This work describes coherent states for a physical system governed by a Hamiltonian operator, in two dimensional space, of spinless charged particles subject to a perpendicular magnetic field B, coupled with a harmonic potential. The…
We complexify a 1-d potential which exhibits bound, reflecting and free states to study various properties of a non-Hermitian system. This potential turns out a PT-symmetric non-Hermitian potential when one of the parameters becomes…
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…
An unusual type of the exact solvability is reported. It is exemplified by the Coulomb plus harmonic oscillator in D dimensions after a complexification of its Hamiltonian which keeps the energies real. Infinitely many bound states are…
A stable physical system has an energy spectrum that is bounded from below. For quantum systems, the dangerous states of unboundedly low energies should decouple and become null. We propose the principle of nullness and apply it to the…
We construct effective Hamiltonians which despite their apparently nonrelativistic form incorporate relativistic effects by involving parameters which depend on the relevant momentum. For some potentials the corresponding energy eigenvalues…
Non-hermiticity presents a vast newly opened territory that harbors new physics and applications such as lasing and sensing. However, only non-Hermitian systems with real eigenenergies are stable, and great efforts have been devoted in…
We reconsider the recently proposed connection between density of states in the so-called ``non-hermitian quantum mechanics'' and the localization length for a particle moving in random potential. We argue that it is indeed possible to find…
A family of discrete Schr\"{o}dinger equations with imaginary potentials $V(x)$ is studied. Inside the domain ${\cal D}$ of unitarity-compatible values of $V(x)$, the reality of all of the bound-state energies survives up to the…
Through a simple and exact analytical derivation, we show that for a particle on a lattice, there is a one-to-one correspondence between the spectra in the presence of an attractive potential $\hat{V}$ and its repulsive counterpart…
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…
Within the framework of quantum mechanics working with one-dimensional, manifestly non-Hermitian Hamiltonians $H=T+V$ the traditional class of the exactly solvable models with local point interactions $V=V(x)$ is generalized. The…
We study numerically the existence and character of bound states for positive and negative point charges shielded by the response of a two-dimensional homogeneous electron gas. The problem is related to many physical situations and has…
In the context of ground states of quantum many-body systems, the locality of entanglement between connected regions of space is directly tied to the locality of the corresponding entanglement Hamiltonian: the latter is dominated by local,…
We propose a framework for the connection between local symmetries of discrete Hamiltonians and the design of compact localized states. Such compact localized states are used for the creation of tunable, local symmetry-induced bound states…
Several families of nonlinear field equations are known to possess space- localized singularity-free solutions which describe fields with finite Hermitian norms. This paper studies the interaction of such fields with given electromagnetic…
We propose that the real spectrum and the orthogonality of the states for several known complex potentials of both types, PT-symmetric and non-PT-symmetric can be understood in terms of currently proposed $\eta$-pseudo-Hermiticity…
The aim of the paper is to study the question whether or not equilibrium states exist in open quantum systems that are embedded in at least two environments and are described by a non-Hermitian Hamilton operator $\cal H$. The eigenfunctions…
Nonlocal Hamiltonians are used widely in first-principles quantum calculations; the nonlocality stems from eliminating undesired degrees of freedom, e.g. core electrons. To date, attempts to couple nonlocal systems to external…