Related papers: Non-Hermitian Hamiltonian versus E=0 localized sta…
We ask whether soft photons, defined by asymptotic charges, can have consequences for the outcome of localised quantum processes. We consider a spatially localised two-state system, at rest in flat spacetime, coupled to a $U(1)$ gauge…
We present an evaluation of some recent attempts at understanding the role of pseudo-Hermitian and PT-symmetric Hamiltonians in modeling unitary quantum systems and elaborate on a particular physical phenomenon whose discovery originated in…
We report on our systematic attempts at finding local interactions for which the lowest-Landau-level projected composite-fermion wave functions are the unique zero energy ground states. For this purpose, we study in detail the simplest…
Locally real states of electromagnetic radiation derived from the underlying quantum mechanical formalism are shown to provide an alternative basis for definite polarized states of the widely accepted probabilistic interpretation. The…
A Half Bound State (HBS) $\psi_*(x)$ can be defined as a single, conditional, zero-energy, continuous solution of the one dimensional Schr{\"o}dinger equation for a scattering potential well $V(x)$ ($s.t ~ V(\pm \infty)=0$). The…
We investigate which nonlocal-interaction energies have a ground state (global minimizer). We consider this question over the space of probability measures and establish a sharp condition for the existence of ground states. We show that…
We discuss the time evolution of physical finite dimensional systems which are modelled by non-hermitian Hamiltonians. We address both general non-hermitian Hamiltonians and pseudo-hermitian ones. We apply the theory of Krein Spaces to…
We attempt to shed light on the following question: What happens to the negative energy states when we take the non-relativistic limit of the Dirac equation? The Levy-Leblond equation is the non-relativistic limit of the Dirac equation and…
It is known that the standard and the inverted harmonic oscillator are different. Replacing thus of {\omega} by i{\omega} in the regular oscillator is necessary going to give the inverted oscillator H^{r}. This replacement would lead to…
This article investigates the existence and properties of ground state solutions to the following nonlocal Hamiltonian elliptic system: \begin{align*} \begin{cases} (-\Delta)^\frac12 u +V_0 u =g(v),~x\in \mathbb{R} (-\Delta)^\frac12 v +V_0…
Previous $\lambda$-deformed {\it non-Hermitian} Hamiltonians with respect to the usual scalar product of Hilbert spaces dealing with harmonic oscillator-like developments are (re)considered with respect to a new scalar product in order to…
A family of spherical non-Hermitian potentials is studied. It is shown that the corresponding non-Hermitian Hamiltonians admit some "new" P$phi$T$phi$-symmetry. It is observed that whilst such P$phi$T$phi$-symmetric Hamiltonians just copy…
Noninteracting fermions, placed in a system with a continuous density of states, may have zeros in the $N$-fermion canonical partition function on the positive real $\beta$ axis (or very close to it), even for a small number of particles.…
Exact solvability of some non-Hermitian $\eta$-weak-pseudo-Hermitian Hamiltonians is explored as a byproduct of $\eta$-weak-pseudo-Hermiticity generators. A class of V_{eff}(x)=V(x)+iW(x) potentials is considered, where the imaginary part…
In this paper we have obtained the exact eigenstates of a two dimensional damped harmonic oscillator in time dependent noncommutative space. It has been observed that for some specific choices of the damping factor and the time dependent…
We consider a rate-independent system with nonconvex energy under discontinuous external loading. The underlying space is finite dimensional and the loads are functions in $BV([0,T];\mathbb{R}^d)$. We investigate the stability of various…
We study a non-Hermitian generalization of quantum systems in which an imaginary vector potential is added to the momentum operator. In the tight-binding approximation, we make the hopping energy asymmetric in the Hermitian Hamiltonian. In…
The spinless Salpeter equation is the combination of relativistic kinematics with some static interaction potential. The nonlocal nature of the Hamiltonian resulting from this approximation renders difficult to obtain rigorous analytic…
Understanding the linear response of any system is the first step towards analyzing its linear and nonlinear dynamics, stability properties, as well as its behavior in the presence of noise. In non-Hermitian Hamiltonian systems, calculating…
Some ideas are presented concerning the question which of the harmonic wavefunctions constructed in [hep-th/9909191] may be annihilated by all supercharges.