Related papers: Waxman's Algorithm for non-Hermitian Hamiltonian O…
The motivation for studying non-Hermitian systems and the role of $\mathcal{PT}$-symmetry is discussed. We investigate the use of a quantum algorithm to find the eigenvalues and eigenvectors of non-Hermitian Hamiltonians, with applications…
In this paper we consider density matrices operator related to non-Hermitian Hamiltonians. In particular, we analyse two natural extensions of what is usually called a density matrix operator (DM), of pure states and of the entropy…
We consider QM with non-Hermitian quasi-diagonalizable Hamiltonians, i.e. the Hamiltonians having a number of Jordan cells in particular biorthogonal bases. The "self-orthogonality" phenomenon is clarified in terms of a correct spectral…
A very simple procedure to calculate eigenenergies of quantum anharmonic oscillators is presented. The method, exact but for numerical computations, consists merely in requiring the vanishing of the Wronskian of two solutions which are…
Optimized, necessary and sufficient conditions for the identification of the Schmidt number will be derived in terms of general Hermitian operators. These conditions apply to arbitrary mixed quantum states. The optimization procedure…
Motivated by the development of on-going optomechanical experiments aimed at constraining non-local effects inspired by some quantum gravity scenarios, the Hamiltonian formulation of a non-local harmonic oscillator, and its coupling to a…
We consider conditions for the existence of boundary modes in non-Hermitian systems with edges of arbitrary co-dimension. Through a universal formulation of formation criteria for boundary modes in terms of local Green functions, we outline…
A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…
. We study the statistical properties of the eigenvalues of non-Hermitian operators assoicated with the dissipative complex systems. By considering the Gaussian ensembles of such operators, a hierarchical relation between the correlators is…
Many-body Green's functions encode all the properties and excitations of interacting electrons. While these are challenging to be evaluated accurately on a classical computer, recent efforts have been directed towards finding quantum…
Non-Hermitian dynamics in quantum systems preserves the rank of the state density operator. Using this insight, we develop a geometric framework to describe its time evolution. In particular, we identify mutually orthogonal coherent and…
The differential-equation eigenvalue problem associated with a recently-introduced Hamiltonian, whose eigenvalues correspond to the zeros of the Riemann zeta function, is analyzed using Fourier and WKB analysis. The Fourier analysis leads…
We investigate some questions on the construction of $\eta$ operators for pseudo-Hermitian Hamiltonians. We give a sufficient condition which can be exploited to systematically generate a sequence of $\eta$ operators starting from a known…
A method for computing lower bounds to eigenvalues of sums of lower semibounded self-adjoint operators is presented. We apply the method to one-electron Hamiltonians. To improve the lower bounds we consider symmetry of molecules and use…
A non-Hermitian operator with a real spectrum and a complete set of eigenvectors may serve as the Hamiltonian operator for a unitary quantum system provided that one makes an appropriate choice for the defining inner product of the physical…
The Magnus expansion offers a method to express a time-ordered exponential as an ordinary operatorial exponential. This representation has advantageous theoretical properties, while still solving the original differential equation. For any…
We find the lattice spacing dependence of the eigenvalue density of the non-Hermitian Wilson Dirac operator in the $\epsilon$-domain. The starting point is the joint probability density of the corresponding random matrix theory. In addition…
We develop a theory for the eigenvalue density of arbitrary non-Hermitian Euclidean matrices. Closed equations for the resolvent and the eigenvector correlator are derived. The theory is applied to the random Green's matrix relevant to wave…
This paper provides a connection to the non-Hermitian operators associated with the geometric potential function $s$ and Baker-Hausdorff formula. The geometric quantum potential is considered in a precise condition. The Ri-operator as a…
The study of topological properties by machine learning approaches has attracted considerable interest recently. Here we propose machine learning the topological invariants that are unique in non-Hermitian systems. Specifically, we train…