Related papers: Accurate calculation of resonances in multiple-wel…
We describe a method for the calculation of accurate energy eigenvalues and expectation values of observables of separable quantum-mechanical models. We discuss the application of the approach to one-dimensional anharmonic oscillators with…
The complex-scaling method can be used to calculate molecular resonances within the Born-Oppenheimer approximation, assuming the electronic coordinates are dilated independently of the nuclear coordinates. With this method, one will…
We draw attention on the fact that the Riccati-Pad\'e method developed some time ago enables the accurate calculation of bound-state eigenvalues as well as of resonances embedded either in the continuum or in the discrete spectrum. We apply…
In this paper, some properties of resonances for multi-dimensional quantum walks are studied. Resonances for quantum walks are defined as eigenvalues of complex translated time evolution operators in the pseudo momentum space. For some…
The eigenvalues of a pure quartic oscillator are computed, applying a canonical operator formulation, generalized from the harmonic oscillator. Solving a 10x10 secular equation produces eigenvalues in agreement, to at least 4 significant…
We apply power series expansion to symmetric multi-well oscillators bounded by two infinite walls. The spectrum and expectation values obtained are compared with available exact and approximate values for the unbounded ones. It is shown…
Finding reliably and efficiently the spectrum of the resonant states of an optical system under varying parameters of the medium surrounding it is a technologically important task, primarily due to various sensing applications.…
Complex eigenvalues, resonances, play an important role in large variety of fields in physics and chemistry. For example, in cold molecular collision experiments and electron scattering experiments, autoionizing and pre-dissociative…
We calculate accurate eigenvalues of a bounded oscillator by means of the Riccati--Pad\'e method that is based on a rational approximation to a regularized logarithmic derivative of the wavefunction. Sequences of roots of Hankel…
The purpose of this paper is the discussion of a pair of coupled linear oscillators that has recently been proposed as a model of a system of two optical resonators. By means of an algebraic approach we show that the frequencies of the…
In this note we discuss the complex version of the Higgs oscillator on the hyperbolic space. The eigenvalues and resonances of the complex Higgs oscillator are computed in different examples in the hyperbolic setting. We also propose open…
We study the consequence of the frequency errors of individual oscillators on the scalability of quantum computing based on nanomechanical resonators. We show the fidelity change of the quantum operation due to the frequency shifts…
We calculate eigenvalues of one-dimensional quantum-systems by the exact numerical solution of the Lippmann-Schwinger equation, analogous to the scattering problem. To illustrate our method, we treat elementary problems: the harmonic and…
Quantum computers are ideal for solving chemistry problems due to their polynomial scaling with system size in contrast to classical computers which scale exponentially. Until now molecular energy calculations using quantum computing…
We derive two methods for simultaneously controlling the resonance frequency, linewidth and multipolar nature of the resonances of radially symmetric structures. Firstly, we formulate an eigenvalue problem for a global shift in the…
We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problem of incommensurate systems. Unlike the conventional practice that approximates the system by a large commensurate supercell, our…
We present a general quantum circuit design for finding eigenvalues of non-unitary matrices on quantum computers using the iterative phase estimation algorithm. In particular, we show how the method can be used for the simulation of…
We consider a class of one-dimensional nonhermitian oscillators and discuss the relationship between the real eigenvalues of PT-symmetric oscillators and the resonances obtained by different authors. We also show the relationship between…
We introduce variational methods for finding approximate eigenfunctions and eigenvalues of quantum Hamiltonians by constructing a set of orthogonal wave functions which approximately solve the eigenvalue equation.
We use a power-series expansion to calculate the eigenvalues of anharmonic oscillators bounded by two infinite walls. We show that for large finite values of the separation of the walls, the calculated eigenvalues are of the same high…