Related papers: Numerical aspects of eigenvalue and eigenfunction …
In a fully 3-D system such as a stellarator, the toroidal mode number $n$ ceases to be a good quantum number--all $n$s within a given mode family being coupled. It is found that the discrete spectrum of unstable ideal MHD…
In this paper we have tested several general numerical methods in solving the quantum billiards, such as the boundary integral method (BIM) and the plane wave decomposition method (PWDM). We performed extensive numerical investigations of…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
We present a comprehensive review of the nodal domains and lines of quantum billiards, emphasizing a quantitative comparison of theoretical findings to experiments. The nodal statistics are shown to distinguish not only between regular and…
Estimating the eigenvalues of a unitary transformation U by standard phase estimation requires the implementation of controlled-U-gates which are not available if U is only given as a black box. We show that a simple trick allows to measure…
We obtain a semiclassical expression for the projector onto eigenfunctions by means of the Fredholm theory. We express the projector in the coherent state basis, thus obtaining the semiclassical Husimi representation of the stadium…
Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…
Eigenvalue transformations appear ubiquitously in scientific computation, ranging from matrix polynomials to differential equations, and are beyond the reach of the quantum singular value transformation framework. In this work, we study the…
In this paper, we employ a semiperturbative theory to study the statistical structural properties of energy eigenfunctions (EFs) in many-body quantum chaotic systems consisting of a central system coupled to an environment. Under certain…
We study the classical and quantum mechanics of a free particle that collides elastically with the walls of a circular disk with the radius varying periodically in time. The quasi-energy spectral properties of the model are obtained from…
A characteristic feature of "quantum chaotic" systems is that their eigenspectra and eigenstates display universal statistical properties described by random matrix theory (RMT). However, eigenstates of local systems also encode structure…
A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance…
For the representation of eigenstates on a Poincar\'e section at the boundary of a billiard different variants have been proposed. We compare these Poincar\'e Husimi functions, discuss their properties and based on this select one…
This article is a brief introduction to quantum algorithms for the eigenvalue problem in quantum many-body systems. Rather than a broad survey of topics, we focus on providing a conceptual understanding of several quantum algorithms that…
Non-Hermitian physics has emerged as a rich field of study, with applications ranging from $PT$-symmetry breaking and skin effects to non-Hermitian topological phase transitions. Yet most studies remain restricted to small-scale or…
Quantum counterparts of certain simple classical systems can exhibit chaotic behaviour through the statistics of their energy levels and the irregular spectra of chaotic systems are modelled by eigenvalues of infinite random matrices. We…
The subleading eigenvalues and associated eigenfunctions of the Perron-Frobenius operator for 2-dimensional area-preserving maps are numerically investigated. We closely examine the validity of the so-called Ulam method, a numerical scheme…
For piecewise expanding one-dimensional maps without periodic turning points we prove that isolated eigenvalues of small (random) perturbations of these maps are close to isolated eigenvalues of the unperturbed system. (Here ``eigenvalue''…
We perform a detailed numerical study of energy-level and wavefunction statistics of a deformable quantum billiard focusing on properties relevant to semiconductor quantum dots. We consider the family of Robnik billiards generated by simple…
We study eigenfunction localization for higher dimensional cat maps, a popular model of quantum chaos. These maps are given by linear symplectic maps in ${\mathrm{Sp}}(2g,\mathbb Z)$, which we take to be ergodic. Under some natural…