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The aim of this paper is to describe efficient algorithms for computing Maass waveforms on subgroups of the modular group PSL(2,Z) with general multiplier systems and real weight. A selection of numerical results obtained with these…
Exact eigenvalue correlation functions are computed for large $N$ hermitian one-matrix models with eigenvalues distributed in two symmetric cuts. An asymptotic form for orthogonal polynomials for arbitrary polynomial potentials that support…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
The problem of the quantum harmonic oscillator is investigated in the framework of bicomplex numbers, which are pairs of complex numbers making up a commutative ring with zero divisors. Starting with the commutator of the bicomplex position…
In this paper we study multivariate polynomial functions in complex variables and the corresponding associated symmetric tensor representations. The focus is on finding conditions under which such complex polynomials/tensors always take…
Exact analytic expression is derived for the matrix elements of the Coulomb interaction in two dimensions in the form of a closed finite sum expression. The orthonormal complete set of eigenfunctions of the harmonic oscillator is used as…
A general treatment of the quantal time-dependent coupled oscillators in presence of the variable magnetic field is presented. The treatment is based on the use of an alternative canonical transformations, time-dependent unitary…
We describe irreducible representations, coherent states and star-products for algebras of integrals of motions (symmetries) of two-dimensional resonance oscillators. We demonstrate how the quantum geometry (quantum K\"ahler form, metric,…
In this review we discuss, from a unified point of view, a variety of Monte Carlo methods used to solve eigenvalue problems in statistical mechanics and quantum mechanics. Although the applications of these methods differ widely, the…
This is the third article in a series of three papers on the resonance energy levels of anharmonic oscillators. Whereas the first two papers mainly dealt with double-well potentials and modifications thereof [see J. Zinn-Justin and U. D.…
A method used previously to calculate the masses of the vector mesons is extended to the calculation of the nucleon resonances. The method is based on the choice of integration kernels which eliminate the unknown parts of the spectrum. We…
We present a numerical method to simulate the dynamics of continuous-variable quantum many-body systems. Our approach is based on custom neural-network many-body quantum states. We focus on dynamics of two-dimensional quantum rotors and…
Optical resonators are widely used in modern photonics. Their spectral response and temporal dynamics are fundamentally driven by their natural resonances, the so-called quasinormal modes (QNMs), with complex frequencies. For optical…
The magnetization of quantum dots is discussed in terms of a relatively simple but exactly solvable model Hamiltonian. The model predicts oscillations in spin polarization as a function of dot radius for a fixed electron density. These…
The optical properties of defects in solids produce rich physics, from gemstone coloration to single-photon emission for quantum networks. Essential to describing optical transitions is electron-phonon coupling, which can be predicted from…
The quantum modes of a new family of relativistic oscillators are studied by using the supersymmetry and shape invariance in a version suitable for (1+1) dimensional relativistic systems. In this way one obtains the Rodrigues formulas of…
Representations of the quantum q-oscillator algebra are studied with particular attention to local Hamiltonian representations of the Schroedinger type. In contrast to the standard harmonic oscillators such systems exhibit a continuous…
The aim of this paper is to derive a formula for the subwavelength resonance frequency of an encapsulated bubble with arbitrary shape in two dimensions. Using Gohberg-Sigal theory, we derive an asymptotic formula for this resonance…
The pseudospectral method is a powerful tool for finding highly precise solutions of Schr\"{o}dinger's equation for few-electron problems. We extend the method's scope to wave functions with non-zero angular momentum and test it on several…
Variational ab-initio methods in quantum chemistry stand out among other methods in providing direct access to the wave function. This allows in principle straightforward extraction of any other observable of interest, besides the energy,…