Related papers: A comparative study of some analytic approximate m…
In semiclassical theories for chaotic systems such as Gutzwiller's periodic orbit theory the energy eigenvalues and resonances are obtained as poles of a non-convergent series g(w)=sum_n A_n exp(i s_n w). We present a general method for the…
The transformation of a classical system into its quantum counterpart is usually done through the well known procedure of canonical quantization. However, on non-Cartesian domains, or on bounded Cartesian domains, this procedure can be…
The new perturbation theory for the problem of nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zero order approximation the exact wave function of harmonic oscillator with variable frequency…
Combinatorial optimization problems are one of the target applications of current quantum technology, mainly because of their industrial relevance, the difficulty of solving large instances of them classically, and their equivalence to…
In this work, the energy eigenvalues are calculated for the quadratic ($\frac{g^2 x^2}{2}$), pure quartic ($\lambda x^4 $), and quartic anharmonic oscillators ($\frac{g^2 x^2}{2} + \lambda x^4 $) by applying variational method. For this,…
The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator and the screened Coulomb potential is developed. Based upon the $\hbar$-expansions and suitable…
Quasi-periodic responses composed of multiple base frequencies widely exist in science and engineering problems. The multiple harmonic balance (MHB) method is one of the most commonly used approaches for such problems. However, it is…
We propose in this work a subgradient extragradient method with inertial and correction terms for solving equilibrium problems in a real Hilbert space. We obtain that the sequence generated by our proposed method converges weakly to a point…
Out-of-time-ordered-correlators (OTOCs) have been suggested as a means to diagnose chaotic behavior in quantum mechanical systems. Recently, it was found that OTOCs display exponential growth for the inverted quantum harmonic oscillator,…
Proposed hybrid algorithms encode a combinatorial cost function into a problem Hamiltonian and optimize its energy by varying over a set of states with low circuit complexity. Classical processing is typically only used for the choice of…
The method of harmonic balance (HB) is a spectrally accurate method used to obtain periodic steady state solutions to dynamical systems subjected to periodic perturbations. We adapt HB to solve for the stress response of the Giesekus model…
A new implementation of the Roe scheme for solving two-layer shallow-water equations is presented in this paper. The proposed A-Roe scheme is based on the analytical solution to the characteristic quartic of the flux matrix, which is an…
The efficient and accurate calculation of how ionic quantum and thermal fluctuations impact the free energy of a crystal, its atomic structure, and phonon spectrum is one of the main challenges of solid state physics, especially when strong…
In this paper we consider several families of potential non-isochronous systems and study their associated period functions. Firstly, we prove some properties of these functions, like their local behavior near the critical point or…
The relativistic Hartree-Fock and electron correlation methods without the negative-energy orbital problem are examined on the basis of the quantum electrodynamics (QED) Hamiltonian. First, several QED Hamiltonians previously proposed are…
For quantum systems with competing potentials, the conventional perturbation theory often yields an asymptotic series and the subsequent numerical outcome becomes uncertain. To tackle such kind of problems, we develop a general solution…
A coupled two frequency Hill's equation is solved. Analytically approximate solution correct up-to first order is derived using modified Lindstedt Poincare perturbation method. For a wide range of controlling parameters we compare the…
In this paper, we present a direct quantum adaptation of the classical shifted power method. The method is very similar to the iterative phase estimation algorithm; however, it does not require any initial estimate of an eigenvector and as…
We show how several important classical problems, with positive definite potential energy, can be solved by starting from the factorization of the total mechanical energy using complex numbers. In particular, we derive in a new way exact…
We propose a new analytical method to solve for nonexactly soluble Schrodinger equation via expansions through some existing quantum numbers. Successfully, it is applied to the rational non-polynomial oscillator potential. Moreover, a…