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This is the second paper in a cycle investigating the exact solution of loop equations in decaying turbulence. We perform numerical simulations of the Euler ensemble, suggested in the previous work, as a solution to the loop equations. We…
We give an algebraic derivation of the eigenvalues of energy of a quantum harmonic oscillator on the surface of constant curvature, i.e. on the sphere or on the hyperbolic plane. We use the method proposed by Daskaloyannis for fixing the…
A new discrete model for energy relaxation of a quantum particle is described via a projection operator, causing the wave function collapse. Power laws for the evolution of the particle coordinate and momentum dispersions are derived. A new…
We study echoes and what we call 'revival echoes' for a collection of atoms that are described by a single quantum wavefunction and are confined in a weakly anharmonic trap. The echoes and revival echoes are induced by applying two,…
Position and momentum observables are considered and their correlation is studied for the simplest quantum system of a free particle moving in one dimension. The algebra and the eigenvalue problem for the correlation observable is presented…
The quantum mechanical time-evolution is studied for a particle under the influence of an explicitly time-dependent rotating potential. We discuss the existence of the propagator and we show that in the limit of rapid rotation it converges…
It is shown that the eigenvalue problem for the Hamiltonians of the standard form, $H=p^2/(2m)+V(x)$, is equivalent to the classical dynamical equation for certain harmonic oscillators with time-dependent frequency. This is another…
Quantum simulators offer the potential to utilize the quantum nature of a physical system to study another physical system. In contrast to conventional simulation, which experiences an exponential increase in computational complexity,…
We study the transition between quantum and classical behavior of particles in a gravitational quantum well. We analyze how an increase in the particles mass turns the energy spectrum into a continuous one, from an experimental point of…
Current models of the effect of spontaneous emission on the electron beam dynamics neglect the discreteness of electron recoil associated with photon emission. We present a novel, one-dimensional model of the effect of spontaneous emission…
The present paper is devoted to the detailed study of quantization and evolution of the point limit of the Pauli-Fierz model for a charged oscillator interacting with the electromagnetic field in dipole approximation. In particular, a well…
Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum ap- proximate optimization algorithms that solve ground…
The quantum description of an atom with a magnetic quadrupole moment in the presence of a uniform effective magnetic field is analysed. The atom is also subject to rotation and a scalar potential proportional to the inverse of the radial…
Scientific knowledge increasingly depends on complex computational processes where both hardware and software layers can influence research outcomes. As computational complexity grows, classical-quantum integration provides a lens for…
In this paper, we analyze classical and quantum physical systems from an optimal control perspective. Specifically, we explore whether their associated dynamics can correspond to an open or closed-loop feedback evolution of a control…
We study the Dunkl anharmonic oscillator (Kerr medium) Hamiltonian from an algebraic approach of the $SU(1,1)$ group. In order to obtain the exact energy spectrum of this problem, we write its Hamiltonian in terms of the Dunkl creation and…
It is argued that, contrary to conventional wisdom, no trustworthy universal self-force/radiative corrections to the Lorentz force equation, can be derived from the basic tenets of classical electrodynamics. This concords with the apparent…
Based on some recent progress on a relation between four dimensional super Yang-Mills gauge theory and quantum integrable system, we study the asymptotic spectrum of the quantum mechanical problems described by the Mathieu equation and the…
Increasing fidelity is the ultimate challenge of quantum information technology. In addition to decoherence and dissipation, fidelity is affected by internal imperfections such as impurities in the system. Here we show that the quality of…
The paper is concerned with the effect of the spatio-temporal heterogeneity on the principal eigenvalue of some linear time-periodic parabolic system. Various asymptotic behaviors of the principal eigenvalue and its monotonicity, as a…