Related papers: A comparative study of some analytic approximate m…
We present a scalable approach to computing nonlinear balancing energy functions for control-affine systems with polynomial nonlinearities. Al'brekht's power-series method is used to solve the Hamilton-Jacobi-Bellman equations for…
Signal recovery from incomplete or partial frequency information is a fundamental problem in harmonic analysis and applied mathematics, with wide-ranging applications in communications, imaging, and data science. Historically, the classical…
In the framework of density functional theory (DFT) simulations of molecules and materials, anharmonic terms of the potential energy surface are commonly computed numerically, with an associated cost that rapidly increases with the size of…
How to develop efficient numerical schemes while preserving the energy stability at the discrete level is a challenging issue for the three component Cahn-Hilliard phase-field model. In this paper, we develop first and second order temporal…
In a uniformly hyperbolic system, we consider the problem of finding the optimal infinitesimal perturbation to apply to the system, from a certain set $P$ of feasible ones, to maximally increase the expectation of a given observation…
We propose a new solvable class of multidimensional quantum harmonic oscillators for a linear diffusive particle and a quadratic energy absorbing well associated with a semi-definite positive matrix force. Under natural and easily checked…
The harmonic oscillator is one of the most studied systems in Physics with a myriad of applications. One of the first problems solved in a Quantum Mechanics course is calculating the energy spectrum of the simple harmonic oscillator with…
The convergence of the Rayleigh-Ritz method with nonlinear parameters optimized through minimization of the trace of the truncated matrix is demonstrated by a comparison with analytically known eigenstates of various quasi-solvable systems.…
We compare and contrast three different perturbative expansions for the quartic anharmonic oscillator wavefunction and apply a modified Borel summation technique to determine the energy eigenvalues. In the first two expansions this provides…
We introduce a semiclassical quantization method which is based on a stroboscopic description of the classical and the quantum flows. We show that this approach emerges naturally when one is interested in extracting the energy spectrum…
Solving combinatorial optimization problems of the kind that can be codified by quadratic unconstrained binary optimization (QUBO) is a promising application of quantum computation. Some problems of this class suitable for practical…
Exact bound state solutions and corresponding normalized eigenfunctions of the radial Schr\"odinger equation are studied for the pseudoharmonic and Mie-type potentials by using the Laplace transform approach. The analytical results are…
Quantum annealing (QA) is a method for solving combinatorial optimization problems. We can estimate the computational time for QA using the adiabatic condition. The adiabatic condition consists of two parts: an energy gap and a transition…
Quantum computing holds the promise of solving computational mechanics problems in polylogarithmic time, meaning computational time scales as $\mathscr{O}((\log N)^c)$, where $N$ is the problem size and $c$ a constant. We propose a quantum…
Recent work has deployed linear combinations of unitaries techniques to reduce the cost of fault-tolerant quantum simulations of correlated electron models. Here, we show that one can sometimes improve upon those results with optimized…
The set of world lines for the non-relativistic quartic oscillator satisfying Newton's equation of motion for all space and time in 1-1 dimensions with no constraints other than the "spring" restoring force is shown to be equivalent…
Quantum annealing is a promising approach for solving combinatorial optimization problems. However, its performance is often limited by the overhead of additional qubits required for embedding logical QUBO models onto quantum annealers.…
It is shown that for the one-dimensional quantum anharmonic oscillator with potential $V(x)= x^2+g^2 x^4$ the Perturbation Theory (PT) in powers of $g^2$ (weak coupling regime) and the semiclassical expansion in powers of $\hbar$ for…
A systematically improvable wave function is proposed for the numerical solution of strongly correlated systems. With a stochastic optimization method, based on the auxiliary field quantum Monte Carlo technique, an effective temperature…
We discuss two alternative methods, based on the Lindstedt--Poincar\'{e} technique, for the removal of secular terms from the equations of perturbation theory. We calculate the period of an anharmonic oscillator by means of both approaches…