Related papers: An Evolutionary approach for solving Shr\"odinger …
This work introduces a methodology to solve ordinary differential equations using the Schur decomposition of the linear representation of the differential equation. This is done by first transforming the system into an upper triangular…
We prove in this paper that the solution of the time-dependent Schr{\"o}dinger equation can be expressed as the solution of a global space-time quadratic minimization problem that is amenable to Galerkin time-space discretization schemes,…
We review an explicit approach to obtaining numerical solutions of the Schr\"odinger equation that is conceptionally straightforward and capable of significant accuracy and efficiency. The method and its efficacy are illustrated with…
We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential…
Evolutionarily stable strategy (ESS) is an important solution concept in game theory which has been applied frequently to biological models. Informally an ESS is a strategy that if followed by the population cannot be taken over by a…
The quantum search algorithm is a technique for searching N possibilities in only sqrt(N) steps. Although the algorithm itself is widely known, not so well known is the series of steps that first led to it, these are quite different from…
The Schr\"{o}dinger equation is solved exactly for some well known potentials. Solutions are obtained reducing the Schr\"{o}dinger equation into a second order differential equation by using an appropriate coordinate transformation. The…
This paper presents a new type of genetic algorithm for the set covering problem. It differs from previous evolutionary approaches first because it is an indirect algorithm, i.e. the actual solutions are found by an external decoder…
In this paper we present a unified picture concerning Lie-Trotter method for solving a large class of semilinear problems: nonlinear Schr\"odinger, Schr\"oginger--Poisson, Gross--Pitaevskii, etc. This picture includes more general schemes…
Based on the generation function of Laguerre polynomials, We proposed a new Laguerre polynomial expansion scheme in the calculation of evolution of time dependent Schr\"odinger equation. Theoretical analysis and numerical test show that the…
Genetic algorithms are modeled after the biological evolutionary processes that use natural selection to select the best species to survive. They are heuristics based and low cost to compute. Genetic algorithms use selection, crossover, and…
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…
We provide general product formulas for the solutions of non-autonomous abstract Cauchy problems. The main technical tool is the application of evolution semigroup methods, allowing the direct application of existing results on autonomous…
In this work, we show how a genetic algorithm (GA) can be used to find step-by-step solutions to introductory physics problems. Our perspective is that the underlying task for this is one of finding a sequence of equations that will lead to…
We introduce Genetic AI, a novel method for multi-objective optimization without external parameters or predefined weights. The method can be applied to all problems that can be formulated in matrix form and allows for a data-less training…
The balance of exploration versus exploitation (EvE) is a key issue on evolutionary computation. In this paper we will investigate how an adaptive controller aimed to perform Operator Selection can be used to dynamically manage the EvE…
For many linear and nonlinear systems that arise from the discretization of partial differential equations the construction of an efficient multigrid solver is a challenging task. Here we present a novel approach for the optimization of…
A nonperturbative procedure of solving the time-dependent Schr\"odinger equation, called the multi-projection approach or phase dynamics of quantum mechanics, is derived and illustrated. In addition to introducing a method with that…
We discuss a new optimization strategy, which considerably improves the effectivity of evolutionary algorithms applied to a certain class of optimization problems. The basic principle is to solve first a simpler related problem, which is…
The Schr\"odinger bridge problem (SBP) finds the most likely stochastic evolution between two probability distributions given a prior stochastic evolution. As well as applications in the natural sciences, problems of this kind have…