相关论文: Polynomial scheme for time evolution of open and c…
In this study, a variety of methods are tested and compared for the numerical solution of the Schr\"odinger equation for few-body systems with explicitely time-dependent Hamiltonians, with the aim to find the optimal one. The configuration…
Polynomial-in-time dependent symmetries are analysed for polynomial-in-time dependent evolution equations. Graded Lie algebras, especially Virasoro algebras, are used to construct nonlinear variable-coefficient evolution equations, both in…
This second part deals with applications of a general method to describe the quantum time evolution determined by a Schroedinger equation with time-dependent Hamiltonian. A new aspect of our approach is that we find all solutions starting…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
A method of calculating probability values from a system of marginal constraints is presented. Previous systems for finding the probability of a single attribute have either made an independence assumption concerning the evidence or have…
It is well-known that time-dependent Schr\"{o}dinger equation can only be exactly solvable in very rare cases, even for two-level quantum systems. Therefore, finding exact quantum dynamics under time-dependent Hamiltonian is not only of…
This paper introduces a novel deep-learning-based approach for numerical simulation of a time-evolving Schr\"odinger equation inspired by stochastic mechanics and generative diffusion models. Unlike existing approaches, which exhibit…
A numerical scheme for solving the time-evolution of wave functions under the time dependent Kohn-Sham equation has been developed. Since the effective Hamiltonian depends on the wave functions, the wave functions and the effective…
We consider the cubic nonlinear Schr\"odinger equation on product manifolds $\mathbb{R}\times \mathbb{T}$. In this paper, we obtain polynomial bounds on the growth in time of high Sobolev norms of the solutions. The main ingredient of the…
We use the optimized trigonometric finite basis method to find energy eigenvalues and eigenfunctions of the time-independent Schrodinger equation with high accuracy. We apply this method to the quartic anharmonic oscillator and the harmonic…
We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schr\"{o}dinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms…
A global solution of the Schr\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is…
In this paper, a novel high-order, mass and energy-conserving scheme is proposed for the regularized logarithmic Schr\"{o}dinger equation(RLogSE). Based on the idea of the supplementary variable method (SVM), we firstly reformulate the…
New exactly solvable quantum models are obtained with the help of the supersymmetric extencion of the nonstationary Schr/"odinger equation.
In this paper, traveling wave solutions to the nonlinearly dispersive Schr\"odinger equation are given in the case of one-dimensional non-relativistic electron confined to a cylindrical quantum well. Investigations gave evidence to the…
We consider the functional Schrodinger equation for a self interacting scalar field in an expanding geometry. By performing a time dependent scale transformation on the argument of the field we derive a functional Schrodinger equation whose…
The theory of Chebyshev approximation has been extensively studied. In most cases, the optimality conditions are based on the notion of alternance or alternating sequence (that is, maximal deviation points with alternating deviation signs).…
Classical molecular dynamics simulation is performed mostly using the established velocity Verlet integrator or other symplectic propagation schemes. In this work, an alternative formulation of numerical propagators for classical molecular…
Quantum computers are known for their potential to achieve up-to-exponential speedup compared to classical computers for certain problems. To exploit the advantages of quantum computers, we propose quantum algorithms for linear stochastic…
We show that the method of factorizing the evolution operator to fourth order with purely positive coefficients, in conjunction with Suzuki's method of implementing time-ordering of operators, produces a new class of powerful algorithms for…