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Investigation on the reflection and transmission properties of complex absorbing potentials
Uwe V. Riss,Hans-Dieter Meyer +1 more
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In this paper, the reflection and transmission properties of different complex absorbing potentials (CAPs) are studied using WKB and scaling procedures which make the results transferable to any mass and kinetic energy.Abstract:
The reflection and transmission properties of different complex absorbing potentials (CAPs) are studied using WKB and scaling procedures which make the results transferable to any mass and kinetic energy. Explicit formulas are obtained which describe the reflection and transmission properties of monomial CAPs −iηxn with high accuracy. These properties are now well understood. The approximate results are compared to exact analytical results available for quadratic CAPs, and to numerical results obtained by wave packet propagation followed by an energy resolved analysis. The approximate, but accurate, description of the action of the CAP is finally used to determine optimal CAP parameters. CAP length, strength, and order can now be chosen in such a way that the sum of reflection and transmission is minimized. Optimal parameters are compiled for different energies and energy intervals.read more
Citations
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The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets
TL;DR: In this article, a review of the multiconfiguration time-dependent Hartree (MCTDH) method for propagating wavepackets is given, and the formal derivation, numerical implementation, and performance of the method are detailed.
Journal ArticleDOI
Complex absorbing potentials
TL;DR: In this article, the authors present a formal theory of scattering for complex potentials in one dimension, as well as a detailed account of the functional forms and construction methods proposed, and demonstrate that part of the acquired knowledge may be transferred to physical absorbing potentials, i.e., effective interactions that can be tailored physically to accomplish e.g. an improved atomic detection by fluorescence.
Journal ArticleDOI
Non-Hermitian electronic theory and applications to clusters
Robin Santra,Lorenz S. Cederbaum +1 more
TL;DR: In this paper, an inner-valence ionized cluster, which releases its excess energy by emitting an electron, is characterized by an efficient energy transfer between monomers in the cluster.
Journal ArticleDOI
Product representation of potential energy surfaces. II
A. Jäckle,Hans-Dieter Meyer +1 more
TL;DR: An efficient method was recently introduced to represent multidimensional potential energy surfaces as a linear combination of products of one-dimensional functions, so-called natural potentials, and weight functions were shown to be easily implemented in the product representation scheme.
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Derivation and reflection properties of a transmission-free absorbing potential
TL;DR: In this article, the authors derived a first order differential equation for a negative imaginary absorbing potential, −ie(r), which switches on as rapidly as possible with increasing r without causing too much reflection.
References
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Journal ArticleDOI
Handbook of Mathematical Functions
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Time-dependent quantum-mechanical methods for molecular dynamics
TL;DR: In this article, a general framework of time-dependent quantum-mechanical methods for molecular dynamics calculations is described, including the Fourier method, which is able to represent a system in phase space with the efficiency of one sampling point per unit volume in phasespace h, so that, with the proper choice of the initial wave function, exponential convergence is obtained in relation to the number of sampling points.
Journal ArticleDOI
Time‐dependent approach to semiclassical dynamics
TL;DR: In this paper, a wave packet is decomposed into time-dependent wave packets, which spread minimally and which execute classical or nearly classical trajectories, assuming a Gaussian form for the wave packets and equations of motion for the Gaussians.
Journal ArticleDOI
A fourier method solution for the time dependent Schrödinger equation as a tool in molecular dynamics
Dan Kosloff,Ronnie Kosloff +1 more
TL;DR: In this paper, a new method is presented for the solution of the time dependent SchrBdinger equation in its application to physical and chemical molecular phenomena, which is based on discretizing space and time on a grid, and using the Fourier method to produce both spatial derivatives, and second order differencing for time derivatives.
BookDOI
Dynamics of Molecular Collisions
TL;DR: In this paper, the potential energy surfaces and their effect on collision processes are discussed. But the authors focus on the nonadiabatic processes in collision theory and not on the classical trajectories of trajectories.
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