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Оптика и спектроскопия

Cosine-type Absorbing Optical Potential for the Modeling of Quantum Dynamics with the Fourier Grid and Optimizer Packages

V. B. Sovkov, Wu J., Ma J.

Published Jan 1, 2022• 1 citation
Publisher

Abstract

In order to model the spectroscopic and scattering properties of a quantum system, we propose and explore a new absorbing complex-type optical potential based on a combination of cosine functions. This function provides a high degree of smoothness to joint with a physical real-type potential. The capabilities of this function are investigated in terms of its effect on otherwise freely evolving quantum dynamics. We use our open-source programs to implement the Fourier Grid method with the Optimizer package (in Matlab), freely available at https://sourceforge.net/projects/optimizer-sovkov/ https://sourceforge.net/projects/optimizer-sovkov/. Keywords: quantum dynamics; damping boundary conditions; optical potential; Fourier Grid method; spectroscopy of ultracold ensembles.

DOI
10.21883/eos.2022.05.54434.7-22

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In order to model the spectroscopic and scattering properties of a quantum system, we propose and explore a new absorbing complex-type optical potential based on a combination of cosine functions. This function provides a high degree of smoothness to joint with a physical real-type potential. The capabilities of this function are investigated in terms of its effect on otherwise freely evolving quantum dynamics. We use our open-source programs to implement the Fourier Grid method with the Optimizer package (in Matlab), freely available at https://sourceforge.net/projects/optimizer-sovkov/ https://sourceforge.net/projects/optimizer-sovkov/. Keywords: quantum dynamics; damping boundary conditions; optical potential; Fourier Grid method; spectroscopy of ultracold ensembles.
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In order to model the spectroscopic and scattering properties of a quantum system, we propose and explore a new absorbing complex-type optical potential based on a combination of cosine functions. This function provides a high degree of smoothness to joint with a physical real-type potential. The capabilities of this function are investigated in terms of its effect on otherwise freely evolving quantum dynamics. We use our open-source programs to implement the Fourier Grid method with the Optimizer package (in Matlab), freely available at https://sourceforge.net/projects/optimizer-sovkov/
This paper presents a novel simulation methodology predicated on quantum principles to enhance the prediction of wavefunction collapse during complex quantum processes. The core claim is to develop a technique that utilizes quantum fluctuations to estimate the state of the system during collapse, thereby offering a more accurate and faster collapse prediction compared to traditional methods. We detail the design of the simulation framework, focusing on the interplay between quantum mechanics, probabilistic modeling, and computational optimization. The research explores the application of quantum-enhanced wave function collapse simulations to analyze systems exhibiting complex dynamics, offering a potential pathway to accelerate the analysis of these systems. This work contributes to the development of advanced computational tools for quantum system research.
The aim of this work is to provide a new conceptually and practically useful method of obtaining the time development and particularly the decay of quantum states initially localized on a domain with dynamically open boundaries. A projection operator derivation and a Markoffian approximation is used to obtain an effective Hamiltonian capable of describing the dynamics on the open domain. The basic algebra is implemented for one dimensional systems and a series of test calculations presented which serve to verify the validity of the approximations and illustrate the accuracy of the new procedure. The absorbing boundary method developed here bears some resemblance to the optical potential methods and the Feshbach projection scheme used in scattering theory and can be applied to dissociation and ionization processes as well as to scattering processes.
MOLSCAT is a general-purpose package for performing non-reactive quantum scattering calculations for atomic and molecular collisions using coupled-channel methods. Simple atom-molecule and molecule-molecule collision types are coded internally and additional ones may be handled with plug-in routines. Plug-in routines may include external magnetic, electric or photon fields (and combinations of them). Simple interaction potentials are coded internally and more complicated ones may be handled with plug-in routines. BOUND is a general-purpose package for performing calculations of bound-state energies in weakly bound atomic and molecular systems using coupled-channel methods. It solves the same sets of coupled equations as MOLSCAT, and can use the same plug-in routines if desired, but with different boundary conditions. FIELD is a development of BOUND that locates external fields at which a bound state exists with a specified energy. One important use is to locate the positions of magnetically tunable Feshbach resonance positions in ultracold collisions. The program source code is available from https://github.com/molscat/molscat