aqora

Scattering Phase Correction for Semiclassical Quantization Rules in Multi-Dimensional Quantum Systems

Huang Wen-Min, Chung‐Yu Mou, Cheng-Hung Chang

While the scattering phase for several one-dimensional potentials can be exactly derived, less is known in multi-dimensional quantum systems. This work provides a method to extend the one-dimensional phase knowledge to multi-dimensional quantization rules. The extension is illustrated in the example of Bogomolny's transfer operator method applied in two quantum wells bounded by step potentials of different heights. This generalized semiclassical method accurately determines the energy spectrum of the systems, which indicates the substantial role of the proposed phase correction. Theoretically, the result can be extended to other semiclassical methods, such as Gutzwiller trace formula, dynamical zeta functions, and semiclassical Landauer–Büttiker formula. In practice, this recipe enhances the applicability of semiclassical methods to multi-dimensional quantum systems bounded by general soft potentials.While the scattering phase for several one-dimensional potentials can be exactly derived, less is known in multi-dimensional quantum systems. This work provides a method to extend the one-dimensional phase knowledge to multi-dimensional quantization rules. The extension is illustrated in the example of Bogomolny's transfer operator method applied in two quantum wells bounded by step potentials of different heights. This generalized semiclassical method accurately determines the energy spectrum of the systems, which indicates the substantial role of the proposed phase correction. Theoretically, the result can be extended to other semiclassical methods, such as Gutzwiller trace formula, dynamical zeta functions, and semiclassical Landauer–Büttiker formula. In practice, this recipe enhances the applicability of semiclassical methods to multi-dimensional quantum systems bounded by general soft potentials.

Communications in Theoretical PhysicsFeb 1, 20101 citation

A scattering theory approach to semiclassical quantization

E. Doron, Uzy Smilansky

Jan 1, 19951 citation

Control problems in quantum systems

Rebing, Wu, Jing +7 more

过去的十年或二在量控制技术的理论和实践见证巨大的进步。衔接从基本粒子物理到纳米技术的不同科学学科，量控制的目标是开发有效、有效的工具因为普通分析和设计，而是更多将重要地为未来铺平道路工艺的应用程序。这篇文章简短从当模特儿，分析和图案的观点考察基本的量控制理论，以及考虑未来研究方向。

中国科学通报：英文版Jan 1, 20120 citations

Semiclassical methods for multi-dimensional systems bounded by finite potentials

Wenmin Huang, Cheng-Hung Chang, Chung‐Yu Mou

This work studies the semiclassical methods in multi-dimensional quantum systems bounded by finite potentials. By replacing the Maslov index by the scattering phase, the modified transfer operator method gives rather accurate corrections to the quantum energies of the circular and square potential pots of finite heights. The result justifies the proposed scattering phase correction which paves the way for correcting other semiclassical methods based on Green functions, like Gutzwiller trace formula, dynamical zeta functions, and Landauer-Büttiker formula.This work studies the semiclassical methods in multi-dimensional quantum systems bounded by finite potentials. By replacing the Maslov index by the scattering phase, the modified transfer operator method gives rather accurate corrections to the quantum energies of the circular and square potential pots of finite heights. The result justifies the proposed scattering phase correction which paves the way for correcting other semiclassical methods based on Green functions, like Gutzwiller trace formula, dynamical zeta functions, and Landauer-Büttiker formula.

arXiv:cond-mat/0412326Dec 13, 20040 citations

Signatures of classical periodic orbits on a smooth quantum system

Daniel Provost

Gutzwiller's trace formula and Bogomolny's formula are applied to a nospecific, nonscalable Hamiltonian system, a two-dimensional anharmonic oscillator. These semiclassical theories reproduce well the exact quantal results over a large spatial and energy range.

arXiv:chao-dyn/9505002Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsJun 1, 19953 citations

Semi-classical correction for quantum-mechanical scattering

Srihari Keshavamurthy, William Hughes Miller

Chemical Physics LettersFeb 1, 199494 citations

Scattering Phase Correction for Semiclassical Quantization Rules in Multi-Dimensional Quantum Systems

Abstract

Related papers

Scattering Phase Correction for Semiclassical Quantization Rules in Multi-Dimensional Quantum Systems

Abstract

Related papers