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理论物理通讯：英文版

Generating Generalized Bessel Equations by Virtue of Bose Operator Algebra and Entangled State Representations

Fan, Hong-Yi, Wang, Yong

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

在 Bose 操作员身份和纠缠的州的表示的帮助下并且基于我们的以前的工作[Phys。Lett。一 325 (2004 ) 188 ] 我们导出也让 Bessel 作为他们的答案工作的一些新概括 Besselequations。它为这些 intricatehigher 顺序意味着那微分方程，没有使用详述的力量系列扩大方法，我们能得到 Bessel 函数解决方案。

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Generating Generalized Bessel Equations by Virtue of Bose Operator Algebra and Entangled State Representations

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With the help of Bose operator identities and entangled state representation and based on our previous work [Phys. Lett. A 325 (2004) 188] we derive some new generalized Bessel equations which also have Bessel function as their solution. It means that for these intricate higher-order differential equations, we can get Bessel function solutions without using the expatiatory power-series expansion method.

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We study the fundamental properties of classical and quantum Markov processes generated by q-Bessel operators and their extension to the algebra of all bounded operators on the Hilbert space [Formula: see text]. In particular, we find a suitable generalized Gorini–Kossakowski–Sudarshan–Lindblad representation for the infinitesimal generator of q-Bessel operator and show that both the classical and quantum Markov processes are transient for α > 0 and recurrent for α = 0. We also show that they do not admit invariant states and, moreover that the support projection of any initial state instantaneously fills the full space.

Open Systems & Information Dynamics•Mar 1, 2020•7 citations
在 Bose 操作员身份和纠缠的州的表示的帮助下并且基于我们的以前的工作[Phys。Lett。一 325 (2004 ) 188 ] 我们导出也让 Bessel 作为他们的答案工作的一些新概括 Besselequations。它为这些 intricatehigher 顺序意味着那微分方程，没有使用详述的力量系列扩大方法，我们能得到 Bessel 函数解决方案。
We study the fundamental properties of classical and quantum Markov processes generated by q-Bessel operators and their extension to the algebra of all bounded operators on the Hilbert space [Formula: see text]. In particular, we find a suitable generalized Gorini–Kossakowski–Sudarshan–Lindblad representation for the infinitesimal generator of q-Bessel operator and show that both the classical and quantum Markov processes are transient for α > 0 and recurrent for α = 0. We also show that they do not admit invariant states and, moreover that the support projection of any initial state instantaneously fills the full space.