论具有玻色应用的特劳特和芝诺积公式的强界值

IF 5.1 2区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY Quantum Pub Date : 2024-07-25 DOI:10.22331/q-2024-07-25-1424
Tim Möbus
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引用次数: 0

摘要

特罗特积公式和量子芝诺效应都是利用实验可行的构件构建时间演化不可或缺的工具。在这项工作中,我们讨论了在巴拿赫空间的强算子拓扑学中可以证明定量边界的假设,并提供了自然玻色子的例子。特别是,我们假定存在一个连续嵌入的巴拿赫空间,它可以相对约束所涉及的生成器,并创建一个具有稳定限制的极限半群不变子空间。在双曲演化系统(随时间变化的半群)领域,对可容许子空间的稍强假设已得到广泛认可,本研究成果也将扩展到这一领域。通过假设访问连续嵌入巴拿赫空间的层次,可以证明铃木高阶边界。在玻色应用中,这些内嵌巴拿赫空间通过数算子自然产生,从而产生了一系列不同的例子,包括玻色纠错中使用的奥恩斯坦-乌伦贝克半群和多光子驱动耗散等著名实例。
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On Strong Bounds for Trotter and Zeno Product Formulas with Bosonic Applications
The Trotter product formula and the quantum Zeno effect are both indispensable tools for constructing time-evolutions using experimentally feasible building blocks. In this work, we discuss assumptions under which quantitative bounds can be proven in the strong operator topology on Banach spaces and provide natural bosonic examples. Specially, we assume the existence of a continuously embedded Banach space, which relatively bounds the involved generators and creates an invariant subspace of the limiting semigroup with a stable restriction. The slightly stronger assumption of admissible subspaces is well-recognized in the realm of hyperbolic evolution systems (time-dependent semigroups), to which the results are extended. By assuming access to a hierarchy of continuously embedded Banach spaces, Suzuki-higher-order bounds can be demonstrated. In bosonic applications, these embedded Banach spaces naturally arise through the number operator, leading to a diverse set of examples encompassing notable instances such as the Ornstein-Uhlenbeck semigroup and multi-photon driven dissipation used in bosonic error correction.
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来源期刊
Quantum
Quantum Physics and Astronomy-Physics and Astronomy (miscellaneous)
CiteScore
9.20
自引率
10.90%
发文量
241
审稿时长
16 weeks
期刊介绍: Quantum is an open-access peer-reviewed journal for quantum science and related fields. Quantum is non-profit and community-run: an effort by researchers and for researchers to make science more open and publishing more transparent and efficient.
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