双井电位中格罗斯-皮塔耶夫斯基方程的准确性

IF 1.1 3区 物理与天体物理 Q4 PHYSICS, APPLIED Journal of Low Temperature Physics Pub Date : 2024-07-29 DOI:10.1007/s10909-024-03192-0
Asaad R. Sakhel, Robert J. Ragan, William J. Mullin
{"title":"双井电位中格罗斯-皮塔耶夫斯基方程的准确性","authors":"Asaad R. Sakhel, Robert J. Ragan, William J. Mullin","doi":"10.1007/s10909-024-03192-0","DOIUrl":null,"url":null,"abstract":"<p>The Gross–Pitaevskii equation (GPE) in a double-well potential produces solutions that break the symmetry of the underlying non-interacting Hamiltonian, i.e., asymmetric solutions. The GPE is derived from the more general second-quantized Fock Schr<span>\\(\\ddot{\\textrm{o}}\\)</span>dinger equation (FSE). We investigate whether such solutions appear in the more general case or are artifacts of the GPE. We use two-mode analyses for a variational treatment of the GPE and to treat the Fock equation. An exact diagonalization of the FSE in dual condensates yields degenerate ground states that are very accurately fitted by phase-state representations of the degenerate asymmetric states found in the GPE. The superposition of degenerate asymmetrical states forms a cat state. An alternative form of cat state results from a change of the two-mode basis set.</p>","PeriodicalId":641,"journal":{"name":"Journal of Low Temperature Physics","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Accuracy of the Gross–Pitaevskii Equation in a Double-Well Potential\",\"authors\":\"Asaad R. Sakhel, Robert J. Ragan, William J. Mullin\",\"doi\":\"10.1007/s10909-024-03192-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The Gross–Pitaevskii equation (GPE) in a double-well potential produces solutions that break the symmetry of the underlying non-interacting Hamiltonian, i.e., asymmetric solutions. The GPE is derived from the more general second-quantized Fock Schr<span>\\\\(\\\\ddot{\\\\textrm{o}}\\\\)</span>dinger equation (FSE). We investigate whether such solutions appear in the more general case or are artifacts of the GPE. We use two-mode analyses for a variational treatment of the GPE and to treat the Fock equation. An exact diagonalization of the FSE in dual condensates yields degenerate ground states that are very accurately fitted by phase-state representations of the degenerate asymmetric states found in the GPE. The superposition of degenerate asymmetrical states forms a cat state. An alternative form of cat state results from a change of the two-mode basis set.</p>\",\"PeriodicalId\":641,\"journal\":{\"name\":\"Journal of Low Temperature Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2024-07-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Low Temperature Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1007/s10909-024-03192-0\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"PHYSICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Low Temperature Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s10909-024-03192-0","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, APPLIED","Score":null,"Total":0}
引用次数: 0

摘要

双阱势中的格罗斯-皮塔耶夫斯基方程(GPE)会产生打破底层非相互作用哈密顿对称性的解,即非对称解。GPE 是由更一般的二次量化福克-施林格方程(FSE)衍生而来的。我们研究了这种解是否出现在更一般的情况下,或者是 GPE 的伪命题。我们使用双模分析法对 GPE 进行变分处理,并对 Fock 方程进行处理。在对偶凝聚态中对 FSE 进行精确的对角化,可以得到退化的基态,这些基态与 GPE 中发现的退化非对称态的相态表示非常精确地拟合。退化不对称态的叠加形成了猫态。猫态的另一种形式产生于双模基集的改变。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

摘要图片

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Accuracy of the Gross–Pitaevskii Equation in a Double-Well Potential

The Gross–Pitaevskii equation (GPE) in a double-well potential produces solutions that break the symmetry of the underlying non-interacting Hamiltonian, i.e., asymmetric solutions. The GPE is derived from the more general second-quantized Fock Schr\(\ddot{\textrm{o}}\)dinger equation (FSE). We investigate whether such solutions appear in the more general case or are artifacts of the GPE. We use two-mode analyses for a variational treatment of the GPE and to treat the Fock equation. An exact diagonalization of the FSE in dual condensates yields degenerate ground states that are very accurately fitted by phase-state representations of the degenerate asymmetric states found in the GPE. The superposition of degenerate asymmetrical states forms a cat state. An alternative form of cat state results from a change of the two-mode basis set.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Journal of Low Temperature Physics
Journal of Low Temperature Physics 物理-物理:凝聚态物理
CiteScore
3.30
自引率
25.00%
发文量
245
审稿时长
1 months
期刊介绍: The Journal of Low Temperature Physics publishes original papers and review articles on all areas of low temperature physics and cryogenics, including theoretical and experimental contributions. Subject areas include: Quantum solids, liquids and gases; Superfluidity; Superconductivity; Condensed matter physics; Experimental techniques; The Journal encourages the submission of Rapid Communications and Special Issues.
期刊最新文献
Development of Kinetic Inductance Detector on ZrO $$_2$$ Substrate for Double-Beta Decay Search Cryogenic Microwave Performance of Silicon Nitride and Amorphous Silicon Deposited Using Low-Temperature ICPCVD Development of 1.5 THz Photon Detectors for Terahertz Intensity Interferometry Advances in the Goertzel Filter Bank Channelizer for Cryogenic Sensors Readout COSINUS:TES-instrumented NaI Crystals for Direct Dark Matter Search
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1