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Higher-order squeezing of both quadrature components in superposition of orthogonal even coherent state and vacuum state 正交偶相干态和真空态叠加时两个正交分量的高阶挤压
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-08-01 DOI: 10.1016/S0034-4877(24)00056-9
Pankaj Kumar, Rakesh Kumar
{"title":"Higher-order squeezing of both quadrature components in superposition of orthogonal even coherent state and vacuum state","authors":"Pankaj Kumar,&nbsp;Rakesh Kumar","doi":"10.1016/S0034-4877(24)00056-9","DOIUrl":"10.1016/S0034-4877(24)00056-9","url":null,"abstract":"<div><div>We study the Hong–Mandel higher-order squeezing of both quadrature components for an arbitrary 2<em>n</em><sup>th</sup>-order (<em>n</em> ≠1) considering the most general Hermitian operator, <em>X<sub>θ</sub> = X</em><sub>1</sub> cos <em>θ + iX</em><sub>2</sub> sin <em>θ</em>, in the superposed state, |<em>Ψ</em>〉 = <em><strong>K</strong></em> [|Ψ<sub>0</sub>) + <em>re</em><sup><em>i</em>ϕ</sup> |0〉] of the orthogonal even coherent state and vacuum state. Here | Ψ<sub>0</sub>〉 = <strong><em>K</em></strong>[|α, +〉 + |iα, +〉] is the orthogonal coherent state, |α, +〉 = <strong><em>K</em></strong>′[|α) + | – α〉] and |<em>i</em>α, +〉 = <strong><em>K</em></strong><em>″</em> [|<em>i</em>α, +〉 + | – <em>i</em>α, +〉] are even coherent states, operators <em>X</em><sub>1,2</sub> are defined by <em>X</em><sub>1</sub> + <em>iX</em><sub>2</sub> = <em>a, a</em> is the annihilation operator, α, <em>θ</em>, <em>r</em> and ϕ are arbitrary parameters and the only restriction on these is the normalization condition of the superposed state |<em>Ψ</em>〉. We find that maximum simultaneous 2<em>n</em><sup>th</sup>-order Hong–Mandel squeezing of both quadrature components <em>X<sub>θ</sub></em> and <em>X<sub>θ+π</sub></em>/2 exhibited by the orthogonal even coherent state enhances in its superposition with vacuum state. We conclude that the values of higher-order momenta in the superposed state become much closer to the best minimum values of the corresponding values of higher-order momenta explored numerically so far than that obtained in orthogonal even coherent state. Variations of 2<em>n</em><sup>th</sup>-order squeezing for <em>n</em> = 2,3 and 4, i.e. fourth, sixth and eighth-order squeezing with different parameters have also been discussed.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 1","pages":"Pages 73-82"},"PeriodicalIF":1.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New operator realization of angular momentum for description of electron's motion in uniform magnetic field 描述电子在匀强磁场中运动的角动量新算子实现方法
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-08-01 DOI: 10.1016/S0034-4877(24)00058-2
Cheng Da , Hony-Yi Fan
{"title":"New operator realization of angular momentum for description of electron's motion in uniform magnetic field","authors":"Cheng Da ,&nbsp;Hony-Yi Fan","doi":"10.1016/S0034-4877(24)00058-2","DOIUrl":"10.1016/S0034-4877(24)00058-2","url":null,"abstract":"<div><div>By introducing appropriate electron's coordinate eigenstate and momentum eigenstate we propose new realization of angular momentum operators for describing electron's motion in uniform magnetic field. The coordinate eigenstates make up a representation and embody quantum entanglement between magnetic field and electron. The eigenstate of angular momentum's lowering-ascending operator <strong><em>L</em><sub>±</sub></strong> are derived, the way we tackle this problem is to make an analogue between the transform\u0000<span><math><mrow><msup><mi>e</mi><mrow><mn>2</mn><mi>f</mi><msub><mi>L</mi><mi>z</mi></msub></mrow></msup><msub><mi>L</mi><mo>±</mo></msub><msup><mi>e</mi><mrow><mo>-</mo><mn>2</mn><mi>f</mi><msub><mi>L</mi><mi>z</mi></msub></mrow></msup></mrow></math></span> to the squeezing mechanism. All these discussions reveal that the quantum theory for charged particles' motion in magnetic field needs to be developed.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 1","pages":"Pages 105-115"},"PeriodicalIF":1.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A note on almost pseudo symmetric spacetimes with certain application to f(R), gravity 关于几乎伪对称时空的说明，以及对 f(R)、引力的某些应用
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-08-01 DOI: 10.1016/S0034-4877(24)00054-5
Uday Chand De, Krishnendu De
{"title":"A note on almost pseudo symmetric spacetimes with certain application to f(R), gravity","authors":"Uday Chand De,&nbsp;Krishnendu De","doi":"10.1016/S0034-4877(24)00054-5","DOIUrl":"10.1016/S0034-4877(24)00054-5","url":null,"abstract":"<div><div>This article deals with the characterization of an almost pseudo symmetric spacetime and we illustrate that a conformally flat almost pseudo symmetric spacetime with nonzero constant scalar curvature represents a perfect fluid spacetime. Also, it is established that the chosen spacetime represents a spacetime of quasi constant sectional curvature and generalized Robertson-Walker spacetime. Besides, we find under what condition the spacetime represents radiation era and dust matter fluid. Further it is shown that under certain restriction in an almost pseudo symmetric spacetime, if the Ricci tensor is Killing, then it represents a static spacetime and it is vacuum. Lastly, we study the impact of this spacetime under <em>f</em>(<em>R)</em> gravity scenario and deduce several energy conditions.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 1","pages":"Pages 35-45"},"PeriodicalIF":1.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Constructive Gibbs measures for the Ising model on the Cayley tree Cayley 树上伊辛模型的构造吉布斯度量
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-06-01 DOI: 10.1016/S0034-4877(24)00043-0
Muzaffar M. Rahmatullaev, Zulxumor A. Burxonova
{"title":"Constructive Gibbs measures for the Ising model on the Cayley tree","authors":"Muzaffar M. Rahmatullaev,&nbsp;Zulxumor A. Burxonova","doi":"10.1016/S0034-4877(24)00043-0","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00043-0","url":null,"abstract":"<div><p>In the present paper, we construct new Gibbs measures for the Ising model on the Cayley tree of order two. Moreover, we find the free energy corresponding to the found measures and compare it with the known ones.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 3","pages":"Pages 361-370"},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141479223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A combined derivative nonlinear SchrÖdinger soliton hierarchy 组合导数非线性薛定谔孤子层次结构
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-06-01 DOI: 10.1016/S0034-4877(24)00040-5
Wen-Xiu Ma
{"title":"A combined derivative nonlinear SchrÖdinger soliton hierarchy","authors":"Wen-Xiu Ma","doi":"10.1016/S0034-4877(24)00040-5","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00040-5","url":null,"abstract":"<div><p>This paper aims to study a Kaup-Newell type matrix eigenvalue problem with four potentials, based on a specific matrix Lie algebra, and construct an associated soliton hierarchy of combined derivative nonlinear Schrödinger (NLS) equations, within the zero curvature formulation. The Liouville integrability of the resulting soliton hierarchy is shown by exploring its hereditary recursion operator and bi-Hamiltonian formulation. The first nonlinear example provides an integrable model consisting of combined derivative NLS equations with two arbitrary constants.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 3","pages":"Pages 313-325"},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141483878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A note on differential equations of logistic type 关于逻辑型微分方程的说明
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-06-01 DOI: 10.1016/S0034-4877(24)00039-9
G. Dattoli, R. Garra
{"title":"A note on differential equations of logistic type","authors":"G. Dattoli,&nbsp;R. Garra","doi":"10.1016/S0034-4877(24)00039-9","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00039-9","url":null,"abstract":"<div><p>Logistic equations play a pivotal role in the study of any nonlinear evolution process exhibiting growth and saturation. The interest for the phenomenology they rule goes well beyond physical processes and covers many aspects of ecology, population growth, economy. . . According to such a broad range of applications, there are different forms of functions and distributions which are recognized as generalized logistics. Sometimes they are obtained by fitting procedures. Therefore, criteria might be needed to infer the associated nonlinear differential equations, useful to guess “hidden” evolution mechanisms. In this article we analyze different forms of logistic functions and use simple means to reconstruct the differential equation they satisfy. Our study includes also differential equations containing nonstandard forms of derivative operators, like those of the Laguerre type.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 3","pages":"Pages 301-312"},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141483877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nonabelianness of fundamental group of flat spacetime 平面时空基本群的非标注性
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-06-01 DOI: 10.1016/S0034-4877(24)00036-3
Gunjan Agrawal, Deepanshi
{"title":"Nonabelianness of fundamental group of flat spacetime","authors":"Gunjan Agrawal,&nbsp;Deepanshi","doi":"10.1016/S0034-4877(24)00036-3","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00036-3","url":null,"abstract":"<div><p>In the present paper, it has been obtained that the fundamental group of <em>n</em>-dimensional Minkowski space with the time topology contains uncountably many copies of the additive group of integers and is not abelian. The result has been first proved for <em>n</em> = 2. Thereafter, it is extended to <em>n</em> &gt; 2 by proving that loops nonhomotopic in <em>M</em><sup>2</sup> continue to be nonhomotopic in <em>M<sup>n</sup></em> using embedding of <em>M</em><sup>2</sup> in <em>M<sup>n</sup></em> as a retract through the projection map.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 3","pages":"Pages 261-270"},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141483875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Complete solvability of the time dependent self-dual equations Of Chern—Simons—Higgs model 时间相关自偶方程的完全可解性 Of Chern-Simons-Higgs model
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-06-01 DOI: 10.1016/S0034-4877(24)00042-9
Hyungjin Huh
{"title":"Complete solvability of the time dependent self-dual equations Of Chern—Simons—Higgs model","authors":"Hyungjin Huh","doi":"10.1016/S0034-4877(24)00042-9","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00042-9","url":null,"abstract":"<div><p>We find an explicit solution formula of the time dependent self-dual equations of Chern—Simons—Higgs model. The solution is expressed completely in terms of initial data.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 3","pages":"Pages 353-360"},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141487044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On nonintegrability of three-dimensional Ising model 论三维伊辛模型的不可控性
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-06-01 DOI: 10.1016/S0034-4877(24)00037-5
Wojciech Niedziółka, Jacek Wojtkiewicz
{"title":"On nonintegrability of three-dimensional Ising model","authors":"Wojciech Niedziółka,&nbsp;Jacek Wojtkiewicz","doi":"10.1016/S0034-4877(24)00037-5","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00037-5","url":null,"abstract":"<div><p>It is well known that the partition function of two-dimensional Ising model can be expressed as a Grassmann integral over the action bilinear in Grassmann variables. The key aspect of the proof of this equivalence is to show that all polygons, appearing in Grassmann integration, enter with fixed sign. For three-dimensional model, the partition function can also be expressed by Grassmann integral. However, the action resulting from low-temperature (L-T) expansion contains quartic terms, which do not allow explicit computation of the integral. We wanted to check — apparently not explored — the possibility that using the high-temperature (H-T) expansion would result in action with only bilinear terms (in two dimensions, L-T and H-T expansions are equivalent, but in three dimensions, they differ from each other). It turned out, however, that polygons obtained by Grassmann integration are not of fixed sign for any ordering of Grassmann variables on sites. This way, it is not possible to express the partition function of three-dimensional Ising model as a Grassmann integral over bilinear action.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 3","pages":"Pages 271-285"},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141487045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Conservation laws and nonexistence of local Hamiltonian structures for generalized Infeld—Rowlands equation 广义因费尔德-罗兰兹方程的守恒定律和局部哈密顿结构的不存在性
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-06-01 DOI: 10.1016/S0034-4877(24)00038-7
Jakub Vašíček
{"title":"Conservation laws and nonexistence of local Hamiltonian structures for generalized Infeld—Rowlands equation","authors":"Jakub Vašíček","doi":"10.1016/S0034-4877(24)00038-7","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00038-7","url":null,"abstract":"<div><p>For a certain natural generalization of the Infeld—Rowlands equation we prove nonexistence of nontrivial local Hamiltonian structures and nontrivial local symplectic structures of any order, as well as of nontrivial local Noether and nontrivial local inverse Noether operators of any order, and exhaustively characterize all cases when the equation in question admits nontrivial local conservation laws of any order; the method of establishing the above nonexistence results can be readily applied to many other PDEs.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 3","pages":"Pages 287-300"},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141483876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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