Communications in Theoretical Physics最新文献

{"title":"Compensation temperatures and hysteresis behaviors of a graphene-like trilayer","authors":"Ying An, Ji Liang, Wei Wang, Mei-mei Du and Feng-ge Zhang","doi":"10.1088/1572-9494/ad3220","DOIUrl":"https://doi.org/10.1088/1572-9494/ad3220","url":null,"abstract":"This work focuses on the ground-state phase diagram, the compensation temperatures and the critical behaviors of a ferrimagnetic graphene-like trilayer induced by crystal fields and exchange couplings. The simulation results show that a negative decrease in crystal field or an increase in exchange coupling can increase the critical temperature. More importantly, an M curve with double compensation temperatures can be observed, which is not predicted by the theory. This remarkable compensation phenomenon has potential application value in the field of magnetic recording.","PeriodicalId":10641,"journal":{"name":"Communications in Theoretical Physics","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}

{"title":"Single-particle spectroscopies of p-wave and d-wave interacting Bose gases in normal phase","authors":"Zeqing Wang, Ran Qi","doi":"10.1088/1572-9494/ad3543","DOIUrl":"https://doi.org/10.1088/1572-9494/ad3543","url":null,"abstract":"Motivated by experiments with interacting quantum gases across high partial wave resonance, we investigate the thermodynamic properties and single-particle spectra of Bose gases in normal phase for different interaction strengths for both p- and d-wave interactions. The equation of state, contact density, momentum distributions and self-energies of single-particle Green’s functions are obtained in the spirit of ladder diagram approximations. The radio-frequency (RF) spectrum, as an important experimental approach for detecting Feshbach molecules or the interaction effect, is calculated at different temperatures. A reversed temperature dependence on the Bose–Einstein condensation side and Bardeen–Cooper–Schrieffer side is identified for both p- and d-wave interactions. An estimate for the signal of RF spectra under typical experimental conditions is also provided.","PeriodicalId":10641,"journal":{"name":"Communications in Theoretical Physics","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140608856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}

{"title":"Learning topological defects formation with neural networks in a quantum phase transition","authors":"Han-Qing Shi, Hai-Qing Zhang","doi":"10.1088/1572-9494/ad3227","DOIUrl":"https://doi.org/10.1088/1572-9494/ad3227","url":null,"abstract":"Neural networks possess formidable representational power, rendering them invaluable in solving complex quantum many-body systems. While they excel at analyzing static solutions, nonequilibrium processes, including critical dynamics during a quantum phase transition, pose a greater challenge for neural networks. To address this, we utilize neural networks and machine learning algorithms to investigate time evolutions, universal statistics, and correlations of topological defects in a one-dimensional transverse-field quantum Ising model. Specifically, our analysis involves computing the energy of the system during a quantum phase transition following a linear quench of the transverse magnetic field strength. The excitation energies satisfy a power-law relation to the quench rate, indicating a proportional relationship between the excitation energy and the kink numbers. Moreover, we establish a universal power-law relationship between the first three cumulants of the kink numbers and the quench rate, indicating a binomial distribution of the kinks. Finally, the normalized kink-kink correlations are also investigated and it is found that the numerical values are consistent with the analytic formula.","PeriodicalId":10641,"journal":{"name":"Communications in Theoretical Physics","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140608852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}

{"title":"Nonclassical correlations in two-dimensional graphene lattices","authors":"Hao Wang","doi":"10.1088/1572-9494/ad2d51","DOIUrl":"https://doi.org/10.1088/1572-9494/ad2d51","url":null,"abstract":"We investigate nonclassical correlations via negativity, local quantum uncertainty (LQU) and local quantum Fisher information (LQFI) for two-dimensional graphene lattices. The explicitly analytical expressions for negativity, LQU and LQFI are given. The close forms of LQU and LQFI confirm the inequality between the quantum Fisher information and skew information, where the LQFI is always greater than or equal to the LQU, and both show very similar behavior with different amplitudes. Moreover, the effects of the different system parameters on the quantified quantum correlation are analyzed. The LQFI reveals more nonclassical correlations than LQU in a two-dimensional graphene lattice system.","PeriodicalId":10641,"journal":{"name":"Communications in Theoretical Physics","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140608857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}

{"title":"Doped holographic superconductors in the Gubser–Rocha model","authors":"Ziyi Zhao, Wenhe Cai, Shuta Ishigaki","doi":"10.1088/1572-9494/ad30f5","DOIUrl":"https://doi.org/10.1088/1572-9494/ad30f5","url":null,"abstract":"We construct a doped holographic superconductor in the Gubser–Rocha model, and realize a superconducting dome in the middle of the temperature-doping phase diagram. It is worth noting that unlike in previous research, the profile of our dome shrinks inward near to zero temperature. From the numerical observation for the coupling dependence of the phase diagram, we find that the coupling between the two gauge fields plays a crucial role in the formation of the dome. We also analytically calculate the DC conductivity of the normal phase of the system in the momentum dissipation and obtain resistivity which is proportional to the temperature. The AC conductivity is calculated numerically.","PeriodicalId":10641,"journal":{"name":"Communications in Theoretical Physics","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140608854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}

{"title":"Bethe ansatz solutions of the 1D extended Hubbard-model","authors":"Haiyang Hou, Pei Sun, Yi Qiao, Xiaotian Xu, Xin Zhang, Tao Yang","doi":"10.1088/1572-9494/ad2c77","DOIUrl":"https://doi.org/10.1088/1572-9494/ad2c77","url":null,"abstract":"We construct an integrable 1D extended Hubbard model within the framework of the quantum inverse scattering method. With the help of the nested algebraic Bethe ansatz method, the eigenvalue Hamiltonian problem is solved by a set of Bethe ansatz equations, whose solutions are supposed to give the correct energy spectrum.","PeriodicalId":10641,"journal":{"name":"Communications in Theoretical Physics","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140608853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}

{"title":"Study of scalar particles through the Klein–Gordon equation under rainbow gravity effects in Bonnor–Melvin-Lambda space-time","authors":"Faizuddin Ahmed, Abdelmalek Bouzenada","doi":"10.1088/1572-9494/ad2e88","DOIUrl":"https://doi.org/10.1088/1572-9494/ad2e88","url":null,"abstract":"In our investigation, we explore the quantum dynamics of charge-free scalar particles through the Klein–Gordon equation within the framework of rainbow gravity, considering the Bonnor–Melvin-Lambda (BML) space-time background. The BML solution is characterized by the magnetic field strength along the axis of the symmetry direction which is related to the cosmological constant Λ and the topological parameter <italic toggle=\"yes\">α</italic> of the geometry. The behavior of charge-free scalar particles described by the Klein–Gordon equation is investigated, utilizing two sets of rainbow functions: (i) <inline-formula>\u0000<tex-math>\u0000<?CDATA $f(chi )=tfrac{({{rm{e}}}^{beta ,chi }-1)}{beta ,chi }$?>\u0000</tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mi>f</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle=\"false\"><mml:mfrac><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"normal\">e</mml:mi></mml:mrow><mml:mrow><mml:mi>β</mml:mi><mml:mspace width=\"0.25em\"></mml:mspace><mml:mi>χ</mml:mi></mml:mrow></mml:msup><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mi>β</mml:mi><mml:mspace width=\"0.25em\"></mml:mspace><mml:mi>χ</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:math>\u0000<inline-graphic xlink:href=\"ctpad2e88ieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>, <italic toggle=\"yes\">h</italic>(<italic toggle=\"yes\">χ</italic>) = 1 and (ii) <italic toggle=\"yes\">f</italic>(<italic toggle=\"yes\">χ</italic>) = 1, <inline-formula>\u0000<tex-math>\u0000<?CDATA $h(chi )=1+tfrac{beta ,chi }{2}$?>\u0000</tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mi>h</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mstyle displaystyle=\"false\"><mml:mfrac><mml:mrow><mml:mi>β</mml:mi><mml:mspace width=\"0.25em\"></mml:mspace><mml:mi>χ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac></mml:mstyle></mml:math>\u0000<inline-graphic xlink:href=\"ctpad2e88ieqn2.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>. Here <inline-formula>\u0000<tex-math>\u0000<?CDATA $0lt left(chi =tfrac{| E| }{{E}_{p}}right)leqslant 1$?>\u0000</tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mn>0</mml:mn><mml:mo>&lt;</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>χ</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle=\"false\"><mml:mfrac><mml:mrow><mml:mo stretchy=\"false\">∣</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy=\"false\">∣</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mfenced><mml:mo>≤</mml:mo><mml:mn>1</mml:mn></mml:math>\u0000<inline-graphic xlink:href=\"ctpad2e88ieqn3.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> with <italic toggle=\"yes\">E</italic> representing the particle’s energy, <ital","PeriodicalId":10641,"journal":{"name":"Communications in Theoretical Physics","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140617596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}

{"title":"Dissociation cross sections of ψ(3770), ψ(4040), ψ(4160), and ψ(4415) mesons with nucleons","authors":"Ruo-Qing Ding, Xiao-Ming Xu, H J Weber","doi":"10.1088/1572-9494/ad2ce1","DOIUrl":"https://doi.org/10.1088/1572-9494/ad2ce1","url":null,"abstract":"We study the dissociation of <italic toggle=\"yes\">ψ</italic>(3770), <italic toggle=\"yes\">ψ</italic>(4040), <italic toggle=\"yes\">ψ</italic>(4160), and <italic toggle=\"yes\">ψ</italic>(4415) mesons in collision with nucleons, which takes place in high-energy proton-nucleus collisions. The quark interchange between a nucleon and a <inline-formula>\u0000<tex-math>\u0000<?CDATA $cbar{c}$?>\u0000</tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mi>c</mml:mi><mml:mover accent=\"true\"><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mo>¯</mml:mo></mml:mrow></mml:mover></mml:math>\u0000<inline-graphic xlink:href=\"ctpad2ce1ieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> meson leads to the dissociation of the <inline-formula>\u0000<tex-math>\u0000<?CDATA $cbar{c}$?>\u0000</tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mi>c</mml:mi><mml:mover accent=\"true\"><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mo>¯</mml:mo></mml:mrow></mml:mover></mml:math>\u0000<inline-graphic xlink:href=\"ctpad2ce1ieqn2.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> meson. We consider the reactions: <inline-formula>\u0000<tex-math>\u0000<?CDATA ${pR}to {{rm{Lambda }}}_{c}^{+}{bar{D}}^{0}$?>\u0000</tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mi mathvariant=\"italic\">pR</mml:mi><mml:mo>→</mml:mo><mml:msubsup><mml:mrow><mml:mi mathvariant=\"normal\">Λ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msubsup><mml:msup><mml:mrow><mml:mover accent=\"true\"><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo>¯</mml:mo></mml:mrow></mml:mover></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:math>\u0000<inline-graphic xlink:href=\"ctpad2ce1ieqn3.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>, <inline-formula>\u0000<tex-math>\u0000<?CDATA ${pR}to {{rm{Lambda }}}_{c}^{+}{bar{D}}^{* 0}$?>\u0000</tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mi mathvariant=\"italic\">pR</mml:mi><mml:mo>→</mml:mo><mml:msubsup><mml:mrow><mml:mi mathvariant=\"normal\">Λ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msubsup><mml:msup><mml:mrow><mml:mover accent=\"true\"><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo>¯</mml:mo></mml:mrow></mml:mover></mml:mrow><mml:mrow><mml:mo>*</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:math>\u0000<inline-graphic xlink:href=\"ctpad2ce1ieqn4.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>, <inline-formula>\u0000<tex-math>\u0000<?CDATA ${pR}to {{rm{Sigma }}}_{c}^{++}{D}^{-}$?>\u0000</tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mi mathvariant=\"italic\">pR</mml:mi><mml:mo>→</mml:mo><mml:msubsup><mml:mrow><mml:mi mathvariant=\"normal\">Σ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mo>++</mml:mo></mml:mrow></mml:msubsup><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:math>\u0000<inline-graphic xlink:href=\"ctpad2ce1ieqn5.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>, <inline-formula>\u0000<tex-math>\u0000","PeriodicalId":10641,"journal":{"name":"Communications in Theoretical Physics","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140569962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}

{"title":"Rogue waves for the (2+1)-dimensional Myrzakulov–Lakshmanan-IV equation on a periodic background","authors":"Xiao-Hui Wang, Zhaqilao","doi":"10.1088/1572-9494/ad2c78","DOIUrl":"https://doi.org/10.1088/1572-9494/ad2c78","url":null,"abstract":"In this paper, the rogue wave solutions of the (2+1)-dimensional Myrzakulov–Lakshmanan (ML)-IV equation, which is described by five component nonlinear evolution equations, are studied on a periodic background. By using the Jacobian elliptic function expansion method, the Darboux transformation (DT) method and the nonlinearization of the Lax pair, two kinds of rogue wave solutions which are expressed by Jacobian elliptic functions dn and cn, are obtained. The relationship between these five kinds of potential is summarized systematically. Firstly, the periodic rogue wave solution of one potential is obtained, and then the periodic rogue wave solutions of the other four potentials are obtained directly. The solutions we find present the dynamic phenomena of higher-order nonlinear wave equations.","PeriodicalId":10641,"journal":{"name":"Communications in Theoretical Physics","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140594041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}

{"title":"Planar matrices and arrays of Feynman diagrams: poles for higher k","authors":"Alfredo Guevara, Yong Zhang","doi":"10.1088/1572-9494/ad1095","DOIUrl":"https://doi.org/10.1088/1572-9494/ad1095","url":null,"abstract":"Planar arrays of tree diagrams were introduced as a generalization of Feynman diagrams that enable the computation of biadjoint amplitudes <inline-formula>\u0000<tex-math>\u0000<?CDATA ${m}_{n}^{(k)}$?>\u0000</tex-math>\u0000<mml:math overflow=\"scroll\"><mml:msubsup><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:msubsup></mml:math>\u0000<inline-graphic xlink:href=\"ctpad1095ieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> for <italic toggle=\"yes\">k</italic> &gt; 2. In this follow-up work, we investigate the poles of <inline-formula>\u0000<tex-math>\u0000<?CDATA ${m}_{n}^{(k)}$?>\u0000</tex-math>\u0000<mml:math overflow=\"scroll\"><mml:msubsup><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:msubsup></mml:math>\u0000<inline-graphic xlink:href=\"ctpad1095ieqn2.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> from the perspective of such arrays. For general <italic toggle=\"yes\">k</italic>, we characterize the underlying polytope as a Flag Complex and propose a computation of the amplitude-based solely on the knowledge of the poles, whose number is drastically less than the number of the full arrays. As an example, we first provide all the poles for the cases (<italic toggle=\"yes\">k</italic>, <italic toggle=\"yes\">n</italic>) = (3, 7), (3, 8), (3, 9), (3, 10), (4, 8) and (4, 9) in terms of their planar arrays of degenerate Feynman diagrams. We then implement simple compatibility criteria together with an addition operation between arrays and recover the full collections/arrays for such cases. Along the way, we implement hard and soft kinematical limits, which provide a map between the poles in kinematic space and their combinatoric arrays. We use the operation to give a proof of a previously conjectured combinatorial duality for arrays in (<italic toggle=\"yes\">k</italic>, <italic toggle=\"yes\">n</italic>) and (<italic toggle=\"yes\">n</italic> − <italic toggle=\"yes\">k</italic>, <italic toggle=\"yes\">n</italic>). We also outline the relation to boundary maps of the hypersimplex Δ_{\u0000<italic toggle=\"yes\">k</italic>,<italic toggle=\"yes\">n</italic>\u0000} and rays in the tropical Grassmannian <inline-formula>\u0000<tex-math>\u0000<?CDATA $mathrm{Tr}(k,n)$?>\u0000</tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mi>Tr</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:math>\u0000<inline-graphic xlink:href=\"ctpad1095ieqn3.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>.","PeriodicalId":10641,"journal":{"name":"Communications in Theoretical Physics","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140313860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}