{"title":"Higher-Order Fermi–Walker Transport Dynamics and the Induced Geometric Phase","authors":"Rıdvan Cem Demirkol","doi":"10.1007/s10773-025-06099-y","DOIUrl":"10.1007/s10773-025-06099-y","url":null,"abstract":"<div><p>We define higher-order Fermi–Walker derivatives of vector fields along curves in Euclidean 3-space using the Frenet–Serret frame. From the incompatibility of successive Fermi–Walker transports, we derive a geometric phase—termed the Fermi–Walker flow transport phase—which depends on the intrinsic geometry of the curve. We then examine this phase for various curve evolutions, including binormal, complex modified Korteweg–de Vries, and other integrable motions. Our formulation provides an explicit and unified method for computing the induced geometric phases in these settings.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"64 9","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144893938","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}
Nauman Raza, Saima Arshed, Muhammad Haider Ali Asghar
{"title":"Traveling wave solutions with modulation instability of coupled nonlinear Schrödinger equations via two analytical approaches","authors":"Nauman Raza, Saima Arshed, Muhammad Haider Ali Asghar","doi":"10.1007/s10773-025-06092-5","DOIUrl":"10.1007/s10773-025-06092-5","url":null,"abstract":"<div><p>This paper investigates the soliton pulses of various kinds and their behavior as they traverse a birefringent optical fiber. Coupled nonlinear Schrödinger equations (CNLSEs) is a nonlinear model to describe light propagation within these fibers that accounts for coherent and incoherent nonlinear coupling phenomena. In particular, this study investigates several optical solitons subjected to third-order nonlinearity and group-velocity dispersion, which is physically significant regarding elliptical core optical fiber. This paper offers dark, bright, singular, periodic, and periodic-singular solitons to CNLSEs by employing the <span>(phi ^6)</span>-expansion technique and the <span>(G'/(bG'+G+a))</span>-expansion technique. It also provides 2D and 3D graphical illustrations of these solutions using fixed parameter values to showcase their physical significance. The modulation instability of the proposed model is also examined in this paper. The methods used are more accessible, effective, and computationally efficient. These methods can be applied to tackle complex problems obtained in mathematical physics, engineering, and optical fiber technology.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"64 9","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144868818","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}
{"title":"On Obtaining New MUBs by Finding Points on Complete Intersection Varieties over (mathbb {R})","authors":"Arindam Banerjee, Kanoy Kumar Das, Ajeet Kumar, Rakesh Kumar, Subhamoy Maitra","doi":"10.1007/s10773-025-06094-3","DOIUrl":"10.1007/s10773-025-06094-3","url":null,"abstract":"<div><p>Mutually Unbiased Bases (MUBs) are closely connected with quantum physics and the structure has a rich mathematical background. We provide equivalent criteria for extending a set of MUBs for <span>(mathbb {C}^n)</span> by studying real points of a certain affine algebraic variety. This variety comes from the relations that determine the extendability of a system of MUBs. Finally, we show that some part of this variety gives rise to complete intersection domains. Further, we show that there is a one-to-one correspondence between MUBs and the maximal commuting classes (bases) of orthogonal normal matrices in <span>(mathcal {M}_n({mathbb {C}}))</span>. It means that for <i>m</i> MUBs in <span>(mathbb {C}^n)</span>, there are <i>m</i> commuting classes each consisting <i>n</i> commuting orthogonal normal matrices and the existence of maximal commuting basis for <span>(mathcal {M}_n({mathbb {C}}))</span> ensures the complete set of MUBs in <span>(mathcal {M}_n({mathbb {C}}))</span>.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"64 9","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144868709","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}
{"title":"Entanglement and Steering of Three-Mode Field in Trio Coherent States","authors":"Ahmed A. Zahia, Eied Khalil, S. Al-Awfi","doi":"10.1007/s10773-025-06072-9","DOIUrl":"10.1007/s10773-025-06072-9","url":null,"abstract":"<div><p>This paper examines quantum correlations of a two-qubit system interacting with a tripartite mode field, focusing on entanglement and directional steering. For the initial trio coherent state and superposition atomic state, the analytical solution of the system is obtained. The tangle negativity measures the entanglement among three mode fields, while the steering function quantifies steerability between each pair of two-mode fields. The results reveal that system parameters, including the coupling strengths, excitation levels of the trio coherent state, and initial atomic state, strongly affect the development of entanglement and steering dynamics. Increasing the coupling strength between mode fields improves the entanglement for the pure states. However, the strength of steerability depends on the mode field interaction, where asymmetric steering is generated.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"64 9","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144861598","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}
{"title":"Soliton and Lump Solutions of a (3+1)-dimensional Generalized B-type Kadomtsev-Petviashvili Equation in Fluid Mechanics","authors":"Zi-Yu Zhang, Da-Wei Zuo","doi":"10.1007/s10773-025-06097-0","DOIUrl":"10.1007/s10773-025-06097-0","url":null,"abstract":"<div><p>In this paper, we investigate the soliton and lump solutions of a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation in fluid mechanics. Through logarithmic transformation, we derive its bilinear form. Via the bilinear equation, both first-order and second-order soliton solutions of this eqaution are constructed. Furthermore, semi-rational solutions of this equation are obtained via Gram determinant approach. Specifically, lump chains and lump-kink solutions of this equation are successfully derived. The analytical results reveal that solitary waves propagate at constant velocities with their amplitudes and velocities exhibiting a proportional relationship. This implies that adjustments to the parameters will concurrently affect both the propagation velocity and amplitude of solitary waves. By employing contour figures and auxiliary lines, the periods and propagation velocities of lump chains and lump-kink waves are systematically computed. Notably, as the parameter <i>N</i> (the order of these solutions) increases, phenomena of fusion or fission emerge among these nonlinear waves. Additionally, by adjusting parameter, distinct types of lump waves can be observed that propagate along with the coordinate axes.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"64 9","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144853667","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}
Bingbing Luo, Jiahua Wei, Zhiqiang Ma, Haoran Hu, Zhen Ren, Ya Wang, Lei Shi
{"title":"Improving the Successful Probability of Quantum Dense Coding Through Bit Flip Channels Using Auxiliary Particles","authors":"Bingbing Luo, Jiahua Wei, Zhiqiang Ma, Haoran Hu, Zhen Ren, Ya Wang, Lei Shi","doi":"10.1007/s10773-025-06093-4","DOIUrl":"10.1007/s10773-025-06093-4","url":null,"abstract":"<div><p>In this paper, an effective proposal for quantum dense coding through bit flip channels is presented with the aid of auxiliary particles. The concrete implementation processes for our scheme are given by means of appropriate quantum circuits. Meanwhile, the whole successful probability of this proposed protocol is calculated in the different situations of the bit flip particle number. It has been demonstrated that the total successful probability of this modified proposal is higher than or at least equal to that of the typical scheme. This is an important advantage of this novel scheme. Moreover, the dense coding task can be performed with the successful probability of 100% at the cost of the introduction of auxiliary particles when the bit flip is occurred on no or only one particle. Furthermore, the channel capacity comparison is made between this proposed protocol and the typical scheme, and the physical realization possibility of this modified proposal is discussed based on the quantum circuits.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"64 8","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810966","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}
{"title":"The Heat Capacity of a Diatomic Gas at High Temperatures","authors":"Ji-Xuan Hou","doi":"10.1007/s10773-025-06095-2","DOIUrl":"10.1007/s10773-025-06095-2","url":null,"abstract":"<div><p>while the <span>(frac{7}{2})</span> plateau is a key theoretical prediction of the equipartition theorem, real-world experiments cannot provide an unambiguous observation on this plateau. This discrepancy underscores the necessity of classical statistical mechanics in explaining thermal behavior. In this paper, we model the diatomic molecule as a stretchable dumbbell, and calculate the partition function and thermodynamic quantities of this model. Our calculation shows that the rotational modes and the vibrational mode cannot be decoupled completely and the equipartition theorem becomes not applicable anymore. For a diatomic molecule with a harmonic interaction between the two atoms, our calculation shows that the heat capacity should reach a <span>(frac{9}{2})</span> plateau instead of the <span>(frac{7}{2})</span> plateau. The height of the plateau can be shifted by the anharmonicity in the potential. Moreover, simulations are performed on our diatomic model by using the Monte Carlo Metropolis algorithm. The Monte Carlo simulations reveal that replacing the interatomic potential with the more realistic Morse potential leads to a heat capacity plateau value higher than <span>(frac{9}{2})</span>, with the plateau increasing as the dissociation energy of the diatomic molecule decreases.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"64 8","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810967","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}
{"title":"Categories of Orthosets and Adjointable Maps","authors":"Jan Paseka, Thomas Vetterlein","doi":"10.1007/s10773-025-06031-4","DOIUrl":"10.1007/s10773-025-06031-4","url":null,"abstract":"<div><p>An orthoset is a non-empty set together with a symmetric and irreflexive binary relation <span>(perp )</span>, called the orthogonality relation. An orthoset with 0 is an orthoset augmented with an additional element 0, called falsity, which is orthogonal to every element. The collection of subspaces of a Hilbert space that are spanned by a single vector provides a motivating example. We say that a map <span>(f :X rightarrow Y)</span> between orthosets with 0 possesses the adjoint <span>(g :Y rightarrow X)</span> if, for any <span>(x in X)</span> and <span>(y in Y)</span>, <span>(f(x) perp y)</span> if and only if <span>(x perp g(y))</span>. We call <i>f</i> in this case adjointable. For instance, any bounded linear map between Hilbert spaces induces a map with this property. We discuss in this paper adjointability from several perspectives and we put a particular focus on maps preserving the orthogonality relation. We moreover investigate the category <span>(mathcal{O}mathcal{S})</span> of all orthosets with 0 and adjointable maps between them. We especially focus on the full subcategory <span>(mathcalligra {i}mathcal{O}mathcal{S})</span> of irredundant orthosets with 0. <span>(mathcalligra {i}mathcal{O}mathcal{S})</span> can be made into a dagger category, the dagger of a morphism being its unique adjoint. <span>(mathcalligra {i}mathcal{O}mathcal{S})</span> contains dagger subcategories of various sorts and provides in particular a framework for the investigation of Hilbert spaces.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"64 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10773-025-06031-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144140191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Spectral Properties of the Zeon Combinatorial Laplacian: Cycles in Finite Graphs","authors":"G. Stacey Staples","doi":"10.1007/s10773-025-06032-3","DOIUrl":"10.1007/s10773-025-06032-3","url":null,"abstract":"<div><p>Given a finite simple graph <i>G</i> on <i>m</i> vertices, the zeon combinatorial Laplacian <span>(Lambda )</span> of <i>G</i> is an <span>(mtimes m)</span> matrix having entries in the complex zeon algebra <span>(mathbb {C}mathfrak {Z})</span>. It is shown here that if the graph has a unique vertex <i>v</i> of degree <i>k</i>, then the Laplacian has a unique zeon eigenvalue <span>(lambda )</span> whose scalar part is <i>k</i>. Moreover, the canonical expansion of the nilpotent (dual) part of <span>(lambda )</span> counts the cycles based at vertex <i>v</i> in <i>G</i>. With an appropriate generalization of the zeon combinatorial Laplacian of <i>G</i>, all cycles in <i>G</i> are counted by <span>(Lambda )</span>. Moreover when a generalized zeon combinatorial Laplacian <span>(Lambda )</span> can be viewed as a self-adjoint operator on the <span>(mathbb {C}mathfrak {Z})</span>-module of <i>m</i>-tuples of zeon elements, it can be interpreted as a quantum random variable whose values reveal the cycle structure of the underlying graph.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"64 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144140289","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}
{"title":"Data-Driven Localized Wave Solutions and Parameters Discovery of the (1+1)-dimensional Ito Integro-Differential Equation","authors":"Yufan Zou, Chuanjian Wang, Mengyao Zhang, Changzhao Li, Hui Fang","doi":"10.1007/s10773-025-06034-1","DOIUrl":"10.1007/s10773-025-06034-1","url":null,"abstract":"<div><p>In this paper, we investigate the data-driven localized wave solutions and parameters discovery of the (1+1)-dimensional Ito integro-differential equation by using the Potential-Function-Transformation PINNs (PFT-PINNs) method. Firstly, through the introduction of a potential function transformation, we convert the original integro-differential equation into the differential form and simultaneously also reduce the order of the differential equation, which provide convenience in solving the (1+1)-dimensional Ito integro-differential equation by using the PINNs method. Secondly, based on the neural networks, the data-driven localized wave solutions including soliton, breather, rogue wave, fusion and fission solutions are obtained with the aid of the potential function transformation. The results show that the PFT-PINNs method possesses the good performance of PFT-PINNs method in solving the forward problem of the (1+1)-dimensional Ito integro-differential equation and can acquire more accurate localized wave solutions than the standard PINNs method. Finally the PFT-PINNs method is used to solve the inverse problem of the (1+1)-dimensional Ito integro-differential equation and the results demonstrate that the unknown coefficient parameters can be satisfactorily identified even with heavily noisy data.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"64 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144135384","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}