Journal of Physics A: Mathematical and Theoretical最新文献

{"title":"The nonlinear Schrödinger equation in cylindrical geometries","authors":"R. Krechetnikov","doi":"10.1088/1751-8121/ad33dd","DOIUrl":"https://doi.org/10.1088/1751-8121/ad33dd","url":null,"abstract":"\u0000 <jats:p>The nonlinear Schrödinger equation was originally derived in nonlinear optics as a model for beam propagation, which naturally requires its application in cylindrical coordinates. However, that derivation was performed in Cartesian coordinates for linearly polarized fields with the Laplacian <jats:inline-formula>\u0000 <jats:tex-math><?CDATA $Delta_{perp} = partial_{x}^{2} + partial_{y}^{2}$?></jats:tex-math>\u0000 <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\">\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mi mathvariant=\"normal\">Δ</mml:mi>\u0000 <mml:mrow>\u0000 <mml:mo>⊥</mml:mo>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:msubsup>\u0000 <mml:mi>∂</mml:mi>\u0000 <mml:mrow>\u0000 <mml:mi>x</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mrow>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:mrow>\u0000 </mml:msubsup>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:msubsup>\u0000 <mml:mi>∂</mml:mi>\u0000 <mml:mrow>\u0000 <mml:mi>y</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mrow>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:mrow>\u0000 </mml:msubsup>\u0000 </mml:mrow>\u0000 </mml:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"aad33ddieqn1.gif\" xlink:type=\"simple\" />\u0000 </jats:inline-formula> transverse to the beam <jats:italic>z</jats:italic>-direction, and then, tacitly assuming covariance, extended to axisymmetric cylindrical setting. As we show, first with a simple example and next with a systematic derivation in cylindrical coordinates for axisymmetric and hence radially polarized fields, <jats:inline-formula>\u0000 <jats:tex-math><?CDATA $Delta_{perp} = partial_{r}^{2} + frac{1}{r} partial_{r}$?></jats:tex-math>\u0000 <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\">\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mi mathvariant=\"normal\">Δ</mml:mi>\u0000 <mml:mrow>\u0000 <mml:mo>⊥</mml:mo>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:msubsup>\u0000 <mml:mi>∂<","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140368753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Improving performance of quantum heat engines using modified Otto cycle","authors":"R. B S, Harsh Sharma, Uma Divakaran","doi":"10.1088/1751-8121/ad38ee","DOIUrl":"https://doi.org/10.1088/1751-8121/ad38ee","url":null,"abstract":"\u0000 The efficiency of a quantum heat engine is maximum when the unitary strokes of the quantum Otto cycle are adiabatic. On the other hand, this may not be always possible due to small energy gaps in the system, especially at the critical point where the gap between the ground state and the first excited state vanishes and the system gets excited. With the aim to regain this lost adiabaticity, we modify one of the unitary strokes of the Otto cycle by allowing the system to first evolve with a time dependent Hamiltonian as in the case of a usual Otto cycle, followed by an additional evolution with a different time independent Hamiltonian so that the system reaches a less excited state. This will help in increasing the magnitude of the heat absorbed from the hot bath so that the work output and efficiency of the engine can be increased. We demonstrate this method using an integrable model and a non-integrable model as the working medium and discuss the generality and limitations of this method. In the case of a two spin system, the optimal value for the time till which the system needs to be freely evolved is calculated analytically in the adiabatic limit. The results show that implementing this modified unitary stroke significantly improves the work output and efficiency of the engine, especially when it crosses the critical point.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"110 20","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140370406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Semi-definite programming and quantum information","authors":"P. Mironowicz","doi":"10.1088/1751-8121/ad2b85","DOIUrl":"https://doi.org/10.1088/1751-8121/ad2b85","url":null,"abstract":"\u0000 This paper presents a comprehensive exploration of semi-definite programming (SDP) techniques within the context of quantum information. It examines the mathematical foundations of convex optimization, duality, and SDP formulations, providing a solid theoretical framework for addressing optimization challenges in quantum systems. By leveraging these tools, researchers and practitioners can characterize classical and quantum correlations, optimize quantum states, and design efficient quantum algorithms and protocols. The paper also discusses implementational aspects, such as solvers for SDP and modeling tools, enabling the effective employment of optimization techniques in quantum information processing. The insights and methodologies presented in this paper have proven instrumental in advancing the field of quantum information, facilitating the development of novel communication protocols, self-testing methods, and a deeper understanding of quantum entanglement.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"2 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140442911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimized shaping and trade-off of superoscillating pulses","authors":"G. Frenkel, Tamir Yehuda, Moshe Schwartz","doi":"10.1088/1751-8121/ad2a1d","DOIUrl":"https://doi.org/10.1088/1751-8121/ad2a1d","url":null,"abstract":"\u0000 In this article, we consider a special family of pulses, which are a part of a band-limited signal and are “too narrow” considering the band limit of the signal. We dub such pulses “superoscillating pulses” although they can be seen at best as half an oscillation. While some of our results are of a more generic nature, the article is devoted to the optimization of superoscillating pulses, The first step consists of approximating a given target signal by a band limited signal in a fixed time interval. The signals to be approximated, exhibit in that interval features that seem to involve frequencies higher than the band limit of the approximant. We define the Mean Square Relative Error (MSRE) as a measure of the adherence of the approximant to the original signal in the chosen interval. We find that the minimization of the MSRE conflicts with the necessity to minimize the energy (or power) expense of the superoscillating signal. We obtain the trade-off relation between optimal energy expense and the MSRE for a family of pulses. This makes it clear that within that family, there exists a specific pulse shape that is better approximated by a superoscillating pulse. Finally, we show how to construct a yield optimized superoscillating pulse that, within a given time interval, has a prescribed narrow width without resorting to a target signal at all.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"52 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139961466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The physical interpretation of point interactions in one-dimensional relativistic quantum mechanics","authors":"C. A. Bonin, J. T. Lunardi, L. Manzoni","doi":"10.1088/1751-8121/ad280e","DOIUrl":"https://doi.org/10.1088/1751-8121/ad280e","url":null,"abstract":"\u0000 We investigate point interactions in one-dimensional relativistic quantum mechanics using a distributional approach based on Schwartz's theory of distributions. From the properties of the most general covariant distribution describing relativistic point interactions we obtain the physical parameters associated with the point potentials that behave as a scalar, a pseudo-scalar and a vector under Lorentz transformations. Then, we establish a one-to-one relationship between these physical parameters and the well-known set of four parameters giving the boundary conditions at the singular point(s), which define a self-adjoint Hamiltonian. By considering the non-relativistic limit, we obtain the most general point interaction in the Schr\"odinger equation in terms of these four physical point potentials. Finally, we study the symmetries of the relativistic point interactions under space inversion, time reversal and charge conjugation, and investigate how requirements of invariance under these symmetry transformations can be used to restrict the set of physical parameters.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":" 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139789988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Remodelling selection to optimise disease forecasts and policies","authors":"Gabriela M Gomes, Andrew M Blagborough, Kate e. Langwig, Beate Ringwald","doi":"10.1088/1751-8121/ad280d","DOIUrl":"https://doi.org/10.1088/1751-8121/ad280d","url":null,"abstract":"\u0000 Mathematical models are increasingly adopted for setting disease prevention and control targets. As model-informed policies are implemented, however, the inaccuracies of some forecasts become apparent, for example overprediction of infection burdens and intervention impacts. Here, we attribute these discrepancies to methodological limitations in capturing the heterogeneities of real-world systems. The mechanisms underpinning risk factors of infection and their interactions determine individual propensities to acquire disease. These factors are potentially so numerous and complex that to attain a full mechanistic description is likely unfeasible. To contribute constructively to the development of health policies, model developers either leave factors out (reductionism) or adopt a broader but coarse description (holism). In our view, predictive capacity requires holistic descriptions of heterogeneity which are currently underutilised in infectious disease epidemiology, in comparison to other population disciplines, such as non-communicable disease epidemiology, demography, ecology and evolution.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":" 15","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139789374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The physical interpretation of point interactions in one-dimensional relativistic quantum mechanics","authors":"C. A. Bonin, J. T. Lunardi, L. Manzoni","doi":"10.1088/1751-8121/ad280e","DOIUrl":"https://doi.org/10.1088/1751-8121/ad280e","url":null,"abstract":"\u0000 We investigate point interactions in one-dimensional relativistic quantum mechanics using a distributional approach based on Schwartz's theory of distributions. From the properties of the most general covariant distribution describing relativistic point interactions we obtain the physical parameters associated with the point potentials that behave as a scalar, a pseudo-scalar and a vector under Lorentz transformations. Then, we establish a one-to-one relationship between these physical parameters and the well-known set of four parameters giving the boundary conditions at the singular point(s), which define a self-adjoint Hamiltonian. By considering the non-relativistic limit, we obtain the most general point interaction in the Schr\"odinger equation in terms of these four physical point potentials. Finally, we study the symmetries of the relativistic point interactions under space inversion, time reversal and charge conjugation, and investigate how requirements of invariance under these symmetry transformations can be used to restrict the set of physical parameters.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"73 2-3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139850165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Remodelling selection to optimise disease forecasts and policies","authors":"Gabriela M Gomes, Andrew M Blagborough, Kate e. Langwig, Beate Ringwald","doi":"10.1088/1751-8121/ad280d","DOIUrl":"https://doi.org/10.1088/1751-8121/ad280d","url":null,"abstract":"\u0000 Mathematical models are increasingly adopted for setting disease prevention and control targets. As model-informed policies are implemented, however, the inaccuracies of some forecasts become apparent, for example overprediction of infection burdens and intervention impacts. Here, we attribute these discrepancies to methodological limitations in capturing the heterogeneities of real-world systems. The mechanisms underpinning risk factors of infection and their interactions determine individual propensities to acquire disease. These factors are potentially so numerous and complex that to attain a full mechanistic description is likely unfeasible. To contribute constructively to the development of health policies, model developers either leave factors out (reductionism) or adopt a broader but coarse description (holism). In our view, predictive capacity requires holistic descriptions of heterogeneity which are currently underutilised in infectious disease epidemiology, in comparison to other population disciplines, such as non-communicable disease epidemiology, demography, ecology and evolution.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"68 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139849377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Competitive random sequential adsorption of binary mixtures of disks and discorectangles","authors":"Nikolai I Lebovka, Michał Cieśla, Luca Petrone, N. Vygornitskii","doi":"10.1088/1751-8121/ad2727","DOIUrl":"https://doi.org/10.1088/1751-8121/ad2727","url":null,"abstract":"\u0000 The two-dimensional (2D) packings of binary mixtures of disks with diameter $d$ and discorectangles with aspect ratio $varepsilon$ (length-to-width ratio $varepsilon=l/d$) were studied numerically. The competitive random sequential adsorption (RSA) with simultaneous deposition of particles was considered. The aspect ratio was changed within the range $varepsilon=1-10$. In the competitive model, the particle was selected with probability $p_d$ (disks) and $p_varepsilon = 1- p_d$ (discorectangles), and then they were placed sequentially on a solid surface without overlapping with previously placed particles. Behavior of the total coverage in jamming state $varphi_T$ at different values of $p_d$ and $varepsilon$ was analyzed. For core-shell structure of the particles the percolation connectivity of films was also discussed.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"9 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139797992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Orthosymplectic Z2 x Z2-graded Lie superalgebras and parastatistics","authors":"N. I. Stoilova, J. Van der Jeugt","doi":"10.1088/1751-8121/ad2726","DOIUrl":"https://doi.org/10.1088/1751-8121/ad2726","url":null,"abstract":"\u0000 A Z2 x Z2-graded Lie superalgebra g is a Z2 x Z2-graded algebra with a bracket [·, ·] that satisfies certain graded versions of the symmetry and Jacobi identity. In particular, despite the common terminology, g is not a Lie superalgebra. We construct the most general orthosymplectic Z2 x Z2-graded Lie superalgebra osp(2m1+1, 2m2|2n1, 2n2) in terms of defining matrices. A special case of this algebra appeared already in work of Tolstoy in 2014. Our construction is based on the notion of graded supertranspose for a Z2 x Z2-graded matrix. Since the orthosymplectic Lie superalgebra osp(2m + 1|2n) is closely related to the definition of parabosons, parafermions and mixed parastatistics, we investigate here the new parastatistics relations following from osp(2m1+1, 2m2|2n1, 2n2). Some special cases are of particular interest, even when one is dealing with parabosons only.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"12 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139857112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}