Alberto EscalantePuebla U., Inst. Fis., P. Fernando Ocaña GarcíaPuebla U., Inst. Fis.
The canonical analysis of the $lambda R$ model extended with the term due to Blas, Pujolas, and Sibiryakov $[BPS]$ is performed. The analysis is developed for any value of $lambda$, but particular attention is paid to the point $lambda=frac{1}{3}$ because of the closeness with linearized General Relativity [GR]. Then, we add the higher-order conformal term, the so-called Cotton-square term, to study the constraint structure of what constitutes an example of kinetic-conformal Horava's gravity. At the conformal point, an extra second-class constraint appears; this does not arise at other values of $lambda$. Then, the Dirac brackets are constructed, and we will observe that the $lambda R$-Cotton-square model shares the same number of degrees of freedom with linearized $GR$.
{"title":"New canonical analysis for consistent extension of $λR$ gravity","authors":"Alberto EscalantePuebla U., Inst. Fis., P. Fernando Ocaña GarcíaPuebla U., Inst. Fis.","doi":"arxiv-2409.11698","DOIUrl":"https://doi.org/arxiv-2409.11698","url":null,"abstract":"The canonical analysis of the $lambda R$ model extended with the term due to\u0000Blas, Pujolas, and Sibiryakov $[BPS]$ is performed. The analysis is developed\u0000for any value of $lambda$, but particular attention is paid to the point\u0000$lambda=frac{1}{3}$ because of the closeness with linearized General\u0000Relativity [GR]. Then, we add the higher-order conformal term, the so-called\u0000Cotton-square term, to study the constraint structure of what constitutes an\u0000example of kinetic-conformal Horava's gravity. At the conformal point, an extra\u0000second-class constraint appears; this does not arise at other values of\u0000$lambda$. Then, the Dirac brackets are constructed, and we will observe that\u0000the $lambda R$-Cotton-square model shares the same number of degrees of\u0000freedom with linearized $GR$.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260387","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}
This paper studies the boundary value problem on the steady compressible Navier-Stokes-Fourier system in a channel domain $(0,1)timesmathbb{T}^2$ with a class of generalized slip boundary conditions that were systematically derived from the Boltzmann equation by Coron cite{Coron-JSP-1989} and later by Aoki et al cite{Aoki-Baranger-Hattori-Kosuge-Martalo-Mathiaud-Mieussens-JSP-2017}. We establish the existence and uniqueness of strong solutions in $(L_{0}^{2}cap H^{2}(Omega))times V^{3}(Omega)times H^{3}(Omega)$ provided that the wall temperature is near a positive constant. The proof relies on the construction of a new variational formulation for the corresponding linearized problem and employs a fixed point argument. The main difficulty arises from the interplay of velocity and temperature derivatives together with the effect of density dependence on the boundary.
本文研究了在通道域$(0,1)timesmathbb{T}^2$中稳定的可压缩纳维尔-斯托克斯-傅里叶系统的边界值问题，该问题具有一类广义滑移边界条件，Coron （cite{Coron-JSP-1989}）以及后来的Aoki et al （cite{Aoki-Baranger-Hattori-Kosuge-Martalo-Mathiaud-Mieussens-JSP-2017}从玻尔兹曼方程中系统地导出了这类边界条件。我们在壁温接近正常数的条件下，建立了$(L_{0}^{2}capH^{2}(Omega))times V^{3}(Omega)times H^{3}(Omega)$中强解的存在性和唯一性。证明依赖于为相应的线性化问题构建一个新的变分公式，并采用定点论证。主要困难来自速度和温度导数的相互作用，以及边界密度依赖性的影响。
{"title":"Steady compressible Navier-Stokes-Fourier system with slip boundary conditions arising from kinetic theory","authors":"Renjun Duan, Junhao Zhang","doi":"arxiv-2409.11809","DOIUrl":"https://doi.org/arxiv-2409.11809","url":null,"abstract":"This paper studies the boundary value problem on the steady compressible\u0000Navier-Stokes-Fourier system in a channel domain $(0,1)timesmathbb{T}^2$ with\u0000a class of generalized slip boundary conditions that were systematically\u0000derived from the Boltzmann equation by Coron cite{Coron-JSP-1989} and later by\u0000Aoki et al\u0000cite{Aoki-Baranger-Hattori-Kosuge-Martalo-Mathiaud-Mieussens-JSP-2017}. We\u0000establish the existence and uniqueness of strong solutions in $(L_{0}^{2}cap\u0000H^{2}(Omega))times V^{3}(Omega)times H^{3}(Omega)$ provided that the wall\u0000temperature is near a positive constant. The proof relies on the construction\u0000of a new variational formulation for the corresponding linearized problem and\u0000employs a fixed point argument. The main difficulty arises from the interplay\u0000of velocity and temperature derivatives together with the effect of density\u0000dependence on the boundary.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260386","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}
This study employs the Riesz-Feller fractional derivative to determine Fisher and Shannon parameters for a one-dimensional harmonic oscillator. By deriving the Riesz fractional derivative of the probability density function, we quantify both Fisher information and Shannon entropy, thus providing valuable insights into the system's probabilistic nature.
{"title":"Determination of Fisher and Shannon Information for 1D Fractional Quantum Harmonic Oscillator","authors":"A. Boumali, K. Zazoua, F. Serdouk","doi":"arxiv-2409.11916","DOIUrl":"https://doi.org/arxiv-2409.11916","url":null,"abstract":"This study employs the Riesz-Feller fractional derivative to determine Fisher\u0000and Shannon parameters for a one-dimensional harmonic oscillator. By deriving\u0000the Riesz fractional derivative of the probability density function, we\u0000quantify both Fisher information and Shannon entropy, thus providing valuable\u0000insights into the system's probabilistic nature.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"149 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260380","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}
Joanna Piwnik, Joanna Gonera, Cezary Gonera, Piotr Kosinski
The light rays trajectories in Kerr metric, resulting from Fermat's principle, are considered from the point of view of integrable systems. It is shown how the counterpart of Carter constant emerges as a result of coupling-constant metamorphosis. The latter provides a convenient method of describing the null geodesics in Kerr metric.
{"title":"Integrable dynamics from Fermat's principle","authors":"Joanna Piwnik, Joanna Gonera, Cezary Gonera, Piotr Kosinski","doi":"arxiv-2409.11896","DOIUrl":"https://doi.org/arxiv-2409.11896","url":null,"abstract":"The light rays trajectories in Kerr metric, resulting from Fermat's\u0000principle, are considered from the point of view of integrable systems. It is\u0000shown how the counterpart of Carter constant emerges as a result of\u0000coupling-constant metamorphosis. The latter provides a convenient method of\u0000describing the null geodesics in Kerr metric.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260383","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}
We propose a stochastic interpretation of spacetime non-commutativity starting from the path integral formulation of quantum mechanical commutation relations. We discuss how the (non-)commutativity of spacetime is inherently related to the continuity or discontinuity of paths in the path integral formulation. Utilizing Wiener processes, we demonstrate that continuous paths lead to commutative spacetime, whereas discontinuous paths correspond to non-commutative spacetime structures. As an example we introduce discontinuous paths from which the $kappa$-Minkowski spacetime commutators can be obtained. Moreover we focus on modifications of the Leibniz rule for differentials acting on discontinuous trajectories. We show how these can be related to the deformed action of translation generators focusing, as a working example, on the $kappa$-Poincar'e algebra. Our findings suggest that spacetime non-commutativity can be understood as a result of fundamental discreteness of spacetime.
{"title":"A Stochastic Origin of Spacetime Non-Commutativity","authors":"Michele Arzano, Folkert Kuipers","doi":"arxiv-2409.11866","DOIUrl":"https://doi.org/arxiv-2409.11866","url":null,"abstract":"We propose a stochastic interpretation of spacetime non-commutativity\u0000starting from the path integral formulation of quantum mechanical commutation\u0000relations. We discuss how the (non-)commutativity of spacetime is inherently\u0000related to the continuity or discontinuity of paths in the path integral\u0000formulation. Utilizing Wiener processes, we demonstrate that continuous paths\u0000lead to commutative spacetime, whereas discontinuous paths correspond to\u0000non-commutative spacetime structures. As an example we introduce discontinuous\u0000paths from which the $kappa$-Minkowski spacetime commutators can be obtained.\u0000Moreover we focus on modifications of the Leibniz rule for differentials acting\u0000on discontinuous trajectories. We show how these can be related to the deformed\u0000action of translation generators focusing, as a working example, on the\u0000$kappa$-Poincar'e algebra. Our findings suggest that spacetime\u0000non-commutativity can be understood as a result of fundamental discreteness of\u0000spacetime.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"83 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260385","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}
Aybike Çatal-Özer, Keremcan Doğan, Cem Yetişmişoğlu
Drinfel'd double of Lie bialgebroids plays an important role in T-duality of string theories. In the presence of $H$ and $R$ fluxes, Lie bialgebroids should be extended to proto Lie bialgebroids. For both cases, the pair is given by two dual vector bundles, and the Drinfel'd double yields a Courant algebroid. However for U-duality, more complicated direct sum decompositions that are not described by dual vector bundles appear. In a previous work, we extended the notion of a Lie bialgebroid for vector bundles that are not necessarily dual. We achieved this by introducing a framework of calculus on algebroids and examining compatibility conditions for various algebroid properties in this framework. Here our aim is two-fold: extending our work on bialgebroids to include both $H$- and $R$-twists, and generalizing proto Lie bialgebroids to pairs of arbitrary vector bundles. To this end, we analyze various algebroid axioms and derive twisted compatibility conditions in the presence of twists. We introduce the notion of proto bialgebroids and their Drinfel'd doubles, where the former generalizes both bialgebroids and proto Lie bialgebroids. We also examine the most general form of vector bundle automorphisms of the double, related to twist matrices, that generate a new bracket from a given one. We analyze various examples from both physics and mathematics literatures in our framework.
{"title":"Drinfel'd Doubles, Twists and All That... in Stringy Geometry and M Theory","authors":"Aybike Çatal-Özer, Keremcan Doğan, Cem Yetişmişoğlu","doi":"arxiv-2409.11973","DOIUrl":"https://doi.org/arxiv-2409.11973","url":null,"abstract":"Drinfel'd double of Lie bialgebroids plays an important role in T-duality of\u0000string theories. In the presence of $H$ and $R$ fluxes, Lie bialgebroids should\u0000be extended to proto Lie bialgebroids. For both cases, the pair is given by two\u0000dual vector bundles, and the Drinfel'd double yields a Courant algebroid.\u0000However for U-duality, more complicated direct sum decompositions that are not\u0000described by dual vector bundles appear. In a previous work, we extended the\u0000notion of a Lie bialgebroid for vector bundles that are not necessarily dual.\u0000We achieved this by introducing a framework of calculus on algebroids and\u0000examining compatibility conditions for various algebroid properties in this\u0000framework. Here our aim is two-fold: extending our work on bialgebroids to\u0000include both $H$- and $R$-twists, and generalizing proto Lie bialgebroids to\u0000pairs of arbitrary vector bundles. To this end, we analyze various algebroid\u0000axioms and derive twisted compatibility conditions in the presence of twists.\u0000We introduce the notion of proto bialgebroids and their Drinfel'd doubles,\u0000where the former generalizes both bialgebroids and proto Lie bialgebroids. We\u0000also examine the most general form of vector bundle automorphisms of the\u0000double, related to twist matrices, that generate a new bracket from a given\u0000one. We analyze various examples from both physics and mathematics literatures\u0000in our framework.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260382","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}
We develop the theory of $N$-mixed-spin-$P$ fields for Fermat-type hypersurfaces in $mathbb{P}(1,1,1,1,2)$, $mathbb{P}(1,1,1,1,4)$, and $mathbb{P}(1,1,1,1,4)$, following the theory developed in arXiv:1809.08806 for the quintic threefold.
{"title":"MSP theory for smooth Calabi-Yau threefolds in weighted $mathbb{P}^4$","authors":"Patrick Lei","doi":"arxiv-2409.11660","DOIUrl":"https://doi.org/arxiv-2409.11660","url":null,"abstract":"We develop the theory of $N$-mixed-spin-$P$ fields for Fermat-type\u0000hypersurfaces in $mathbb{P}(1,1,1,1,2)$, $mathbb{P}(1,1,1,1,4)$, and\u0000$mathbb{P}(1,1,1,1,4)$, following the theory developed in arXiv:1809.08806 for\u0000the quintic threefold.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260388","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}
Gaussian unitary transformations are generated by quadratic Hamiltonians, i.e., Hamiltonians containing quadratic terms in creations and annihilation operators, and are heavily used in many areas of quantum physics, ranging from quantum optics and condensed matter theory to quantum information and quantum field theory in curved spacetime. They are known to form a representation of the metaplectic and spin group for bosons and fermions, respectively. These groups are the double covers of the symplectic and special orthogonal group, respectively, and our goal is to analyze the behavior of the sign ambiguity that one needs to deal with when moving between these groups and their double cover. We relate this sign ambiguity to expectation values of the form $langle 0|exp{(-ihat{H})}|0rangle$, where $|0rangle$ is a Gaussian state and $hat{H}$ an arbitrary quadratic Hamiltonian. We provide closed formulas for $langle 0|exp{(-ihat{H})}|0rangle$ and show how we can efficiently describe group multiplications in the double cover without the need of going to a faithful representation on an exponentially large or even infinite-dimensional space. Our construction relies on an explicit parametrization of these two groups (metaplectic, spin) in terms of symplectic and orthogonal group elements together with a twisted U(1) group.
{"title":"Representation theory of Gaussian unitary transformations for bosonic and fermionic systems","authors":"Tommaso Guaita, Lucas Hackl, Thomas Quella","doi":"arxiv-2409.11628","DOIUrl":"https://doi.org/arxiv-2409.11628","url":null,"abstract":"Gaussian unitary transformations are generated by quadratic Hamiltonians,\u0000i.e., Hamiltonians containing quadratic terms in creations and annihilation\u0000operators, and are heavily used in many areas of quantum physics, ranging from\u0000quantum optics and condensed matter theory to quantum information and quantum\u0000field theory in curved spacetime. They are known to form a representation of\u0000the metaplectic and spin group for bosons and fermions, respectively. These\u0000groups are the double covers of the symplectic and special orthogonal group,\u0000respectively, and our goal is to analyze the behavior of the sign ambiguity\u0000that one needs to deal with when moving between these groups and their double\u0000cover. We relate this sign ambiguity to expectation values of the form $langle\u00000|exp{(-ihat{H})}|0rangle$, where $|0rangle$ is a Gaussian state and\u0000$hat{H}$ an arbitrary quadratic Hamiltonian. We provide closed formulas for\u0000$langle 0|exp{(-ihat{H})}|0rangle$ and show how we can efficiently describe\u0000group multiplications in the double cover without the need of going to a\u0000faithful representation on an exponentially large or even infinite-dimensional\u0000space. Our construction relies on an explicit parametrization of these two\u0000groups (metaplectic, spin) in terms of symplectic and orthogonal group elements\u0000together with a twisted U(1) group.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260389","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}
We prove the finite generation conjecture of arXiv:hep-th/0406078 for the Gromov-Witten potentials of the Calabi-Yau hypersurfaces $Z_6 subset mathbb{P}(1,1,1,1,2)$, $Z_8 subset mathbb{P}(1,1,1,1,4)$, and $Z_{10} subset mathbb{P}(1,1,1,2,5)$ using the theory of MSP fields.
{"title":"Higher-genus Gromov-Witten theory of one-parameter Calabi-Yau threefolds I: Polynomiality","authors":"Patrick Lei","doi":"arxiv-2409.11659","DOIUrl":"https://doi.org/arxiv-2409.11659","url":null,"abstract":"We prove the finite generation conjecture of arXiv:hep-th/0406078 for the\u0000Gromov-Witten potentials of the Calabi-Yau hypersurfaces $Z_6 subset\u0000mathbb{P}(1,1,1,1,2)$, $Z_8 subset mathbb{P}(1,1,1,1,4)$, and $Z_{10}\u0000subset mathbb{P}(1,1,1,2,5)$ using the theory of MSP fields.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260396","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}
We study the emergence of chaos in a 2d system corresponding to a classical Hamiltonian system $V= frac{1}{2}(omega_x^2x^2+omega_y^2y^2)+epsilon xy^2$ consisting of two interacting harmonic oscillators and compare the classical and the Bohmian quantum trajectories for increasing values of $epsilon$. In particular we present an initial quantum state composed of two coherent states in $x$ and $y$, which in the absence of interaction produces ordered trajectories (Lissajous figures) and an initial state which contains {both chaotic and ordered} trajectories for $epsilon=0$. In both cases we find that, in general, Bohmian trajectories become chaotic in the long run, but chaos emerges at times which depend on the strength of the interaction between the oscillators.
{"title":"A comparison between classical and Bohmian quantum chaos","authors":"Athanasios C. Tzemos, George Contopoulos","doi":"arxiv-2409.12056","DOIUrl":"https://doi.org/arxiv-2409.12056","url":null,"abstract":"We study the emergence of chaos in a 2d system corresponding to a classical\u0000Hamiltonian system $V= frac{1}{2}(omega_x^2x^2+omega_y^2y^2)+epsilon xy^2$\u0000consisting of two interacting harmonic oscillators and compare the classical\u0000and the Bohmian quantum trajectories for increasing values of $epsilon$. In\u0000particular we present an initial quantum state composed of two coherent states\u0000in $x$ and $y$, which in the absence of interaction produces ordered\u0000trajectories (Lissajous figures) and an initial state which contains {both\u0000chaotic and ordered} trajectories for $epsilon=0$. In both cases we find that,\u0000in general, Bohmian trajectories become chaotic in the long run, but chaos\u0000emerges at times which depend on the strength of the interaction between the\u0000oscillators.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260384","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}
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