This paper deals with the uniqueness of mild solutions to the forced or unforced Navier-Stokes equations in the whole space. It is known that the uniqueness of mild solutions to the unforced Navier-Stokes equations holds in $big(L^{infty}((0,T);L^d(mathbb{R}^d))big)^d$ when $dgeq 4$, and in $big(C([0,T];L^d(mathbb{R}^d))big)^d$ when $dgeq3$. As for the forced Navier-Stokes equations, when $dgeq3$ the uniqueness of mild solutions in $big(C([0,T];L^{d}(mathbb{R}^d))big)^d$ with force $f$ in some Lorentz space is known. In this paper we show that for $dgeq3$, the uniqueness of mild solutions to the forced Navier-Stokes equations in $big(C((0,T];L^d(mathbb{R}^d))cap L^infty((0,T);L^d(mathbb{R}^d))big)^d$ holds when there is a mild solution in $big(C([0,T];L^d(mathbb{R}^d))big)^d$ with the same initial data and force. As a corollary of this result, we establish the uniqueness of mild solutions to the unforced Navier-Stokes equations in $big(C((0,T];L^3(mathbb{R}^3))cap L^infty((0,T);L^3(mathbb{R}^3))big)^3$.
{"title":"Uniqueness of mild solutions to the Navier-Stokes equations in $big(C((0,T];L^d(mathbb{R}^d))cap L^infty((0,T);L^d(mathbb{R}^d))big)^d$","authors":"Zhirun Zhan","doi":"arxiv-2402.01174","DOIUrl":"https://doi.org/arxiv-2402.01174","url":null,"abstract":"This paper deals with the uniqueness of mild solutions to the forced or\u0000unforced Navier-Stokes equations in the whole space. It is known that the\u0000uniqueness of mild solutions to the unforced Navier-Stokes equations holds in\u0000$big(L^{infty}((0,T);L^d(mathbb{R}^d))big)^d$ when $dgeq 4$, and in\u0000$big(C([0,T];L^d(mathbb{R}^d))big)^d$ when $dgeq3$. As for the forced\u0000Navier-Stokes equations, when $dgeq3$ the uniqueness of mild solutions in\u0000$big(C([0,T];L^{d}(mathbb{R}^d))big)^d$ with force $f$ in some Lorentz space\u0000is known. In this paper we show that for $dgeq3$, the uniqueness of mild\u0000solutions to the forced Navier-Stokes equations in\u0000$big(C((0,T];L^d(mathbb{R}^d))cap L^infty((0,T);L^d(mathbb{R}^d))big)^d$\u0000holds when there is a mild solution in $big(C([0,T];L^d(mathbb{R}^d))big)^d$\u0000with the same initial data and force. As a corollary of this result, we\u0000establish the uniqueness of mild solutions to the unforced Navier-Stokes\u0000equations in $big(C((0,T];L^3(mathbb{R}^3))cap\u0000L^infty((0,T);L^3(mathbb{R}^3))big)^3$.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769029","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}
G. O. Heymans, N. F. Svaiter, B. F. Svaiter, G. Krein
Critical Casimir effect appears when critical fluctuations of an order parameter interact with classical boundaries. We investigate this effect in the setting of a Landau-Ginzburg model with continuous symmetry in the presence of quenched disorder. The quenched free energy is written as an asymptotic series of moments of the models partition function. Our main result is that, in the presence of a strong disorder, Goldstone modes of the system contribute either with an attractive or with a repulsive force. This result was obtained using the distributional zeta-function method without relying on any particular ansatz in the functional space of the moments of the partition function.
{"title":"Critical Casimir effect in a disordered $O(2)$-symmetric model","authors":"G. O. Heymans, N. F. Svaiter, B. F. Svaiter, G. Krein","doi":"arxiv-2402.01588","DOIUrl":"https://doi.org/arxiv-2402.01588","url":null,"abstract":"Critical Casimir effect appears when critical fluctuations of an order\u0000parameter interact with classical boundaries. We investigate this effect in the\u0000setting of a Landau-Ginzburg model with continuous symmetry in the presence of\u0000quenched disorder. The quenched free energy is written as an asymptotic series\u0000of moments of the models partition function. Our main result is that, in the\u0000presence of a strong disorder, Goldstone modes of the system contribute either\u0000with an attractive or with a repulsive force. This result was obtained using\u0000the distributional zeta-function method without relying on any particular\u0000ansatz in the functional space of the moments of the partition function.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139768942","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}
Recent experiments discovered fractional Chern insulator states at zero magnetic field in twisted bilayer MoTe$_2$ [C23,Z23] and WSe$_2$ [MD23]. In this article, we study the MacDonald Hamiltonian for twisted transition metal dichalcogenides (TMDs) and analyze the low-lying spectrum in TMDs in the limit of small twisting angles. Unlike in twisted bilayer graphene Hamiltonians, we show that TMDs do not exhibit flat bands. The flatness in TMDs for small twisting angles is due to spatial confinement by a matrix-valued potential. We show that by generalizing semiclassical techniques developed by Simon [Si83] and Helffer-Sj"ostrand [HS84] to matrix-valued potentials, there exists a wide range of model parameters such that the low-lying bands are of exponentially small width in the twisting angle, topologically trivial, and obey a harmonic oscillator-type spacing with explicit parameters.
{"title":"Twisted TMDs in the small-angle limit: exponentially flat and trivial bands","authors":"Simon Becker, Mengxuan Yang","doi":"arxiv-2401.06078","DOIUrl":"https://doi.org/arxiv-2401.06078","url":null,"abstract":"Recent experiments discovered fractional Chern insulator states at zero\u0000magnetic field in twisted bilayer MoTe$_2$ [C23,Z23] and WSe$_2$ [MD23]. In\u0000this article, we study the MacDonald Hamiltonian for twisted transition metal\u0000dichalcogenides (TMDs) and analyze the low-lying spectrum in TMDs in the limit\u0000of small twisting angles. Unlike in twisted bilayer graphene Hamiltonians, we\u0000show that TMDs do not exhibit flat bands. The flatness in TMDs for small\u0000twisting angles is due to spatial confinement by a matrix-valued potential. We\u0000show that by generalizing semiclassical techniques developed by Simon [Si83]\u0000and Helffer-Sj\"ostrand [HS84] to matrix-valued potentials, there exists a wide\u0000range of model parameters such that the low-lying bands are of exponentially\u0000small width in the twisting angle, topologically trivial, and obey a harmonic\u0000oscillator-type spacing with explicit parameters.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463738","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 dispersionless limit of the recently introduced Toda lattice hierarchy with constraint of type B (the B-Toda hierarchy) and compare it with that of the DKP and C-Toda hierarchies. The dispersionless limits of the B-Toda and C-Toda hierarchies turn out to be the same.
我们研究了最近引入的带有 B 型约束的户田网格体系（B-户田体系）的无离散极限，并将其与 DKP 和 C-户田体系进行了比较。结果表明，B-Toda 和 C-Toda 层次结构的无色散极限是相同的。
{"title":"Dispersionless limit of the B-Toda hierarchy","authors":"A. Zabrodin","doi":"arxiv-2401.05919","DOIUrl":"https://doi.org/arxiv-2401.05919","url":null,"abstract":"We study the dispersionless limit of the recently introduced Toda lattice\u0000hierarchy with constraint of type B (the B-Toda hierarchy) and compare it with\u0000that of the DKP and C-Toda hierarchies. The dispersionless limits of the B-Toda\u0000and C-Toda hierarchies turn out to be the same.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463650","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 show that nearest-neighbor spin chains composed of projectors to 2-qudit product states are integrable. The $R$-matrices (with a multidimensional spectral parameter) include additive as well as non-additive parameters. They satisfy the colored Yang-Baxter equation. The local terms of the resulting Hamiltonians exhaust projectors with all possible ranks for a 2-qudit space. The Hamiltonian can be Hermitian or not, with or without frustration. The ground state structures of the frustration-free qubit spin chains are analysed. These systems have either global or local non-invertible symmetries. In particular, the rank 1 case has two product ground states that break global non-invertible symmetries (analogous to the case of the two ferromagnetic states breaking the global $mathbb{Z}_2$ symmetry of the $XXX$ spin chain). The Bravyi-Gosset conditions for spectral gaps show that these systems are gapped. The associated Yang-Baxter algebra and the spectrum of the transfer matrix are also studied.
{"title":"Integrability and non-invertible symmetries of projector spin chains","authors":"Pramod Padmanabhan, Kun Hao, Vladimir Korepin","doi":"arxiv-2401.05662","DOIUrl":"https://doi.org/arxiv-2401.05662","url":null,"abstract":"We show that nearest-neighbor spin chains composed of projectors to 2-qudit\u0000product states are integrable. The $R$-matrices (with a multidimensional\u0000spectral parameter) include additive as well as non-additive parameters. They\u0000satisfy the colored Yang-Baxter equation. The local terms of the resulting\u0000Hamiltonians exhaust projectors with all possible ranks for a 2-qudit space.\u0000The Hamiltonian can be Hermitian or not, with or without frustration. The\u0000ground state structures of the frustration-free qubit spin chains are analysed.\u0000These systems have either global or local non-invertible symmetries. In\u0000particular, the rank 1 case has two product ground states that break global\u0000non-invertible symmetries (analogous to the case of the two ferromagnetic\u0000states breaking the global $mathbb{Z}_2$ symmetry of the $XXX$ spin chain).\u0000The Bravyi-Gosset conditions for spectral gaps show that these systems are\u0000gapped. The associated Yang-Baxter algebra and the spectrum of the transfer\u0000matrix are also studied.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463861","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}
The quantum Rabi model is essential for understanding interacting quantum systems. It serves as the simplest non-integrable yet solvable model describing the interaction between a two-level system and a single mode of a bosonic field. In this study, we delve into the exploration of the generalized quantum Rabi model, wherein the bosonic mode of the field undergoes squeezing. Utilizing the Segal-Bargmann representation of the infinite-dimensional Hilbert space, we demonstrate that the energy spectrum of the generalized quantum Rabi model, when both the Rabi coupling strength and the squeezing strength are not significantly large compared to the field mode frequency, can be analytically determined by a bi-confluent Fuchsian equation with two regular singularities at 0 and 1 and an irregular singularity of rank two at infinity.
{"title":"Analytical approximations for generalized quantum Rabi models","authors":"Chon-Fai Kam, Yang Chen","doi":"arxiv-2401.05615","DOIUrl":"https://doi.org/arxiv-2401.05615","url":null,"abstract":"The quantum Rabi model is essential for understanding interacting quantum\u0000systems. It serves as the simplest non-integrable yet solvable model describing\u0000the interaction between a two-level system and a single mode of a bosonic\u0000field. In this study, we delve into the exploration of the generalized quantum\u0000Rabi model, wherein the bosonic mode of the field undergoes squeezing.\u0000Utilizing the Segal-Bargmann representation of the infinite-dimensional Hilbert\u0000space, we demonstrate that the energy spectrum of the generalized quantum Rabi\u0000model, when both the Rabi coupling strength and the squeezing strength are not\u0000significantly large compared to the field mode frequency, can be analytically\u0000determined by a bi-confluent Fuchsian equation with two regular singularities\u0000at 0 and 1 and an irregular singularity of rank two at infinity.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463781","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}
Quantum $L_infty$ algebras are higher loop generalizations of cyclic $L_infty$ algebras. Motivated by the problem of defining morphisms between such algebras, we construct a linear category of $(-1)$-shifted symplectic vector spaces and distributional half-densities, originally proposed by v{S}evera. Morphisms in this category can be given both by formal half-densities and Lagrangian relations; we prove that the composition of such morphisms recovers the construction of homotopy transfer of quantum $L_infty$ algebras. Finally, using this category, we propose a new notion of a relation between quantum $L_infty$ algebras.
{"title":"Lagrangian Relations and Quantum $L_infty$ Algebras","authors":"Branislav Jurčo, Ján Pulmann, Martin Zika","doi":"arxiv-2401.06110","DOIUrl":"https://doi.org/arxiv-2401.06110","url":null,"abstract":"Quantum $L_infty$ algebras are higher loop generalizations of cyclic\u0000$L_infty$ algebras. Motivated by the problem of defining morphisms between\u0000such algebras, we construct a linear category of $(-1)$-shifted symplectic\u0000vector spaces and distributional half-densities, originally proposed by\u0000v{S}evera. Morphisms in this category can be given both by formal\u0000half-densities and Lagrangian relations; we prove that the composition of such\u0000morphisms recovers the construction of homotopy transfer of quantum $L_infty$\u0000algebras. Finally, using this category, we propose a new notion of a relation\u0000between quantum $L_infty$ algebras.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139458769","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 introduces a novel approach for solving the cosmological field equations within scalar field theory by employing the Eisenhart lift. The field equations are reformulated as a system of geodesic equations for the Eisenhart metric. In the case of an exponential potential, the Eisenhart metric is shown to be conformally flat. By applying basic geometric principles, a new set of dynamical variables is identified, allowing for the linearization of the field equations and the derivation of classical cosmological solutions. However, the quantization of the Eisenhart system reveals a distinct set of solutions for the wavefunction, particularly in the presence of symmetry breaking at the quantum level.
{"title":"Classical and Quantum solutions in Scalar field cosmology via the Eisenhart lift and linearization","authors":"Andronikos Paliathanasis","doi":"arxiv-2401.05775","DOIUrl":"https://doi.org/arxiv-2401.05775","url":null,"abstract":"This study introduces a novel approach for solving the cosmological field\u0000equations within scalar field theory by employing the Eisenhart lift. The field\u0000equations are reformulated as a system of geodesic equations for the Eisenhart\u0000metric. In the case of an exponential potential, the Eisenhart metric is shown\u0000to be conformally flat. By applying basic geometric principles, a new set of\u0000dynamical variables is identified, allowing for the linearization of the field\u0000equations and the derivation of classical cosmological solutions. However, the\u0000quantization of the Eisenhart system reveals a distinct set of solutions for\u0000the wavefunction, particularly in the presence of symmetry breaking at the\u0000quantum level.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463784","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 consider a generalized model of random walk in dynamical random environment, and we show that the multiplicative-noise stochastic heat equation (SHE) describes the fluctuations of the quenched density at a certain precise location in the tail. The distribution of transition kernels is fixed rather than changing under the diffusive rescaling of space-time, i.e., there is no critical tuning of the model parameters when scaling to the stochastic PDE limit. The proof is done by pushing the methods developed in [arxiv 2304.14279, arXiv 2311.09151] to their maximum, substantially weakening the assumptions and obtaining fairly sharp conditions under which one expects to see the SHE arise in a wide variety of random walk models in random media. In particular we are able to get rid of conditions such as nearest-neighbor interaction as well as spatial independence of quenched transition kernels. Moreover, we observe an entire hierarchy of moderate deviation exponents at which the SHE can be found, confirming a physics prediction of J. Hass.
我们考虑了动态游走环境中的广义随机游走模型，并证明乘法噪声随机热方程（SHE）描述了尾部某一精确定位处的淬火密度波动。过渡核的分布是固定的，而不是在时空的扩散性重缩放下发生变化的，也就是说，当缩放到随机PDE极限时，模型参数不存在临界调整。证明是通过将[arxiv 2304.14279,arXiv 2311.09151]中开发的方法推向极致来完成的，大大弱化了假设，并获得了相当尖锐的条件，在这些条件下，我们有望看到SHE出现在随机介质中的各种随机行走模型中。特别是，我们可以摆脱近邻相互作用等条件，以及淬火转换核的空间独立性。此外，我们还观察到了中等偏差指数的整个层次结构，在这个层次上可以发现 SHE，这证实了 J. Hass 的物理学预测。
{"title":"Invariance principle for the KPZ equation arising in stochastic flows of kernels","authors":"Shalin Parekh","doi":"arxiv-2401.06073","DOIUrl":"https://doi.org/arxiv-2401.06073","url":null,"abstract":"We consider a generalized model of random walk in dynamical random\u0000environment, and we show that the multiplicative-noise stochastic heat equation\u0000(SHE) describes the fluctuations of the quenched density at a certain precise\u0000location in the tail. The distribution of transition kernels is fixed rather\u0000than changing under the diffusive rescaling of space-time, i.e., there is no\u0000critical tuning of the model parameters when scaling to the stochastic PDE\u0000limit. The proof is done by pushing the methods developed in [arxiv 2304.14279,\u0000arXiv 2311.09151] to their maximum, substantially weakening the assumptions and\u0000obtaining fairly sharp conditions under which one expects to see the SHE arise\u0000in a wide variety of random walk models in random media. In particular we are\u0000able to get rid of conditions such as nearest-neighbor interaction as well as\u0000spatial independence of quenched transition kernels. Moreover, we observe an\u0000entire hierarchy of moderate deviation exponents at which the SHE can be found,\u0000confirming a physics prediction of J. Hass.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463823","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}
In this paper we establish almost-optimal stability estimates in quantum optimal transport pseudometrics for the semiclassical limit of the Hartree dynamics to the Vlasov-Poisson equation, in the regime where the solutions have bounded densities. We combine Golse and Paul's method from [Arch. Ration. Mech. Anal. 223:57-94, 2017], which uses a semiclassical version of the optimal transport distance and which was adapted to the case of the Coulomb and gravitational interactions by the second author in [J. Stat. Phys. 177:20-60, 2019], with a new approach developed by the first author in [Arch. Ration. Mech. Anal. 244:27-50, 2022] to quantitatively improve stability estimates in kinetic theory.
{"title":"Enhanced Stability in Quantum Optimal Transport Pseudometrics: From Hartree to Vlasov-Poisson","authors":"Mikaela Iacobelli, Laurent Lafleche","doi":"arxiv-2401.05773","DOIUrl":"https://doi.org/arxiv-2401.05773","url":null,"abstract":"In this paper we establish almost-optimal stability estimates in quantum\u0000optimal transport pseudometrics for the semiclassical limit of the Hartree\u0000dynamics to the Vlasov-Poisson equation, in the regime where the solutions have\u0000bounded densities. We combine Golse and Paul's method from [Arch. Ration. Mech.\u0000Anal. 223:57-94, 2017], which uses a semiclassical version of the optimal\u0000transport distance and which was adapted to the case of the Coulomb and\u0000gravitational interactions by the second author in [J. Stat. Phys. 177:20-60,\u00002019], with a new approach developed by the first author in [Arch. Ration.\u0000Mech. Anal. 244:27-50, 2022] to quantitatively improve stability estimates in\u0000kinetic theory.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463618","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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