We generalize the double bracket vector fields defined on compact semi-simple Lie algebras to the case of general Poisson manifolds endowed with a pseudo-Riemannian metric. We construct a generalization of the normal metric such that the above vector fields, when restricted to a symplectic leaf, become gradient vector fields. We illustrate the discussion at a variety of examples and carefully discuss complications that arise when the pseudo-Riemannian metric does not induce a non-degenerate metric on parts of the symplectic leaves.
{"title":"Double bracket vector fields on Poisson manifolds","authors":"Petre Birtea, Zohreh Ravanpak, Cornelia Vizman","doi":"arxiv-2404.03221","DOIUrl":"https://doi.org/arxiv-2404.03221","url":null,"abstract":"We generalize the double bracket vector fields defined on compact semi-simple\u0000Lie algebras to the case of general Poisson manifolds endowed with a\u0000pseudo-Riemannian metric. We construct a generalization of the normal metric\u0000such that the above vector fields, when restricted to a symplectic leaf, become\u0000gradient vector fields. We illustrate the discussion at a variety of examples\u0000and carefully discuss complications that arise when the pseudo-Riemannian\u0000metric does not induce a non-degenerate metric on parts of the symplectic\u0000leaves.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587662","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 build a discrete model that simulates the ubiquitous competition between the free internal evolution of a two-level system and the decoherence induced by the interaction with its surrounding environment. It is aimed at being as universal as possible, so that no specific Hamiltonian is assumed. This leads to an analytic criterion, depending on the level of short time decoherence, allowing to determine whether the system will freeze due to the Zeno effect. We check this criterion on several classes of functions which correspond to different physical situations. In the most generic case, the free evolution wins over decoherence, thereby explaining why the universe is indeed not frozen.
{"title":"Why is the universe not frozen by the quantum Zeno effect?","authors":"Antoine Soulas","doi":"arxiv-2404.01913","DOIUrl":"https://doi.org/arxiv-2404.01913","url":null,"abstract":"We build a discrete model that simulates the ubiquitous competition between\u0000the free internal evolution of a two-level system and the decoherence induced\u0000by the interaction with its surrounding environment. It is aimed at being as\u0000universal as possible, so that no specific Hamiltonian is assumed. This leads\u0000to an analytic criterion, depending on the level of short time decoherence,\u0000allowing to determine whether the system will freeze due to the Zeno effect. We\u0000check this criterion on several classes of functions which correspond to\u0000different physical situations. In the most generic case, the free evolution\u0000wins over decoherence, thereby explaining why the universe is indeed not\u0000frozen.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587798","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 phase-field system is a nonlinear model that has significant applications in material sciences. In this paper, we are concerned with the uniqueness of determining the nonlinear energy potential in a phase-field system consisted of Cahn-Hilliard and Allen-Cahn equations. This system finds widespread applications in the development of alloys engineered to withstand extreme temperatures and pressures. The goal is to reconstruct the nonlinear energy potential through the measurements of concentration fields. We establish the local well-posedness of the phase-field system based on the implicit function theorem in Banach spaces. Both of the uniqueness results for recovering time-independent and time-dependent energy potential functions are provided through the higher order linearization technique.
{"title":"A uniqueness theory on determining the nonlinear energy potential in phase-field system","authors":"Tianhao Ni, Jun Lai","doi":"arxiv-2404.00587","DOIUrl":"https://doi.org/arxiv-2404.00587","url":null,"abstract":"The phase-field system is a nonlinear model that has significant applications\u0000in material sciences. In this paper, we are concerned with the uniqueness of\u0000determining the nonlinear energy potential in a phase-field system consisted of\u0000Cahn-Hilliard and Allen-Cahn equations. This system finds widespread\u0000applications in the development of alloys engineered to withstand extreme\u0000temperatures and pressures. The goal is to reconstruct the nonlinear energy\u0000potential through the measurements of concentration fields. We establish the\u0000local well-posedness of the phase-field system based on the implicit function\u0000theorem in Banach spaces. Both of the uniqueness results for recovering\u0000time-independent and time-dependent energy potential functions are provided\u0000through the higher order linearization technique.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140602771","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 Gross-Neveu model is a quantum field theory model of Dirac fermions in two dimensions with a quartic interaction term. Like Yang-Mills theory in four dimensions, the model is renormalizable (but not super-renormalizable) and asymptotically free (i.e. its short-distance behaviour is governed by the free theory). We give a new construction of the massive Euclidean Gross-Neveu model in infinite volume based on the renormalization group flow equation. The construction does not involve cluster expansion or discretization of phase-space. We express the Schwinger functions of the Gross-Neveu model in terms of the effective potential and construct the effective potential by solving the flow equation using the Banach fixed point theorem. Since we use crucially the fact that fermionic fields can be represented as bounded operators our construction does not extend to models including bosons. However, it is applicable to other asymptotically free purely fermionic theories such as the symplectic fermion model.
{"title":"Construction of Gross-Neveu model using Polchinski flow equation","authors":"Paweł Duch","doi":"arxiv-2403.18562","DOIUrl":"https://doi.org/arxiv-2403.18562","url":null,"abstract":"The Gross-Neveu model is a quantum field theory model of Dirac fermions in\u0000two dimensions with a quartic interaction term. Like Yang-Mills theory in four\u0000dimensions, the model is renormalizable (but not super-renormalizable) and\u0000asymptotically free (i.e. its short-distance behaviour is governed by the free\u0000theory). We give a new construction of the massive Euclidean Gross-Neveu model\u0000in infinite volume based on the renormalization group flow equation. The\u0000construction does not involve cluster expansion or discretization of\u0000phase-space. We express the Schwinger functions of the Gross-Neveu model in\u0000terms of the effective potential and construct the effective potential by\u0000solving the flow equation using the Banach fixed point theorem. Since we use\u0000crucially the fact that fermionic fields can be represented as bounded\u0000operators our construction does not extend to models including bosons. However,\u0000it is applicable to other asymptotically free purely fermionic theories such as\u0000the symplectic fermion model.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140316217","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}
Jitendra Kethepalli, Manas Kulkarni, Anupam Kundu, Satya N. Majumdar, David Mukamel, Grégory Schehr
We investigate the full counting statistics (FCS) of a harmonically confined 1d short-range Riesz gas consisting of $N$ particles in equilibrium at finite temperature. The particles interact with each other through a repulsive power-law interaction with an exponent $k>1$ which includes the Calogero-Moser model for $k=2$. We examine the probability distribution of the number of particles in a finite domain $[-W, W]$ called number distribution, denoted by $mathcal{N}(W, N)$. We analyze the probability distribution of $mathcal{N}(W, N)$ and show that it exhibits a large deviation form for large $N$ characterised by a speed $N^{frac{3k+2}{k+2}}$ and by a large deviation function of the fraction $c = mathcal{N}(W, N)/N$ of the particles inside the domain and $W$. We show that the density profiles that create the large deviations display interesting shape transitions as one varies $c$ and $W$. This is manifested by a third-order phase transition exhibited by the large deviation function that has discontinuous third derivatives. Monte-Carlo (MC) simulations show good agreement with our analytical expressions for the corresponding density profiles. We find that the typical fluctuations of $mathcal{N}(W, N)$, obtained from our field theoretic calculations are Gaussian distributed with a variance that scales as $N^{nu_k}$, with $nu_k = (2-k)/(2+k)$. We also present some numerical findings on the mean and the variance. Furthermore, we adapt our formalism to study the index distribution (where the domain is semi-infinite $(-infty, W])$, linear statistics (the variance), thermodynamic pressure and bulk modulus.
{"title":"Full counting statistics of 1d short-range Riesz gases in confinement","authors":"Jitendra Kethepalli, Manas Kulkarni, Anupam Kundu, Satya N. Majumdar, David Mukamel, Grégory Schehr","doi":"arxiv-2403.18750","DOIUrl":"https://doi.org/arxiv-2403.18750","url":null,"abstract":"We investigate the full counting statistics (FCS) of a harmonically confined\u00001d short-range Riesz gas consisting of $N$ particles in equilibrium at finite\u0000temperature. The particles interact with each other through a repulsive\u0000power-law interaction with an exponent $k>1$ which includes the Calogero-Moser\u0000model for $k=2$. We examine the probability distribution of the number of\u0000particles in a finite domain $[-W, W]$ called number distribution, denoted by\u0000$mathcal{N}(W, N)$. We analyze the probability distribution of $mathcal{N}(W,\u0000N)$ and show that it exhibits a large deviation form for large $N$\u0000characterised by a speed $N^{frac{3k+2}{k+2}}$ and by a large deviation\u0000function of the fraction $c = mathcal{N}(W, N)/N$ of the particles inside the\u0000domain and $W$. We show that the density profiles that create the large\u0000deviations display interesting shape transitions as one varies $c$ and $W$.\u0000This is manifested by a third-order phase transition exhibited by the large\u0000deviation function that has discontinuous third derivatives. Monte-Carlo (MC)\u0000simulations show good agreement with our analytical expressions for the\u0000corresponding density profiles. We find that the typical fluctuations of\u0000$mathcal{N}(W, N)$, obtained from our field theoretic calculations are\u0000Gaussian distributed with a variance that scales as $N^{nu_k}$, with $nu_k =\u0000(2-k)/(2+k)$. We also present some numerical findings on the mean and the\u0000variance. Furthermore, we adapt our formalism to study the index distribution\u0000(where the domain is semi-infinite $(-infty, W])$, linear statistics (the\u0000variance), thermodynamic pressure and bulk modulus.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140316130","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}
An analytic method to calculate the vortex number on a torus is constructed, focusing on analytic vortex solutions to the Chern-Simons-Higgs theory, whose governing equation is the so-called Jackiw-Pi equation. The equation is one of the integrable vortex equations and is reduced to Liouville's equation. The requirement of continuity of the Higgs field strongly restricts the characteristics and the fundamental domain of the vortices. Also considered are the decompactification limits of the vortices on a torus, in which "flux loss" phenomena occasionally occur.
{"title":"Analytic Approach for Computation of Topological Number of Integrable Vortex on Torus","authors":"Kaoru Miyamoto, Atsushi Nakamula","doi":"arxiv-2403.18264","DOIUrl":"https://doi.org/arxiv-2403.18264","url":null,"abstract":"An analytic method to calculate the vortex number on a torus is constructed,\u0000focusing on analytic vortex solutions to the Chern-Simons-Higgs theory, whose\u0000governing equation is the so-called Jackiw-Pi equation. The equation is one of\u0000the integrable vortex equations and is reduced to Liouville's equation. The\u0000requirement of continuity of the Higgs field strongly restricts the\u0000characteristics and the fundamental domain of the vortices. Also considered are\u0000the decompactification limits of the vortices on a torus, in which \"flux loss\"\u0000phenomena occasionally occur.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140316129","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 work examines a special behavior of the magnetic conductivity of metals that arises when chaotic electron trajectories appear on the Fermi surface. This behavior is due to the scattering of electrons at singular points of the dynamic system describing the dynamics of electrons in $, {bf p}$-space, and caused by small-angle scattering of electrons on phonons. In this situation, the electronic system is described by a "non-standard" relaxation time, which plays the main role in a certain range of temperature and magnetic field values.
{"title":"Specificity of $τ$ -- approximation for chaotic electron trajectories on complex Fermi surfaces","authors":"A. Ya. Maltsev","doi":"arxiv-2403.18457","DOIUrl":"https://doi.org/arxiv-2403.18457","url":null,"abstract":"The work examines a special behavior of the magnetic conductivity of metals\u0000that arises when chaotic electron trajectories appear on the Fermi surface.\u0000This behavior is due to the scattering of electrons at singular points of the\u0000dynamic system describing the dynamics of electrons in $, {bf p}$-space, and\u0000caused by small-angle scattering of electrons on phonons. In this situation,\u0000the electronic system is described by a \"non-standard\" relaxation time, which\u0000plays the main role in a certain range of temperature and magnetic field\u0000values.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140316132","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}
A unified analytical solution is presented for constructing the phase space near collinear libration points in the Circular Restricted Three-body Problem (CRTBP), encompassing Lissajous orbits and quasihalo orbits, their invariant manifolds, as well as transit and non-transit orbits. Traditional methods could only derive separate analytical solutions for the invariant manifolds of Lissajous orbits and halo orbits, falling short for the invariant manifolds of quasihalo orbits. By introducing a coupling coefficient {eta} and a bifurcation equation, a unified series solution for these orbits is systematically developed using a coupling-induced bifurcation mechanism and Lindstedt-Poincar'e method. Analyzing the third-order bifurcation equation reveals bifurcation conditions for halo orbits, quasihalo orbits, and their invariant manifolds. Furthermore, new families of periodic orbits similar to halo orbits are discovered, and non-periodic/quasi-periodic orbits, such as transit orbits and non-transit orbits, are found to undergo bifurcations. When {eta} = 0, the series solution describes Lissajous orbits and their invariant manifolds, transit, and non-transit orbits. As {eta} varies from zero to non-zero values, the solution seamlessly transitions to describe quasihalo orbits and their invariant manifolds, as well as newly bifurcated transit and non-transit orbits. This unified analytical framework provides a more comprehensive understanding of the complex phase space structures near collinear libration points in the CRTBP.
{"title":"Analytical computation of bifurcation of orbits near collinear libration point in the restricted three-body problem","authors":"Mingpei Lin, Tong Luo, Hayato Chiba","doi":"arxiv-2403.18237","DOIUrl":"https://doi.org/arxiv-2403.18237","url":null,"abstract":"A unified analytical solution is presented for constructing the phase space\u0000near collinear libration points in the Circular Restricted Three-body Problem\u0000(CRTBP), encompassing Lissajous orbits and quasihalo orbits, their invariant\u0000manifolds, as well as transit and non-transit orbits. Traditional methods could\u0000only derive separate analytical solutions for the invariant manifolds of\u0000Lissajous orbits and halo orbits, falling short for the invariant manifolds of\u0000quasihalo orbits. By introducing a coupling coefficient {eta} and a\u0000bifurcation equation, a unified series solution for these orbits is\u0000systematically developed using a coupling-induced bifurcation mechanism and\u0000Lindstedt-Poincar'e method. Analyzing the third-order bifurcation equation\u0000reveals bifurcation conditions for halo orbits, quasihalo orbits, and their\u0000invariant manifolds. Furthermore, new families of periodic orbits similar to\u0000halo orbits are discovered, and non-periodic/quasi-periodic orbits, such as\u0000transit orbits and non-transit orbits, are found to undergo bifurcations. When\u0000{eta} = 0, the series solution describes Lissajous orbits and their invariant\u0000manifolds, transit, and non-transit orbits. As {eta} varies from zero to\u0000non-zero values, the solution seamlessly transitions to describe quasihalo\u0000orbits and their invariant manifolds, as well as newly bifurcated transit and\u0000non-transit orbits. This unified analytical framework provides a more\u0000comprehensive understanding of the complex phase space structures near\u0000collinear libration points in the CRTBP.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140316214","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}
Stephen Ebert, Christian Ferko, Cian Luke Martin, Gabriele Tartaglino-Mazzucchelli
We study interacting theories of $N$ left-moving and $overline{N}$ right-moving Floreanini-Jackiw bosons in two dimensions. A parameterized family of such theories is shown to enjoy (non-manifest) Lorentz invariance if and only if its Lagrangian obeys a flow equation driven by a function of the energy-momentum tensor. We discuss the canonical quantization of such theories along classical stress tensor flows, focusing on the case of the root-$T overline{T}$ deformation, where we obtain perturbative results for the deformed spectrum in a certain large-momentum limit. In the special case $N = overline{N}$, we consider the quantum effective action for the root-$T overline{T}$-deformed theory by expanding around a general classical background, and we find that the one-loop contribution vanishes for backgrounds with constant scalar gradients. Our analysis can also be interpreted via dual $U(1)$ Chern-Simons theories in three dimensions, which might be used to describe deformations of charged $mathrm{AdS}_3$ black holes or quantum Hall systems.
{"title":"Flows in the Space of Interacting Chiral Boson Theories","authors":"Stephen Ebert, Christian Ferko, Cian Luke Martin, Gabriele Tartaglino-Mazzucchelli","doi":"arxiv-2403.18242","DOIUrl":"https://doi.org/arxiv-2403.18242","url":null,"abstract":"We study interacting theories of $N$ left-moving and $overline{N}$\u0000right-moving Floreanini-Jackiw bosons in two dimensions. A parameterized family\u0000of such theories is shown to enjoy (non-manifest) Lorentz invariance if and\u0000only if its Lagrangian obeys a flow equation driven by a function of the\u0000energy-momentum tensor. We discuss the canonical quantization of such theories\u0000along classical stress tensor flows, focusing on the case of the root-$T\u0000overline{T}$ deformation, where we obtain perturbative results for the\u0000deformed spectrum in a certain large-momentum limit. In the special case $N =\u0000overline{N}$, we consider the quantum effective action for the root-$T\u0000overline{T}$-deformed theory by expanding around a general classical\u0000background, and we find that the one-loop contribution vanishes for backgrounds\u0000with constant scalar gradients. Our analysis can also be interpreted via dual\u0000$U(1)$ Chern-Simons theories in three dimensions, which might be used to\u0000describe deformations of charged $mathrm{AdS}_3$ black holes or quantum Hall\u0000systems.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140316110","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}
Fermion functional integrals are calculated for the Dirac operator of a finite real spectral triple. Complex, real and chiral functional integrals are considered for each KO-dimension where they are non-trivial, and phase ambiguities in the definition are noted.
对无穷实谱三重的狄拉克算子计算了费米子函数积分。对每个 KO 维度的复积分、实积分和手性功能积分进行了非三维考虑，并指出了定义中的相位差。
{"title":"Fermion integrals for finite spectral triples","authors":"John W. Barrett","doi":"arxiv-2403.18428","DOIUrl":"https://doi.org/arxiv-2403.18428","url":null,"abstract":"Fermion functional integrals are calculated for the Dirac operator of a\u0000finite real spectral triple. Complex, real and chiral functional integrals are\u0000considered for each KO-dimension where they are non-trivial, and phase\u0000ambiguities in the definition are noted.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140316127","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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