This paper is concerned with the existence of solutions to the Kirchhoff-type equation −a+b∫R3|∇u|2Δu+(V+λ)u=|u|p−2u+μ|u|q−2uinR3 under the normalized constraint ∫R3u2=ρ2, where a, b, ρ > 0, 14/3 < q < p ⩽ 6, μ > 0 is a constant, and λ∈R appears as a Lagrange multiplier. Under an explicit assumption on V, we can prove the existence of positive ground state solutions to the above equation. A new concentration compactness type result is established to recover compactness in the Sobolev critical case.
{"title":"Normalized solutions to the mass supercritical Kirchhoff-type equation with non-trapping potential","authors":"T. Rong, Fuyi Li","doi":"10.1063/5.0155818","DOIUrl":"https://doi.org/10.1063/5.0155818","url":null,"abstract":"This paper is concerned with the existence of solutions to the Kirchhoff-type equation −a+b∫R3|∇u|2Δu+(V+λ)u=|u|p−2u+μ|u|q−2uinR3 under the normalized constraint ∫R3u2=ρ2, where a, b, ρ > 0, 14/3 < q < p ⩽ 6, μ > 0 is a constant, and λ∈R appears as a Lagrange multiplier. Under an explicit assumption on V, we can prove the existence of positive ground state solutions to the above equation. A new concentration compactness type result is established to recover compactness in the Sobolev critical case.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"86 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85873171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work is concerned with the notion of eigenstates for C*-algebras. After reviewing some basic and structural results, we explore the possibility of reinterpreting certain typical concepts of quantum mechanics (e.g., dynamical equilibrium states, ground states, gapped states, Fermi surfaces) in terms of (algebraic) eigenstates.
{"title":"About the notion of eigenstates for C*-algebras and some application in quantum mechanics","authors":"G. De Nittis, Danilo Polo Ojito","doi":"10.1063/5.0153219","DOIUrl":"https://doi.org/10.1063/5.0153219","url":null,"abstract":"This work is concerned with the notion of eigenstates for C*-algebras. After reviewing some basic and structural results, we explore the possibility of reinterpreting certain typical concepts of quantum mechanics (e.g., dynamical equilibrium states, ground states, gapped states, Fermi surfaces) in terms of (algebraic) eigenstates.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"5 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85937455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We give a short account of our new approach to study models in the Kardar–Parisi–Zhang universality class by connecting them to free fermions at positive temperature. Our ideas and methods are explained mainly for the semi-discrete directed polymer model due to O’Connell and Yor.
我们给出了一个简短的叙述，我们的新方法，研究模型在kardar - paris - zhang普适类连接到自由费米子在正温度。本文主要针对O 'Connell和Yor的半离散定向聚合物模型阐述了我们的思想和方法。
{"title":"New approach to KPZ models through free fermions at positive temperature","authors":"T. Imamura, Matteo Mucciconi, T. Sasamoto","doi":"10.1063/5.0089778","DOIUrl":"https://doi.org/10.1063/5.0089778","url":null,"abstract":"We give a short account of our new approach to study models in the Kardar–Parisi–Zhang universality class by connecting them to free fermions at positive temperature. Our ideas and methods are explained mainly for the semi-discrete directed polymer model due to O’Connell and Yor.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"117 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75865524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. Eom, M. Machida, G. Nakamura, G. Nishimura, C. L. Sun
Light propagation through diffusive media can be described by the diffusion equation in a space–time domain. Furthermore, fluorescence can be described by a system of coupled diffusion equations. This paper analyzes time-domain measurements. In particular, the temporal point-spread function is measured at the boundary of a diffusive medium. Moreover, the temporal profile of fluorescence is considered. In both cases, we refer to the maximum temporal position of measured light as the peak time. In this paper, we provide proofs of the existence and uniqueness of the peak time and give explicit expressions of the peak time. The relationship between the peak time and the object position in a medium is clarified.
{"title":"Expressions of the peak time for time-domain boundary measurements of diffuse light","authors":"J. Eom, M. Machida, G. Nakamura, G. Nishimura, C. L. Sun","doi":"10.1063/5.0081169","DOIUrl":"https://doi.org/10.1063/5.0081169","url":null,"abstract":"Light propagation through diffusive media can be described by the diffusion equation in a space–time domain. Furthermore, fluorescence can be described by a system of coupled diffusion equations. This paper analyzes time-domain measurements. In particular, the temporal point-spread function is measured at the boundary of a diffusive medium. Moreover, the temporal profile of fluorescence is considered. In both cases, we refer to the maximum temporal position of measured light as the peak time. In this paper, we provide proofs of the existence and uniqueness of the peak time and give explicit expressions of the peak time. The relationship between the peak time and the object position in a medium is clarified.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"145 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77495562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
An equilibrium point of a differential system in R3 such that the eigenvalues of the Jacobian matrix of the system at the equilibrium are 0 and ±ωi with ω > 0 is called a zero-Hopf equilibrium point. First, we prove that the Chua’s circuit can have three zero-Hopf equilibria varying its three parameters. Later, we show that from the zero-Hopf equilibrium point localized at the origin of coordinates can bifurcate one periodic orbit. Moreover, we provide an analytic estimation of the expression of this periodic orbit and we have determined the kind of the stability of the periodic orbit in function of the parameters of the perturbation. The tool used for proving these results is the averaging theory of second order.
{"title":"Zero-Hopf bifurcation in the Chua’s circuit","authors":"J. Ginoux, J. Llibre","doi":"10.1063/5.0137020","DOIUrl":"https://doi.org/10.1063/5.0137020","url":null,"abstract":"An equilibrium point of a differential system in R3 such that the eigenvalues of the Jacobian matrix of the system at the equilibrium are 0 and ±ωi with ω > 0 is called a zero-Hopf equilibrium point. First, we prove that the Chua’s circuit can have three zero-Hopf equilibria varying its three parameters. Later, we show that from the zero-Hopf equilibrium point localized at the origin of coordinates can bifurcate one periodic orbit. Moreover, we provide an analytic estimation of the expression of this periodic orbit and we have determined the kind of the stability of the periodic orbit in function of the parameters of the perturbation. The tool used for proving these results is the averaging theory of second order.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"9 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79243910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study the initial value problem for the generalized Boussineq equation with weak damping. The existence and time-decay rates of global solutions and its derivatives are established for all space dimensions d ≥ 1, provided that the norm of the initial data is suitably small. The negative Sobolev norms of the initial data in low frequency are shown to be preserved along time evolution and enhance the decay rates of global solutions. The proof is based on the energy method and flexible interpolation trick without investigating the corresponding linear equation.
{"title":"Global existence and time-decay rates of solutions to the generalized Boussinesq equation with weak damping","authors":"Yinxia Wang, Zehua Luo, Dan Li","doi":"10.1063/5.0135436","DOIUrl":"https://doi.org/10.1063/5.0135436","url":null,"abstract":"In this paper, we study the initial value problem for the generalized Boussineq equation with weak damping. The existence and time-decay rates of global solutions and its derivatives are established for all space dimensions d ≥ 1, provided that the norm of the initial data is suitably small. The negative Sobolev norms of the initial data in low frequency are shown to be preserved along time evolution and enhance the decay rates of global solutions. The proof is based on the energy method and flexible interpolation trick without investigating the corresponding linear equation.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"58 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78365597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We are concerned with the global structure of the radial positive solution set of the radially symmetric prescribed curvature problem with the Neumann boundary condition in some Friedmann–Lemaître–Robertson–Walker spacetimes. The proof of our main result is based on bifurcation techniques.
{"title":"Global bifurcation of positive solutions of a quasilinear indefinite Neumann problem in some FLRW spacetimes","authors":"Zhongzi Zhao, R. Ma","doi":"10.1063/5.0145781","DOIUrl":"https://doi.org/10.1063/5.0145781","url":null,"abstract":"We are concerned with the global structure of the radial positive solution set of the radially symmetric prescribed curvature problem with the Neumann boundary condition in some Friedmann–Lemaître–Robertson–Walker spacetimes. The proof of our main result is based on bifurcation techniques.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"123 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76719956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We construct a new exact solution that represents a Pollard-like, three-dimensional, nonlinear internal wave propagating on a uniform zonal current in the presence of the Earth’s rotation. The solution is presented in Lagrangian coordinates, and in the process, we derive a dispersion relation for the internal waves in a stably stratified ocean. We show that the presence of a mean zonal current produces an intrinsically nonlinear mode of wave motion, representing a slow, inertial, internal wave.
{"title":"Exact internal waves in the presence of mean currents and rotation","authors":"Jordan McCarney","doi":"10.1063/5.0155193","DOIUrl":"https://doi.org/10.1063/5.0155193","url":null,"abstract":"We construct a new exact solution that represents a Pollard-like, three-dimensional, nonlinear internal wave propagating on a uniform zonal current in the presence of the Earth’s rotation. The solution is presented in Lagrangian coordinates, and in the process, we derive a dispersion relation for the internal waves in a stably stratified ocean. We show that the presence of a mean zonal current produces an intrinsically nonlinear mode of wave motion, representing a slow, inertial, internal wave.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"23 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88341530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we constructively solve the Riemann problem for the relativistic Euler equations with the logarithmic equation of state. The concentration and cavitation phenomena are observed and analyzed during the process of vanishing pressure in the Riemann solutions. It is rigorously proved that, as the pressure vanishes, they tend to the two kinds of Riemann solutions to the zero-pressure relativistic Euler equations, which include a delta shock formed by a weighted δ-measure and a vacuum state.
{"title":"Concentration and cavitation in the vanishing pressure limit of solutions to the relativistic Euler equations with the logarithmic equation of state","authors":"Zhoutong Lei, Z. Shao","doi":"10.1063/5.0157277","DOIUrl":"https://doi.org/10.1063/5.0157277","url":null,"abstract":"In this paper, we constructively solve the Riemann problem for the relativistic Euler equations with the logarithmic equation of state. The concentration and cavitation phenomena are observed and analyzed during the process of vanishing pressure in the Riemann solutions. It is rigorously proved that, as the pressure vanishes, they tend to the two kinds of Riemann solutions to the zero-pressure relativistic Euler equations, which include a delta shock formed by a weighted δ-measure and a vacuum state.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82667580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Charged massive scalar fields on charged black hole backgrounds are investigated through methods of spectral analysis in Krein spaces. We consider, on the three charged black hole backgrounds (Nariai, Reissner-Nordström, ultracold-II) taken into account, a necessary condition for the existence of complex eigenvalues. We show that even if it is satisfied, in two cases (Nariai and ultracold-II), by direct calculation, they actually cannot exist. In both cases, the Klein paradox occurs without restriction on the parameters. In the third case, the condition for their existence is shown to coincide with the condition, allowing the quantum discharge phenomenon associated with the Klein paradox. We also clarify the role of “classical potentials,” which appear in the physical literature on the subject, giving rise to the so-called level-crossing appearing in semiclassical calculations, and we comment on problems occurring in quantum field theory in the presence of complex eigenvalues.
{"title":"Spectral properties for the Klein-Gordon Hamiltonian in charged black hole backgrounds","authors":"F. Belgiorno, S. Cacciatori","doi":"10.1063/5.0137054","DOIUrl":"https://doi.org/10.1063/5.0137054","url":null,"abstract":"Charged massive scalar fields on charged black hole backgrounds are investigated through methods of spectral analysis in Krein spaces. We consider, on the three charged black hole backgrounds (Nariai, Reissner-Nordström, ultracold-II) taken into account, a necessary condition for the existence of complex eigenvalues. We show that even if it is satisfied, in two cases (Nariai and ultracold-II), by direct calculation, they actually cannot exist. In both cases, the Klein paradox occurs without restriction on the parameters. In the third case, the condition for their existence is shown to coincide with the condition, allowing the quantum discharge phenomenon associated with the Klein paradox. We also clarify the role of “classical potentials,” which appear in the physical literature on the subject, giving rise to the so-called level-crossing appearing in semiclassical calculations, and we comment on problems occurring in quantum field theory in the presence of complex eigenvalues.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"42 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73556317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：