Pub Date : 2022-09-14DOI: 10.1142/s0129055x22500404
A. Luczak, H. Podsędkowska, Rafał M. Wieczorek
{"title":"Relative and quasi entropies in semifinite von neumann algebras","authors":"A. Luczak, H. Podsędkowska, Rafał M. Wieczorek","doi":"10.1142/s0129055x22500404","DOIUrl":"https://doi.org/10.1142/s0129055x22500404","url":null,"abstract":"","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44025592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-07DOI: 10.1142/s0129055x23500174
S. Herschenfeld, P. Hislop
We use the method of eigenvalue level spacing developed by Dietlein and Elgart (arXiv:1712.03925) to prove that the local eigenvalue statistics (LES) for the Anderson model on $Z^d$, with uniform higher-rank $m geq 2$, single-site perturbations, is given by a Poisson point process with intensity measure $n(E_0)~ds$, where $n(E_0)$ is the density of states at energy $E_0$ in the region of localization near the spectral band edges. This improves the result of Hislop and Krishna (arXiv:1809.01236), who proved that the LES is a compound Poisson process with L'evy measure supported on the set ${1, 2, ldots, m }$. Our proofs are an application of the ideas of Dieltein and Elgart to these higher-rank lattice models with two spectral band edges, and illustrate, in a simpler setting, the key steps of the proof of Dieltein and Elgart.
我们使用Dietlein和Elgart (arXiv:1712.03925)提出的特征值水平间隔方法证明了具有均匀高阶$m geq 2$单点扰动的$Z^d$上的Anderson模型的局部特征值统计量(LES)是由强度测度为$n(E_0)~ds$的泊松点过程给出的，其中$n(E_0)$是谱带边缘附近局域化区域中能量$E_0$处的态密度。这改进了Hislop和Krishna (arXiv:1809.01236)证明LES是在集合${1, 2, ldots, m }$上支持lsamvy测度的复合泊松过程的结果。我们的证明是Dieltein和Elgart的思想在这些具有两个谱带边缘的高阶晶格模型中的应用，并在一个更简单的设置中说明了Dieltein和Elgart证明的关键步骤。
{"title":"Local Eigenvalue Statistics for Higher-Rank Anderson Models After Dietlein-Elgart","authors":"S. Herschenfeld, P. Hislop","doi":"10.1142/s0129055x23500174","DOIUrl":"https://doi.org/10.1142/s0129055x23500174","url":null,"abstract":"We use the method of eigenvalue level spacing developed by Dietlein and Elgart (arXiv:1712.03925) to prove that the local eigenvalue statistics (LES) for the Anderson model on $Z^d$, with uniform higher-rank $m geq 2$, single-site perturbations, is given by a Poisson point process with intensity measure $n(E_0)~ds$, where $n(E_0)$ is the density of states at energy $E_0$ in the region of localization near the spectral band edges. This improves the result of Hislop and Krishna (arXiv:1809.01236), who proved that the LES is a compound Poisson process with L'evy measure supported on the set ${1, 2, ldots, m }$. Our proofs are an application of the ideas of Dieltein and Elgart to these higher-rank lattice models with two spectral band edges, and illustrate, in a simpler setting, the key steps of the proof of Dieltein and Elgart.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"43 21","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41298002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-27DOI: 10.1142/S0129055X23500010
H. Sati, U. Schreiber
While the classification of noninteracting crystalline topological insulator phases by equivariant K-theory has become widely accepted, its generalization to anyonic interacting phases — hence to phases with topologically ordered ground states supporting topological braid quantum gates — has remained wide open. On the contrary, the success of K-theory with classifying noninteracting phases seems to have tacitly been perceived as precluding a K-theoretic classification of interacting topological order; and instead a mix of other proposals has been explored. However, only K-theory connects closely to the actual physics of valence electrons; and self-consistency demands that any other proposal must connect to K-theory. Here, we provide a detailed argument for the classification of symmetry protected/enhanced [Formula: see text]-anyonic topological order, specifically in interacting 2d semi-metals, by the twisted equivariant differential (TED) K-theory of configuration spaces of points in the complement of nodal points inside the crystal’s Brillouin torus orbi-orientifold. We argue, in particular, that: (1) topological 2d semi-metal phases modulo global mass terms are classified by the flat differential twisted equivariant K-theory of the complement of the nodal points; (2) [Formula: see text]-electron interacting phases are classified by the K-theory of configuration spaces of [Formula: see text] points in the Brillouin torus; (3) the somewhat neglected twisting of equivariant K-theory by “inner local systems” reflects the effective “fictitious” gauge interaction of Chen, Wilczeck, Witten and Halperin (1989), which turns fermions into anyonic quanta; (4) the induced [Formula: see text]-anyonic topological order is reflected in the twisted Chern classes of the interacting valence bundle over configuration space, constituting the hypergeometric integral construction of monodromy braid representations. A tight dictionary relates these arguments to those for classifying defect brane charges in string theory [H. Sati and U. Schreiber, Anyonic defect branes in TED-K-theory, arXiv:2203.11838], which we expect to be the images of momentum-space [Formula: see text]-anyons under a nonperturbative version of the AdS/CMT correspondence.
虽然用等变k理论对非相互作用晶体拓扑绝缘体相进行分类已被广泛接受，但将其推广到任意相互作用相——因此推广到具有拓扑有序基态支持拓扑编织量子门的相——仍然存在很大的开放性。相反，k理论在分类非相互作用相方面的成功似乎被默认为排除了k理论对相互作用拓扑顺序的分类;取而代之的是一系列其他的建议。然而，只有k理论与价电子的实际物理学密切相关;自洽要求任何其他提议都必须与k理论相联系。在这里，我们提供了一个详细的论点来分类对称保护/增强[公式:见文本]-任意子拓扑秩序，特别是在相互作用的二维半金属中，通过扭曲等变微分(TED) k -理论在晶体的布里温环面轨道取向褶内的节点补中的点的构型空间。特别地，我们论证了:(1)拓扑二维半金属相位模整体质量项由节点补的平微分扭曲等变k理论分类;(2)[公式:见文]-用布里渊环面上[公式:见文]点的构型空间k理论对电子相互作用相进行分类;(3)“内局域系统”对等变k理论的扭曲反映了Chen、Wilczeck、Witten和Halperin(1989)的有效“虚拟”规范相互作用，它将费米子转变为任意子量子;(4)诱导的[公式:见文]-任意子拓扑序反映在构型空间上相互作用价束的扭曲Chern类中，构成了单编织表示的超几何积分构造。一个紧密字典将这些论点与弦理论中对缺陷膜电荷的分类联系起来[H]。Sati和U. Schreiber, ted - k理论中的任意子缺陷膜，在AdS/CMT对应的非摄动版本下，我们期望它是动量空间-任意子的图像[公式:见文本]。
{"title":"Anyonic topological order in twisted equivariant differential (TED) K-theory","authors":"H. Sati, U. Schreiber","doi":"10.1142/S0129055X23500010","DOIUrl":"https://doi.org/10.1142/S0129055X23500010","url":null,"abstract":"While the classification of noninteracting crystalline topological insulator phases by equivariant K-theory has become widely accepted, its generalization to anyonic interacting phases — hence to phases with topologically ordered ground states supporting topological braid quantum gates — has remained wide open. On the contrary, the success of K-theory with classifying noninteracting phases seems to have tacitly been perceived as precluding a K-theoretic classification of interacting topological order; and instead a mix of other proposals has been explored. However, only K-theory connects closely to the actual physics of valence electrons; and self-consistency demands that any other proposal must connect to K-theory. Here, we provide a detailed argument for the classification of symmetry protected/enhanced [Formula: see text]-anyonic topological order, specifically in interacting 2d semi-metals, by the twisted equivariant differential (TED) K-theory of configuration spaces of points in the complement of nodal points inside the crystal’s Brillouin torus orbi-orientifold. We argue, in particular, that: (1) topological 2d semi-metal phases modulo global mass terms are classified by the flat differential twisted equivariant K-theory of the complement of the nodal points; (2) [Formula: see text]-electron interacting phases are classified by the K-theory of configuration spaces of [Formula: see text] points in the Brillouin torus; (3) the somewhat neglected twisting of equivariant K-theory by “inner local systems” reflects the effective “fictitious” gauge interaction of Chen, Wilczeck, Witten and Halperin (1989), which turns fermions into anyonic quanta; (4) the induced [Formula: see text]-anyonic topological order is reflected in the twisted Chern classes of the interacting valence bundle over configuration space, constituting the hypergeometric integral construction of monodromy braid representations. A tight dictionary relates these arguments to those for classifying defect brane charges in string theory [H. Sati and U. Schreiber, Anyonic defect branes in TED-K-theory, arXiv:2203.11838], which we expect to be the images of momentum-space [Formula: see text]-anyons under a nonperturbative version of the AdS/CMT correspondence.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48674533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-10DOI: 10.1142/S0129055X22500386
Fridolin Melong
In this paper, we construct the super Witt algebra and super Virasoro algebra in the framework of the $mathcal{R}(p,q)$-deformed quantum algebras. Moreover, we perform the super $mathcal{R}(p,q)$-deformed Witt $n$-algebra, the $mathcal{R}(p,q)$-deformed Virasoro $n$-algebra and discuss the super $mathcal{R}(p,q)$-Virasoro $n$-algebra ($n$ even). Besides, we define and construct another super $mathcal{R}(p,q)$-deformed Witt $n$-algebra and study a toy model for the super $mathcal{R}(p,q)$-Virasoro constraints. Relevant particular cases induced from the quantum algebras known in the literature are deduced from the formalism developped.
{"title":"ℛ(p,q)− deformed super Virasoro n− algebras","authors":"Fridolin Melong","doi":"10.1142/S0129055X22500386","DOIUrl":"https://doi.org/10.1142/S0129055X22500386","url":null,"abstract":"In this paper, we construct the super Witt algebra and super Virasoro algebra in the framework of the $mathcal{R}(p,q)$-deformed quantum algebras. Moreover, we perform the super $mathcal{R}(p,q)$-deformed Witt $n$-algebra, the $mathcal{R}(p,q)$-deformed Virasoro $n$-algebra and discuss the super $mathcal{R}(p,q)$-Virasoro $n$-algebra ($n$ even). Besides, we define and construct another super $mathcal{R}(p,q)$-deformed Witt $n$-algebra and study a toy model for the super $mathcal{R}(p,q)$-Virasoro constraints. Relevant particular cases induced from the quantum algebras known in the literature are deduced from the formalism developped.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46006915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-07DOI: 10.1142/S0129055X22500398
U. Rozikov, F. Haydarov
We consider a hard core (HC) model with a countable set $mathbb{Z}$ of spin values on the Cayley tree. This model is defined by a countable set of parameters $lambda_{i}>0, i in mathbb{Z}setminus{0}$. For all possible values of parameters, we give limit points of the dynamical system generated by a function which describes the consistency condition for finite-dimensional measures. Also, we prove that every periodic Gibbs measure for the given model is either translation-invariant or periodic with period two. Moreover, we construct uncountable set of Gibbs measures for this HC model.
{"title":"A HC model with countable set of spin values: uncountable set of Gibbs measures","authors":"U. Rozikov, F. Haydarov","doi":"10.1142/S0129055X22500398","DOIUrl":"https://doi.org/10.1142/S0129055X22500398","url":null,"abstract":"We consider a hard core (HC) model with a countable set $mathbb{Z}$ of spin values on the Cayley tree. This model is defined by a countable set of parameters $lambda_{i}>0, i in mathbb{Z}setminus{0}$. For all possible values of parameters, we give limit points of the dynamical system generated by a function which describes the consistency condition for finite-dimensional measures. Also, we prove that every periodic Gibbs measure for the given model is either translation-invariant or periodic with period two. Moreover, we construct uncountable set of Gibbs measures for this HC model.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48970898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-05DOI: 10.1142/S0129055X2350023X
Truong Xuan Pham
In this paper, we establish the asymptotic behaviour along outgoing and incoming radial geodesics, i.e., the peeling property for the tensorial Fackrell-Ipser and spin $pm 1$ Teukolsky equations on Schwarzschild spacetime. Our method combines a conformal compactification with vector field techniques to prove the two-side estimates of the energies of tensorial fields through the future and past null infinity $mathscr{I}^pm$ and the initial Cauchy hypersurface $Sigma_0 = left{ t=0 right}$ in a neighbourhood of spacelike infinity $i_0$ far away from the horizon and future timelike infinity. Our results obtain the optimal initial data which guarantees the peeling at all orders.
{"title":"Peeling for tensorial wave equations on Schwarzschild spacetime","authors":"Truong Xuan Pham","doi":"10.1142/S0129055X2350023X","DOIUrl":"https://doi.org/10.1142/S0129055X2350023X","url":null,"abstract":"In this paper, we establish the asymptotic behaviour along outgoing and incoming radial geodesics, i.e., the peeling property for the tensorial Fackrell-Ipser and spin $pm 1$ Teukolsky equations on Schwarzschild spacetime. Our method combines a conformal compactification with vector field techniques to prove the two-side estimates of the energies of tensorial fields through the future and past null infinity $mathscr{I}^pm$ and the initial Cauchy hypersurface $Sigma_0 = left{ t=0 right}$ in a neighbourhood of spacelike infinity $i_0$ far away from the horizon and future timelike infinity. Our results obtain the optimal initial data which guarantees the peeling at all orders.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43572656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-13DOI: 10.1142/s0129055x22500246
Y. Suh
{"title":"Yamabe and Gradient Yamabe Solitons in the Complex Hyperbolic Two-Plane Grassmannians","authors":"Y. Suh","doi":"10.1142/s0129055x22500246","DOIUrl":"https://doi.org/10.1142/s0129055x22500246","url":null,"abstract":"","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48070497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-29DOI: 10.1142/S0129055X22500416
Kaito Kawaai, Yugo Maruyama, F. Nakano
We consider Schr"odinger operator with random decaying potential on $ell^2 ({bf Z}^d)$ and showed that, (i) IDS coincides with that of free Laplacian in general cases, and (ii) the set of extremal eigenvalues, after rescaling, converges to a inhomogeneous Poisson process, under certain condition on the single-site distribution, and (iii) there are"border-line"cases, such that we have Poisson statistics in the sense of (ii) above if the potential does not decay, while we do not if the potential does decay.
{"title":"Limiting distribution of extremal eigenvalues of d-dimensional random Schrodinger operator","authors":"Kaito Kawaai, Yugo Maruyama, F. Nakano","doi":"10.1142/S0129055X22500416","DOIUrl":"https://doi.org/10.1142/S0129055X22500416","url":null,"abstract":"We consider Schr\"odinger operator with random decaying potential on $ell^2 ({bf Z}^d)$ and showed that, (i) IDS coincides with that of free Laplacian in general cases, and (ii) the set of extremal eigenvalues, after rescaling, converges to a inhomogeneous Poisson process, under certain condition on the single-site distribution, and (iii) there are\"border-line\"cases, such that we have Poisson statistics in the sense of (ii) above if the potential does not decay, while we do not if the potential does decay.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45772069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-29DOI: 10.1142/S0129055X23500071
M. Bischoff, S. Del Vecchio, L. Giorgetti
On a conformal net $mathcal{A}$, one can consider collections of unital completely positive maps on each local algebra $mathcal{A}(I)$, subject to natural compatibility, vacuum preserving and conformal covariance conditions. We call emph{quantum operations} on $mathcal{A}$ the subset of extreme such maps. The usual automorphisms of $mathcal{A}$ (the vacuum preserving invertible unital *-algebra morphisms) are examples of quantum operations, and we show that the fixed point subnet of $mathcal{A}$ under all quantum operations is the Virasoro net generated by the stress-energy tensor of $mathcal{A}$. Furthermore, we show that every irreducible conformal subnet $mathcal{B}subsetmathcal{A}$ is the fixed points under a subset of quantum operations. When $mathcal{B}subsetmathcal{A}$ is discrete (or with finite Jones index), we show that the set of quantum operations on $mathcal{A}$ that leave $mathcal{B}$ elementwise fixed has naturally the structure of a compact (or finite) hypergroup, thus extending some results of [Bis17]. Under the same assumptions, we provide a Galois correspondence between intermediate conformal nets and closed subhypergroups. In particular, we show that intermediate conformal nets are in one-to-one correspondence with intermediate subfactors, extending a result of Longo in the finite index/completely rational conformal net setting [Lon03].
{"title":"Quantum Operations On Conformal Nets","authors":"M. Bischoff, S. Del Vecchio, L. Giorgetti","doi":"10.1142/S0129055X23500071","DOIUrl":"https://doi.org/10.1142/S0129055X23500071","url":null,"abstract":"On a conformal net $mathcal{A}$, one can consider collections of unital completely positive maps on each local algebra $mathcal{A}(I)$, subject to natural compatibility, vacuum preserving and conformal covariance conditions. We call emph{quantum operations} on $mathcal{A}$ the subset of extreme such maps. The usual automorphisms of $mathcal{A}$ (the vacuum preserving invertible unital *-algebra morphisms) are examples of quantum operations, and we show that the fixed point subnet of $mathcal{A}$ under all quantum operations is the Virasoro net generated by the stress-energy tensor of $mathcal{A}$. Furthermore, we show that every irreducible conformal subnet $mathcal{B}subsetmathcal{A}$ is the fixed points under a subset of quantum operations. When $mathcal{B}subsetmathcal{A}$ is discrete (or with finite Jones index), we show that the set of quantum operations on $mathcal{A}$ that leave $mathcal{B}$ elementwise fixed has naturally the structure of a compact (or finite) hypergroup, thus extending some results of [Bis17]. Under the same assumptions, we provide a Galois correspondence between intermediate conformal nets and closed subhypergroups. In particular, we show that intermediate conformal nets are in one-to-one correspondence with intermediate subfactors, extending a result of Longo in the finite index/completely rational conformal net setting [Lon03].","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43585556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-08DOI: 10.1142/s0129055x22500143
W. Dybalski, A. Pizzo
We consider the massless Nelson model with two types of massive particles which we call atoms and electrons. The atoms interact with photons via an infrared regular form-factor and thus they are Wigner-type particles with sharp mass-shells. The electrons have an infrared singular form-factor and thus they are infraparticles accompanied by soft-photon clouds correlated with their velocities. In the weak coupling regime, we construct scattering states of one atom and one electron, and demonstrate their asymptotic clustering into individual particles. The proof relies on the Cook’s argument, clustering estimates, and the non-stationary phase method. The latter technique requires sharp estimates on derivatives of the ground state wave functions of the fiber Hamiltonians of the model, which were proven in the earlier papers of this series. Although we rely on earlier studies of the atom–atom and electron–photon scattering in the Nelson model, the paper is written in a self-contained manner. A perspective on the open problem of the electron–electron scattering in this model is also given.
{"title":"Coulomb scattering in the massless Nelson model IV. Atom–electron scattering","authors":"W. Dybalski, A. Pizzo","doi":"10.1142/s0129055x22500143","DOIUrl":"https://doi.org/10.1142/s0129055x22500143","url":null,"abstract":"We consider the massless Nelson model with two types of massive particles which we call atoms and electrons. The atoms interact with photons via an infrared regular form-factor and thus they are Wigner-type particles with sharp mass-shells. The electrons have an infrared singular form-factor and thus they are infraparticles accompanied by soft-photon clouds correlated with their velocities. In the weak coupling regime, we construct scattering states of one atom and one electron, and demonstrate their asymptotic clustering into individual particles. The proof relies on the Cook’s argument, clustering estimates, and the non-stationary phase method. The latter technique requires sharp estimates on derivatives of the ground state wave functions of the fiber Hamiltonians of the model, which were proven in the earlier papers of this series. Although we rely on earlier studies of the atom–atom and electron–photon scattering in the Nelson model, the paper is written in a self-contained manner. A perspective on the open problem of the electron–electron scattering in this model is also given.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47033370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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