Pub Date : 2022-01-05DOI: 10.1142/s0129055x23500277
Xiao-Wei Han, Giovanni Landi, Yang Liu
We present two classes of examples of Hopf algebroids associated with noncommutative principal bundles. The first comes from deforming the principal bundle while leaving unchanged the structure Hopf algebra. The second is related to deforming a quantum homogeneous space; this needs a careful deformation of the structure Hopf algebra in order to preserve the compatibilities between the Hopf algebra operations.
{"title":"Hopf Algebroids from Noncommutative Bundles","authors":"Xiao-Wei Han, Giovanni Landi, Yang Liu","doi":"10.1142/s0129055x23500277","DOIUrl":"https://doi.org/10.1142/s0129055x23500277","url":null,"abstract":"We present two classes of examples of Hopf algebroids associated with noncommutative principal bundles. The first comes from deforming the principal bundle while leaving unchanged the structure Hopf algebra. The second is related to deforming a quantum homogeneous space; this needs a careful deformation of the structure Hopf algebra in order to preserve the compatibilities between the Hopf algebra operations.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48409973","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 : 2022-01-02DOI: 10.1142/S0129055X22500301
F. Fidaleo
In the present note, which is the second part of a work concerning the study of the set of the symmetric states, we introduce the extension of the Klein transformation for general Fermi tensor product of two Z graded C-algebras, under the condition that the grading of one of the involved algebras is inner. After extending the construction to C-inductive limits, such a Klein transformation realises a canonical ∗-isomorphism between two Z-graded C-algebras made of the infinite Fermi C-tensor product AF := ( F N B, F N α ) , and the infinite C-tensor product AX := ( X N B, X N α ) of a single Z-graded C-algebra (B, α), both built with respect to the corresponding minimal C-cross norms. It preserves the grading, and its transpose sends even product states of AX in (necessarily even) product states on AF, and therefore induces an isomorphism of simplexes SP(AF) = SP×Z2(AF) ∼ SP×Z2(AX) , which allows to reduce the study of the structure of the symmetric states for C-Fermi systems to the corresponding even symmetric states on the usual infinite C-tensor product. Other relevant properties of symmetric states on the Fermi algebra will be proved without the use of the Klein transformation. We end with an example for which such a Klein transformation is not implementable, simply because the Fermi tensor product does not generate a usual tensor product. Therefore, in general, the study of the symmetric states on the Fermi algebra cannot be reduced to that of the corresponding symmetric states on the usual infinite tensor product, even if both share many common properties. Mathematics Subject Classification: 46L53, 46L05, 60G09, 46L30, 46N50.
本文是关于对称态集研究的第二部分，在其中一个代数的级数为内的条件下，我们引入了两个Z分次C代数的广义费米张量积的Klein变换的推广。在将构造扩展到C-归纳极限之后，这样的克莱因变换实现了由单个Z-分级C-代数（B，α）的无限Fermi C-张量积AF:=（F N B，F Nα）和无限C张量积AX:=（X N B，X Nα）组成的两个Z-分级C代数之间的正则*-同构，这两个代数都是关于相应的最小C-交叉范数建立的。它保留了分级，并且它的转置在AF上的（必然是偶数的）乘积状态中发送AX的偶数乘积状态，因此诱导了单纯形SP（AF）=SP×Z2。费米代数上对称态的其他相关性质将在不使用克莱因变换的情况下得到证明。我们以一个例子结束，对于这个例子，这样的克莱因变换是不可实现的，仅仅是因为费米张量积不会生成通常的张量积。因此，一般来说，对费米代数上对称态的研究不能简化为对通常的无限张量积上相应对称态的学习，即使两者都有许多共同的性质。数学科目分类：46L53、46L05、60G09、46L30、46N50。
{"title":"Symmetric states for C*-fermi systems","authors":"F. Fidaleo","doi":"10.1142/S0129055X22500301","DOIUrl":"https://doi.org/10.1142/S0129055X22500301","url":null,"abstract":"In the present note, which is the second part of a work concerning the study of the set of the symmetric states, we introduce the extension of the Klein transformation for general Fermi tensor product of two Z graded C-algebras, under the condition that the grading of one of the involved algebras is inner. After extending the construction to C-inductive limits, such a Klein transformation realises a canonical ∗-isomorphism between two Z-graded C-algebras made of the infinite Fermi C-tensor product AF := ( F N B, F N α ) , and the infinite C-tensor product AX := ( X N B, X N α ) of a single Z-graded C-algebra (B, α), both built with respect to the corresponding minimal C-cross norms. It preserves the grading, and its transpose sends even product states of AX in (necessarily even) product states on AF, and therefore induces an isomorphism of simplexes SP(AF) = SP×Z2(AF) ∼ SP×Z2(AX) , which allows to reduce the study of the structure of the symmetric states for C-Fermi systems to the corresponding even symmetric states on the usual infinite C-tensor product. Other relevant properties of symmetric states on the Fermi algebra will be proved without the use of the Klein transformation. We end with an example for which such a Klein transformation is not implementable, simply because the Fermi tensor product does not generate a usual tensor product. Therefore, in general, the study of the symmetric states on the Fermi algebra cannot be reduced to that of the corresponding symmetric states on the usual infinite tensor product, even if both share many common properties. Mathematics Subject Classification: 46L53, 46L05, 60G09, 46L30, 46N50.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48039045","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 : 2022-01-01DOI: 10.1142/s0129055x23500290
J. Bjornberg, Benjamin Lees
We elucidate connections between four models in statistical physics and probability theory: (1) the toric code model of Kitaev, (2) the uniform eight-vertex model, (3) random walk on a hypercube, and (4) a classical Ising model with four-body interaction. As a consequence of our analysis (and of the GKS-inequalities for the Ising model) we obtain correlation inequalities for the toric code model and the uniform eight-vertex model.
{"title":"Correlation Inequalities for the Uniform 8-Vertex Model and the Toric Code Model","authors":"J. Bjornberg, Benjamin Lees","doi":"10.1142/s0129055x23500290","DOIUrl":"https://doi.org/10.1142/s0129055x23500290","url":null,"abstract":"We elucidate connections between four models in statistical physics and probability theory: (1) the toric code model of Kitaev, (2) the uniform eight-vertex model, (3) random walk on a hypercube, and (4) a classical Ising model with four-body interaction. As a consequence of our analysis (and of the GKS-inequalities for the Ising model) we obtain correlation inequalities for the toric code model and the uniform eight-vertex model.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46265785","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 : 2021-12-26DOI: 10.1142/S0129055X22500313
D. Spiegel, J. Moreno, Marvin Qi, M. Hermele, A. Beaudry, M. Pflaum
We consider how the outputs of the Kadison transitivity theorem and Gelfand-Naimark-Segal construction may be obtained in families when the initial data are varied. More precisely, for the Kadison transitivity theorem, we prove that for any nonzero irreducible representation $(mathcal{H}, pi)$ of a $C^*$-algebra $mathfrak{A}$ and $n in mathbb{N}$, there exists a continuous function $A:X rightarrow mathfrak{A}$ such that $pi(A(mathbf{x}, mathbf{y}))x_i = y_i$ for all $i in {1, ldots, n}$, where $X$ is the set of pairs of $n$-tuples $(mathbf{x}, mathbf{y}) in mathcal{H}^n times mathcal{H}^n$ such that the components of $mathbf{x}$ are linearly independent. Versions of this result where $A$ maps into the self-adjoint or unitary elements of $mathfrak{A}$ are also presented. Regarding the Gelfand-Naimark-Segal construction, we prove that given a topological $C^*$-algebra fiber bundle $p:mathfrak{A} rightarrow Y$, one may construct a topological fiber bundle $mathscr{P}(mathfrak{A}) rightarrow Y$ whose fiber over $y in Y$ is the space of pure states of $mathfrak{A}_y$ (with the norm topology), as well as bundles $mathscr{H} rightarrow mathscr{P}(mathfrak{A})$ and $mathscr{N} rightarrow mathscr{P}(mathfrak{A})$ whose fibers $mathscr{H}_omega$ and $mathscr{N}_omega$ over $omega in mathscr{P}(mathfrak{A})$ are the GNS Hilbert space and closed left ideal, respectively, corresponding to $omega$. When $p:mathfrak{A} rightarrow Y$ is a smooth fiber bundle, we show that $mathscr{P}(mathfrak{A}) rightarrow Y$ and $mathscr{H}rightarrow mathscr{P}(mathfrak{A})$ are also smooth fiber bundles; this involves proving that the group of $*$-automorphisms of a $C^*$-algebra is a Banach-Lie group. In service of these results, we review the geometry of the topology and pure state space. A simple non-interacting quantum spin system is provided as an example.
{"title":"Continuous Dependence on the Initial Data in the Kadison Transitivity Theorem and GNS Construction","authors":"D. Spiegel, J. Moreno, Marvin Qi, M. Hermele, A. Beaudry, M. Pflaum","doi":"10.1142/S0129055X22500313","DOIUrl":"https://doi.org/10.1142/S0129055X22500313","url":null,"abstract":"We consider how the outputs of the Kadison transitivity theorem and Gelfand-Naimark-Segal construction may be obtained in families when the initial data are varied. More precisely, for the Kadison transitivity theorem, we prove that for any nonzero irreducible representation $(mathcal{H}, pi)$ of a $C^*$-algebra $mathfrak{A}$ and $n in mathbb{N}$, there exists a continuous function $A:X rightarrow mathfrak{A}$ such that $pi(A(mathbf{x}, mathbf{y}))x_i = y_i$ for all $i in {1, ldots, n}$, where $X$ is the set of pairs of $n$-tuples $(mathbf{x}, mathbf{y}) in mathcal{H}^n times mathcal{H}^n$ such that the components of $mathbf{x}$ are linearly independent. Versions of this result where $A$ maps into the self-adjoint or unitary elements of $mathfrak{A}$ are also presented. Regarding the Gelfand-Naimark-Segal construction, we prove that given a topological $C^*$-algebra fiber bundle $p:mathfrak{A} rightarrow Y$, one may construct a topological fiber bundle $mathscr{P}(mathfrak{A}) rightarrow Y$ whose fiber over $y in Y$ is the space of pure states of $mathfrak{A}_y$ (with the norm topology), as well as bundles $mathscr{H} rightarrow mathscr{P}(mathfrak{A})$ and $mathscr{N} rightarrow mathscr{P}(mathfrak{A})$ whose fibers $mathscr{H}_omega$ and $mathscr{N}_omega$ over $omega in mathscr{P}(mathfrak{A})$ are the GNS Hilbert space and closed left ideal, respectively, corresponding to $omega$. When $p:mathfrak{A} rightarrow Y$ is a smooth fiber bundle, we show that $mathscr{P}(mathfrak{A}) rightarrow Y$ and $mathscr{H}rightarrow mathscr{P}(mathfrak{A})$ are also smooth fiber bundles; this involves proving that the group of $*$-automorphisms of a $C^*$-algebra is a Banach-Lie group. In service of these results, we review the geometry of the topology and pure state space. A simple non-interacting quantum spin system is provided as an example.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47428212","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 : 2021-12-02DOI: 10.1142/s0129055x22300059
W. Wreszinski
We review our approach to the second law of thermodynamics as a theorem assering the growth of the mean (Gibbs-von Neumann) entropy of a class of quantum spin systems undergoing automorphic (unitary) adiabatic transformations. Non-automorphic interactions with the environment, although known to produce on the average a strict reduction of the entropy of systems with finite number of degrees of freedom, are proved to conserve the mean entropy on the average. The results depend crucially on two properties of the mean entropy, proved by Robinson and Ruelle for classical systems, and Lanford and Robinson for quantum lattice systems: upper semicontinuity and affinity.
{"title":"The second law of thermodynamics as a deterministic theorem for quantum spin systems","authors":"W. Wreszinski","doi":"10.1142/s0129055x22300059","DOIUrl":"https://doi.org/10.1142/s0129055x22300059","url":null,"abstract":"We review our approach to the second law of thermodynamics as a theorem assering the growth of the mean (Gibbs-von Neumann) entropy of a class of quantum spin systems undergoing automorphic (unitary) adiabatic transformations. Non-automorphic interactions with the environment, although known to produce on the average a strict reduction of the entropy of systems with finite number of degrees of freedom, are proved to conserve the mean entropy on the average. The results depend crucially on two properties of the mean entropy, proved by Robinson and Ruelle for classical systems, and Lanford and Robinson for quantum lattice systems: upper semicontinuity and affinity.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47484866","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 : 2021-11-07DOI: 10.1142/S0129055X23500101
Yasumichi Matsuzawa, A. Suzuki, Yohei Tanaka, Noriaki Teranishi, K. Wada
It is recently shown that a split-step quantum walk possesses a chiral symmetry, and that a certain well-defined index can be naturally assigned to it. The index is a well-defined Fredholm index if and only if the associated unitary time-evolution operator has spectral gaps at both $+1$ and $-1.$ In this paper we extend the existing index formula for the Fredholm case to encompass the non-Fredholm case (i.e., gapless case). We make use of a natural extension of the Fredholm index to the non-Fredholm case, known as the Witten index. The aim of this paper is to fully classify the Witten index of the split-step quantum walk by employing the spectral shift function for a rank one perturbation of a fourth order difference operator. It is also shown in this paper that the Witten index can take half-integer values in the non-Fredholm case.
{"title":"The Witten index for one-dimensional split-step quantum walks under the non-Fredholm condition","authors":"Yasumichi Matsuzawa, A. Suzuki, Yohei Tanaka, Noriaki Teranishi, K. Wada","doi":"10.1142/S0129055X23500101","DOIUrl":"https://doi.org/10.1142/S0129055X23500101","url":null,"abstract":"It is recently shown that a split-step quantum walk possesses a chiral symmetry, and that a certain well-defined index can be naturally assigned to it. The index is a well-defined Fredholm index if and only if the associated unitary time-evolution operator has spectral gaps at both $+1$ and $-1.$ In this paper we extend the existing index formula for the Fredholm case to encompass the non-Fredholm case (i.e., gapless case). We make use of a natural extension of the Fredholm index to the non-Fredholm case, known as the Witten index. The aim of this paper is to fully classify the Witten index of the split-step quantum walk by employing the spectral shift function for a rank one perturbation of a fourth order difference operator. It is also shown in this paper that the Witten index can take half-integer values in the non-Fredholm case.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45921890","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 : 2021-10-25DOI: 10.1142/s0129055x22300011
Yalong Cao
The mathematical development of Yang–Mills theory is an extremely fruitful subject. The purpose of this paper is to give non-experts and researchers in interdisciplinary areas a quick overview of some history, key ideas and recent developments in this subject.
{"title":"Yang–Mills theories on geometric spaces","authors":"Yalong Cao","doi":"10.1142/s0129055x22300011","DOIUrl":"https://doi.org/10.1142/s0129055x22300011","url":null,"abstract":"The mathematical development of Yang–Mills theory is an extremely fruitful subject. The purpose of this paper is to give non-experts and researchers in interdisciplinary areas a quick overview of some history, key ideas and recent developments in this subject.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48587316","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 : 2021-10-21DOI: 10.1142/s0129055x22300060
Miguel Angel Berbel, M. L'opez
Rigid body with rotors is a widespread mechanical system modeled after the direct product SO(3)×S×S×S, which under mild assumptions is the symmetry group of the system. In this paper, the authors present and compare different Lagrangian reduction procedures: Euler-Poincaré reduction by the whole group and reduction by stages in different orders or using different connections. The exposition keeps track of the equivalence of equations as well as corresponding conservation laws. Mathematics Subject Classification 2020: Primary 70E05; Secondary 37J51, 70G65.
{"title":"Rigid Body with Rotors and Reduction by Stages","authors":"Miguel Angel Berbel, M. L'opez","doi":"10.1142/s0129055x22300060","DOIUrl":"https://doi.org/10.1142/s0129055x22300060","url":null,"abstract":"Rigid body with rotors is a widespread mechanical system modeled after the direct product SO(3)×S×S×S, which under mild assumptions is the symmetry group of the system. In this paper, the authors present and compare different Lagrangian reduction procedures: Euler-Poincaré reduction by the whole group and reduction by stages in different orders or using different connections. The exposition keeps track of the equivalence of equations as well as corresponding conservation laws. Mathematics Subject Classification 2020: Primary 70E05; Secondary 37J51, 70G65.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45591034","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 : 2021-10-01DOI: 10.1142/s0129055x2350006x
M. Falconi, Nikolai Leopold, D. Mitrouskas, S. Petrat
We study the time evolution of the Nelson model in a mean-field limit in which N nonrelativistic bosons weakly couple (w.r.t. the particle number) to a positive or zero mass quantized scalar field. Our main result is the derivation of the Bogoliubov dynamics and higher-order corrections. More precisely, we prove the convergence of the approximate wave function to the many-body wave function in norm, with a convergence rate proportional to the number of corrections taken into account in the approximation. We prove an analogous result for the unitary propagator. As an application, we derive a simple system of PDEs describing the time evolution of the firstand second-order approximation to the one-particle reduced density matrices of the particles and the quantum field, respectively. MSC class: 35Q40, 35Q55, 81Q05, 81T10, 81V73, 82C10
{"title":"Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model","authors":"M. Falconi, Nikolai Leopold, D. Mitrouskas, S. Petrat","doi":"10.1142/s0129055x2350006x","DOIUrl":"https://doi.org/10.1142/s0129055x2350006x","url":null,"abstract":"We study the time evolution of the Nelson model in a mean-field limit in which N nonrelativistic bosons weakly couple (w.r.t. the particle number) to a positive or zero mass quantized scalar field. Our main result is the derivation of the Bogoliubov dynamics and higher-order corrections. More precisely, we prove the convergence of the approximate wave function to the many-body wave function in norm, with a convergence rate proportional to the number of corrections taken into account in the approximation. We prove an analogous result for the unitary propagator. As an application, we derive a simple system of PDEs describing the time evolution of the firstand second-order approximation to the one-particle reduced density matrices of the particles and the quantum field, respectively. MSC class: 35Q40, 35Q55, 81Q05, 81T10, 81V73, 82C10","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46665547","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 : 2021-08-29DOI: 10.1142/S0129055X22500234
H. Mizutani, N. Schiavone
In this paper we are interested in generalizing Keller-type eigenvalue estimates for the non-selfadjoint Schr"{o}dinger operator to the Dirac operator, imposing some suitable rigidity conditions on the matricial structure of the potential, without necessarily requiring the smallness of its norm.
{"title":"Spectral enclosures for Dirac operators perturbed by rigid potentials","authors":"H. Mizutani, N. Schiavone","doi":"10.1142/S0129055X22500234","DOIUrl":"https://doi.org/10.1142/S0129055X22500234","url":null,"abstract":"In this paper we are interested in generalizing Keller-type eigenvalue estimates for the non-selfadjoint Schr\"{o}dinger operator to the Dirac operator, imposing some suitable rigidity conditions on the matricial structure of the potential, without necessarily requiring the smallness of its norm.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48550743","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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