Annales Henri Poincaré最新文献

{"title":"Pleijel’s Theorem for Schrödinger Operators","authors":"Philippe Charron,&nbsp;Corentin Léna","doi":"10.1007/s00023-024-01536-w","DOIUrl":"10.1007/s00023-024-01536-w","url":null,"abstract":"<div><p>We are concerned in this paper with the real eigenfunctions of Schrödinger operators. We prove an asymptotic upper bound for the number of their nodal domains, which implies in particular that the inequality stated in Courant’s theorem is strict, except for finitely many eigenvalues. Results of this type originated in 1956 with Pleijel’s theorem on the Dirichlet Laplacian and were obtained for some classes of Schrödinger operators by the first author, alone and in collaboration with B. Helffer and T. Hoffmann-Ostenhof. Using methods in part inspired by work of the second author on Neumann and Robin Laplacians, we greatly extend the scope of these previous results.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 3","pages":"759 - 786"},"PeriodicalIF":1.4,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01536-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143726718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generalized Pentagon Equations","authors":"Anton Alekseev,&nbsp;Florian Naef,&nbsp;Muze Ren","doi":"10.1007/s00023-024-01523-1","DOIUrl":"10.1007/s00023-024-01523-1","url":null,"abstract":"<div><p>Drinfeld defined the Knizhnik–Zamolodchikov (KZ) associator <span>(Phi _{textrm{KZ}})</span> by considering the regularized holonomy of the KZ connection along the <i>droit chemin</i> [0, 1]. The KZ associator is a group-like element of the free associative algebra with two generators, and it satisfies the pentagon equation. In this paper, we consider paths on <span>({mathbb {C}}backslash { z_1, dots , z_n})</span> which start and end at tangential base points. These paths are not necessarily straight, and they may have a finite number of transversal self-intersections. We show that the regularized holonomy <i>H</i> of the KZ connection associated with such a path satisfies a generalization of Drinfeld’s pentagon equation. In this equation, we encounter <i>H</i>, <span>(Phi _{textrm{KZ}})</span>, and new factors associated with self-intersections, tangential base points, and the rotation number of the path.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 3","pages":"877 - 894"},"PeriodicalIF":1.4,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01523-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143726655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Convergence of Bipartite Open Quantum Systems Stabilized by Reservoir Engineering","authors":"Rémi Robin,&nbsp;Pierre Rouchon,&nbsp;Lev-Arcady Sellem","doi":"10.1007/s00023-024-01481-8","DOIUrl":"10.1007/s00023-024-01481-8","url":null,"abstract":"<div><p>We study a generic family of Lindblad master equations modeling bipartite open quantum systems, where one tries to stabilize a quantum system by carefully designing its interaction with another, dissipative, quantum system—a strategy known as <i>quantum reservoir engineering</i>. We provide sufficient conditions for convergence of the considered Lindblad equations; our setting accommodates the case where steady-states are not unique but rather supported on a given subspace of the underlying Hilbert space. We apply our result to a Lindblad master equation modeling engineered multi-photon emission and absorption processes, a setting that received considerable attention in recent years due to its potential applications for the stabilization of so-called <i>cat qubits</i>.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 5","pages":"1769 - 1819"},"PeriodicalIF":1.4,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143925688","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}

{"title":"Lieb–Robinson Bounds in the Continuum Via Localized Frames","authors":"Sven Bachmann,&nbsp;Giuseppe De Nittis","doi":"10.1007/s00023-024-01511-5","DOIUrl":"10.1007/s00023-024-01511-5","url":null,"abstract":"<div><p>We study the dynamics of interacting fermions in the continuum. Our approach uses the concept of lattice-localized frames, which we introduce here. We first prove a Lieb-Robinson bound that is valid for a general class of local interactions, which implies the existence of the dynamics at the level of the CAR algebra. We then turn to the physical situation relevant to the (fractional) quantum Hall effect, namely the quasi-free second quantized Landau Hamiltonian to which electron–electron interactions can be added.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 1","pages":"1 - 40"},"PeriodicalIF":1.4,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143184743","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}

{"title":"Correction to: Free Energy Fluctuations of the Bipartite Spherical SK Model at Critical Temperature","authors":"Elizabeth W. Collins-Woodfin,&nbsp;Han Gia Le","doi":"10.1007/s00023-024-01498-z","DOIUrl":"10.1007/s00023-024-01498-z","url":null,"abstract":"","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 2","pages":"755 - 756"},"PeriodicalIF":1.4,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143423043","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}

{"title":"A New Gauge for Gravitational Perturbations of Kerr Spacetimes I: The Linearised Theory","authors":"Gabriele Benomio","doi":"10.1007/s00023-024-01472-9","DOIUrl":"10.1007/s00023-024-01472-9","url":null,"abstract":"<div><p>We propose a new geometric framework to address the stability of the Kerr solution to gravitational perturbations in the full sub-extremal range <span>(|a|&lt;M)</span>. Central to our framework is a new formulation of nonlinear gravitational perturbations of Kerr, whose two novel ingredients are the choice of a geometric gauge and non-integrable null frames both tailored to the <i>outgoing principal null geodesics</i> of Kerr. The vacuum Einstein equations for the perturbations are formulated in our gauge as a system of equations for the connection coefficients and curvature components relative to the chosen frames. When renormalised with respect to Kerr, the null structure equations with the form of <i>outgoing</i> transport equations do <i>not</i> possess any derivatives of renormalised connection coefficients on the right hand side. In this work, we derive the linearised vacuum Einstein equations around Kerr in the new framework. The system of linearised gravity exhibits two key structural properties. The first is well-known and consists of the exact decoupling of two <i>gauge invariant</i> linearised quantities in the system, satisfying two decoupled spin <span>(pm , 2)</span> Teukolsky equations. The second is a <i>new</i>, <i>gauge dependent</i> structure in the <i>outgoing</i> transport equations for the linearised connection coefficients inherited from the nonlinear system: Unlike previous works, these equations do <i>not</i> contain any derivatives of linearised connection coefficients on the right hand side and induce a <i>new hierarchy</i> of only outgoing transport equations including all gauge dependent linearised quantities. Our new framework is designed to effectively capture the stabilising properties of the <i>red-shifted</i> transport equations, thereby isolating one of the crucial structures of the problem. Such a feature is suggestive of future simplifications in the analysis. As an illustration, our companion work (Benomio in A new gauge for gravitational perturbations of Kerr spacetimes II: The linear stability of Schwarzschild revisited, 2022) employs the system of linearised gravity and its enhanced red-shifted transport equations, specialised to the <span>(|a|=0)</span> case, to produce a new simplified proof of linear stability of the Schwarzschild solution. The full linear stability analysis in the full sub-extremal range <span>(|a|&lt;M)</span> is deferred to future work. As already apparent from (Benomio 2022), our framework will allow to combine the new structure in the transport equations with the elliptic part of the system to establish a linear orbital stability result <i>without loss of derivatives</i>, indicating that the framework may be well suited to address nonlinear stability in the full sub-extremal range <span>(|a|&lt;M)</span>.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 5","pages":"1573 - 1731"},"PeriodicalIF":1.4,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01472-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143925486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Interpolating Between Rényi Entanglement Entropies for Arbitrary Bipartitions via Operator Geometric Means","authors":"Dávid Bugár, Péter Vrana","doi":"10.1007/s00023-024-01486-3","DOIUrl":"https://doi.org/10.1007/s00023-024-01486-3","url":null,"abstract":"<p>The asymptotic restriction problem for tensors can be reduced to finding all parameters that are normalized, monotone under restrictions, additive under direct sums and multiplicative under tensor products, the simplest of which are the flattening ranks. Over the complex numbers, a refinement of this problem, originating in the theory of quantum entanglement, is to find the optimal rate of entanglement transformations as a function of the error exponent. This trade-off can also be characterized in terms of the set of normalized, additive, multiplicative functionals that are monotone in a suitable sense, which includes the restriction-monotones as well. For example, the flattening ranks generalize to the (exponentiated) Rényi entanglement entropies of order <span>(alpha in [0,1])</span>. More complicated parameters of this type are known, which interpolate between the flattening ranks or Rényi entropies for special bipartitions, with one of the parts being a single tensor factor. We introduce a new construction of subadditive and submultiplicative monotones in terms of a regularized Rényi divergence between many copies of the pure state represented by the tensor and a suitable sequence of positive operators. We give explicit families of operators that correspond to the flattening-based functionals, and show that they can be combined in a nontrivial way using weighted operator geometric means. This leads to a new characterization of the previously known additive and multiplicative monotones, and gives new submultiplicative and subadditive monotones that interpolate between the Rényi entropies for all bipartitions. We show that for each such monotone there exist pointwise smaller multiplicative and additive ones as well. In addition, we find lower bounds on the new functionals that are superadditive and supermultiplicative.</p>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"21 1","pages":""},"PeriodicalIF":1.55,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269833","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}

{"title":"Schur Function Expansion in Non-Hermitian Ensembles and Averages of Characteristic Polynomials","authors":"Alexander Serebryakov, Nick Simm","doi":"10.1007/s00023-024-01483-6","DOIUrl":"https://doi.org/10.1007/s00023-024-01483-6","url":null,"abstract":"<p>We study <i>k</i>-point correlators of characteristic polynomials in non-Hermitian ensembles of random matrices, focusing on the Ginibre and truncated unitary random matrices. Our approach is based on the technique of character expansions, which expresses the correlator as a sum over partitions involving Schur functions. We show how to sum the expansions in terms of representations which interchange the role of <i>k</i> with the matrix size <i>N</i>. We also provide a probabilistic interpretation of the character expansion analogous to the Schur measure, linking the correlators to the distribution of the top row in certain Young diagrams. In more specific examples, we evaluate these expressions in terms of <span>(k times k)</span> determinants or Pfaffians.</p>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"110 1","pages":""},"PeriodicalIF":1.55,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216776","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}

{"title":"A Meta Logarithmic-Sobolev Inequality for Phase-Covariant Gaussian Channels","authors":"Salman Beigi, Saleh Rahimi-Keshari","doi":"10.1007/s00023-024-01487-2","DOIUrl":"https://doi.org/10.1007/s00023-024-01487-2","url":null,"abstract":"<p>We introduce a meta logarithmic-Sobolev (log-Sobolev) inequality for the Lindbladian of all single-mode phase-covariant Gaussian channels of bosonic quantum systems and prove that this inequality is saturated by thermal states. We show that our inequality provides a general framework to derive information theoretic results regarding phase-covariant Gaussian channels. Specifically, by using the optimality of thermal states, we explicitly compute the optimal constant <span>(alpha _p)</span>, for <span>(1le ple 2)</span>, of the <i>p</i>-log-Sobolev inequality associated with the quantum Ornstein–Uhlenbeck semigroup. Prior to our work, the optimal constant was only determined for <span>(p=1)</span>. Our meta log-Sobolev inequality also enables us to provide an alternative proof for the constrained minimum output entropy conjecture in the single-mode case. Specifically, we show that for any single-mode phase-covariant Gaussian channel <span>(Phi )</span>, the minimum of the von Neumann entropy <span>(Sbig (Phi (rho )big ))</span> over all single-mode states <span>(rho )</span> with a given lower bound on <span>(S(rho ))</span> is achieved at a thermal state.\u0000</p>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"97 1","pages":""},"PeriodicalIF":1.55,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216787","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}

{"title":"Kac–Ward Solution of the 2D Classical and 1D Quantum Ising Models","authors":"Georgios Athanasopoulos, Daniel Ueltschi","doi":"10.1007/s00023-024-01479-2","DOIUrl":"https://doi.org/10.1007/s00023-024-01479-2","url":null,"abstract":"<p>We give a rigorous derivation of the free energy of (i) the classical Ising model on the triangular lattice with translation-invariant coupling constants and (ii) the one-dimensional quantum Ising model. We use the method of Kac and Ward. The novel aspect is that the coupling constants may have negative signs. We describe the logarithmic singularity of the specific heat of the classical model and the validity of the Cimasoni–Duminil-Copin–Li formula for the critical temperature. We also discuss the quantum phase transition of the quantum model.\u0000</p>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"52 1","pages":""},"PeriodicalIF":1.55,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216779","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}