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New Variants of Arithmetic Quantum Ergodicity
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-02-17 DOI: 10.1007/s00220-024-05203-3
Peter Humphries, Jesse Thorner
{"title":"New Variants of Arithmetic Quantum Ergodicity","authors":"Peter Humphries,&nbsp;Jesse Thorner","doi":"10.1007/s00220-024-05203-3","DOIUrl":"10.1007/s00220-024-05203-3","url":null,"abstract":"<div><p>We establish two new variants of arithmetic quantum ergodicity. The first is for self-dual <span>(textrm{GL}_2)</span> Hecke–Maaß newforms over <span>(mathbb {Q})</span> as the level and Laplace eigenvalue vary jointly. The second is a nonsplit analogue wherein almost all restrictions of Hilbert (respectively Bianchi) Hecke–Maaß cusp forms to the modular surface dissipate as their Laplace eigenvalues grow.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05203-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143430890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
引用次数: 0
On Homological Reduction of Poisson Structures
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-02-17 DOI: 10.1007/s00220-025-05232-6
Pedro H. Carvalho
{"title":"On Homological Reduction of Poisson Structures","authors":"Pedro H. Carvalho","doi":"10.1007/s00220-025-05232-6","DOIUrl":"10.1007/s00220-025-05232-6","url":null,"abstract":"<div><p>Given a <span>({mathfrak {g}})</span>-action on a Poisson manifold <span>((M, pi ))</span> and an equivariant map <span>(J: M rightarrow {{mathfrak {h}}}^*,)</span> for <span>({{mathfrak {h}}})</span> a <span>({mathfrak {g}})</span>-module, we obtain, under natural compatibility and regularity conditions previously considered by Cattaneo–Zambon, a homotopy Poisson algebra generalizing the classical BFV algebra described by Kostant–Sternberg in the usual hamiltonian setting. As an application of our methods, we also derive homological models for the reduced spaces associated to quasi-Poisson and hamiltonian quasi-Poisson spaces.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143430891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
引用次数: 0
New Lower Bounds for the (Near) Critical Ising and (varphi ^4) Models’ Two-Point Functions
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-02-17 DOI: 10.1007/s00220-025-05236-2
Hugo Duminil-Copin, Romain Panis
{"title":"New Lower Bounds for the (Near) Critical Ising and (varphi ^4) Models’ Two-Point Functions","authors":"Hugo Duminil-Copin,&nbsp;Romain Panis","doi":"10.1007/s00220-025-05236-2","DOIUrl":"10.1007/s00220-025-05236-2","url":null,"abstract":"<div><p>We study the nearest-neighbour Ising and <span>(varphi ^4)</span> models on <span>({mathbb {Z}}^d)</span> with <span>(dge 3)</span> and obtain new lower bounds on their two-point functions at (and near) criticality. Together with the classical infrared bound, these bounds turn into up to constant estimates when <span>(dge 5)</span>. When <span>(d=4)</span>, we obtain an “almost” sharp lower bound corrected by a logarithmic factor. As a consequence of these results, we show that <span>(eta =0)</span> and <span>(nu =1/2)</span> when <span>(dge 4)</span>, where <span>(eta )</span> is the critical exponent associated with the decay of the model’s two-point function at criticality and <span>(nu )</span> is the critical exponent of the correlation length <span>(xi (beta ))</span>. When <span>(d=3)</span>, we improve previous results and obtain that <span>(eta le 1/2)</span>. As a byproduct of our proofs, we also derive the blow-up at criticality of the so-called bubble diagram when <span>(d=3,4)</span>.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143430893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
引用次数: 0
Limiting Absorption Principles and Linear Inviscid Damping in the Euler–Boussinesq System in the Periodic Channel
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-02-17 DOI: 10.1007/s00220-024-05224-y
Michele Coti Zelati, Marc Nualart
{"title":"Limiting Absorption Principles and Linear Inviscid Damping in the Euler–Boussinesq System in the Periodic Channel","authors":"Michele Coti Zelati,&nbsp;Marc Nualart","doi":"10.1007/s00220-024-05224-y","DOIUrl":"10.1007/s00220-024-05224-y","url":null,"abstract":"<div><p>We consider the long-time behavior of solutions to the two dimensional non-homogeneous Euler equations under the Boussinesq approximation posed on a periodic channel. We study the linearized system near a linearly stratified Couette flow and prove inviscid damping of the perturbed density and velocity field for any positive Richardson number, with optimal rates. Our methods are based on time-decay properties of oscillatory integrals obtained using a limiting absorption principle, and require a careful understanding of the asymptotic expansion of the generalized eigenfunction near the critical layer. As a by-product of our analysis, we provide a precise description of the spectrum of the linearized operator, which, for sufficiently large Richardson number, consists of an essential spectrum (as expected according to classical hydrodynamic problems) as well as discrete neutral eigenvalues (giving rise to oscillatory modes) accumulating towards the endpoints of the essential spectrum.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05224-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143430892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
引用次数: 0
A Gauss–Bonnet Formula for the Renormalized Area of Minimal Submanifolds of Poincaré–Einstein Manifolds
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-02-17 DOI: 10.1007/s00220-024-05228-8
Jeffrey S. Case, C Robin Graham, Tzu-Mo Kuo, Aaron J. Tyrrell, Andrew Waldron
{"title":"A Gauss–Bonnet Formula for the Renormalized Area of Minimal Submanifolds of Poincaré–Einstein Manifolds","authors":"Jeffrey S. Case,&nbsp;C Robin Graham,&nbsp;Tzu-Mo Kuo,&nbsp;Aaron J. Tyrrell,&nbsp;Andrew Waldron","doi":"10.1007/s00220-024-05228-8","DOIUrl":"10.1007/s00220-024-05228-8","url":null,"abstract":"<div><p>Assuming the extrinsic <i>Q</i>-curvature admits a decomposition into the Pfaffian, a scalar conformal submanifold invariant, and a tangential divergence, we prove that the renormalized area of an even-dimensional minimal submanifold of a Poincaré–Einstein manifold can be expressed as a linear combination of its Euler characteristic and the integral of a scalar conformal submanifold invariant. We derive such a decomposition of the extrinsic <i>Q</i>-curvature in dimensions two and four, thereby recovering and generalizing results of Alexakis–Mazzeo and Tyrrell, respectively. We also conjecture such a decomposition for general natural submanifold scalars whose integral over compact submanifolds is conformally invariant, and verify our conjecture in dimensions two and four. Our results also apply to the area of a compact even-dimensional minimal submanifold of an Einstein manifold.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143430952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
引用次数: 0
Exponential Mixing and Limit Theorems of Quasi-periodically Forced 2D Stochastic Navier–Stokes Equations in the Hypoelliptic Setting
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-02-17 DOI: 10.1007/s00220-025-05231-7
Rongchang Liu, Kening Lu
{"title":"Exponential Mixing and Limit Theorems of Quasi-periodically Forced 2D Stochastic Navier–Stokes Equations in the Hypoelliptic Setting","authors":"Rongchang Liu,&nbsp;Kening Lu","doi":"10.1007/s00220-025-05231-7","DOIUrl":"10.1007/s00220-025-05231-7","url":null,"abstract":"<div><p>We consider the incompressible 2D Navier–Stokes equations on the torus driven by a deterministic time quasi-periodic force and a noise that is white in time and degenerate in Fourier space. We show that the asymptotic statistical behavior is characterized by a quasi-periodic invariant measure that exponentially attracts the law of all solutions. The result is true for any value of the viscosity <span>(nu &gt;0)</span> and does not depend on the strength of the external forces. By utilizing this quasi-periodic invariant measure, we establish a quantitative version of the strong law of large numbers and central limit theorem for the continuous time inhomogeneous solution processes with explicit convergence rates. It turns out that the convergence rate in the central limit theorem depends on the time inhomogeneity through the Diophantine approximation property on the quasi-periodic frequency of the quasi-periodic force. The scheme of analyzing the statistical behavior of the time inhomogeneous solution process by the quasi-periodic invariant measure is new and could be extended to other inhomogeneous Markov processes.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143430894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
引用次数: 0
The (varvec{d_gamma /2})-Variation of Distance Profiles in (varvec{gamma })-Liouville Quantum Gravity
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-02-17 DOI: 10.1007/s00220-024-05206-0
Manan Bhatia
{"title":"The (varvec{d_gamma /2})-Variation of Distance Profiles in (varvec{gamma })-Liouville Quantum Gravity","authors":"Manan Bhatia","doi":"10.1007/s00220-024-05206-0","DOIUrl":"10.1007/s00220-024-05206-0","url":null,"abstract":"<div><p>For Brownian surfaces with boundary and an interior marked point, a natural observable to consider is the distance profile, defined as the process of distances from the marked point to a variable point lying on the boundary. When the boundary is parametrized by the natural length measure on it, this distance profile turns out to be locally absolutely continuous to Brownian motion, and as a result, the boundary length measure itself has a natural interpretation as the quadratic variation process of the distance profile. In this paper, we extend this interpretation to <span>(gamma )</span>-Liouville quantum gravity (<span>(gamma )</span>-LQG), a one-parameter family of models of random geometry which is known to specialize to the case of Brownian geometry for the case <span>(gamma =sqrt{8/3})</span>. With <span>(d_gamma )</span> denoting the Hausdorff dimension of <span>(gamma )</span>-LQG, we show that for a <span>(gamma )</span>-LQG surface with boundary, the natural boundary length measure can be interpreted (up to a constant factor) as the <span>(d_gamma /2)</span>-variation process of the distance profile from an interior point.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143430888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
引用次数: 0
Reflexions on Mahler: Dessins, Modularity and Gauge Theories
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-02-17 DOI: 10.1007/s00220-024-05183-4
Jiakang Bao, Yang-Hui He, Ali Zahabi
{"title":"Reflexions on Mahler: Dessins, Modularity and Gauge Theories","authors":"Jiakang Bao,&nbsp;Yang-Hui He,&nbsp;Ali Zahabi","doi":"10.1007/s00220-024-05183-4","DOIUrl":"10.1007/s00220-024-05183-4","url":null,"abstract":"<div><p>We provide a unified framework of Mahler measure, dessins d’enfants, and gauge theory. With certain physically motivated Newton polynomials from reflexive polygons, the Mahler measure and the dessin are in one-to-one correspondence. From the Mahler measure, one can construct a Hauptmodul for a congruence subgroup of the modular group, which contains the subgroup associated to the dessin. We also discuss their connections to the quantum periods of del Pezzo surfaces, as well as certain elliptic pencils. We also study how, in F-theory, 7-branes and their monodromies arise in the context of dessins.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143430950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
引用次数: 0
Lower Bound for Simulation Cost of Open Quantum Systems: Lipschitz Continuity Approach
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-02-17 DOI: 10.1007/s00220-025-05240-6
Zhiyan Ding, Marius Junge, Philipp Schleich, Peixue Wu
{"title":"Lower Bound for Simulation Cost of Open Quantum Systems: Lipschitz Continuity Approach","authors":"Zhiyan Ding,&nbsp;Marius Junge,&nbsp;Philipp Schleich,&nbsp;Peixue Wu","doi":"10.1007/s00220-025-05240-6","DOIUrl":"10.1007/s00220-025-05240-6","url":null,"abstract":"<div><p>Simulating quantum dynamics is one of the most promising applications of quantum computers. While the upper bound of the simulation cost has been extensively studied through various quantum algorithms, much less work has focused on establishing the lower bound, particularly for the simulation of open quantum system dynamics. In this work, we present a general framework to calculate the lower bound for simulating a broad class of quantum Markov semigroups. Given a fixed accessible unitary set, we introduce the concept of convexified gate count to quantify the quantum simulation cost and analyze the necessary gate count to construct a quantum simulation scheme that achieves a specific order. Our framework can be applied to both unital and non-unital quantum dynamics, and the tightness of our lower bound technique is illustrated by showing that the upper and lower bounds coincide in several examples.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143430889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
引用次数: 0
Averaging and Passage Through Resonances in Two-Frequency Systems Near Separatrices
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-02-17 DOI: 10.1007/s00220-025-05230-8
Anatoly Neishtadt, Alexey Okunev
{"title":"Averaging and Passage Through Resonances in Two-Frequency Systems Near Separatrices","authors":"Anatoly Neishtadt,&nbsp;Alexey Okunev","doi":"10.1007/s00220-025-05230-8","DOIUrl":"10.1007/s00220-025-05230-8","url":null,"abstract":"<div><p>In this paper we obtain sharp asymptotic estimates for the accuracy of the averaging method for time-periodic perturbations of one-frequency Hamiltonian systems while passing through a separatrix. The Hamiltonian depends on a parameter that slowly changes for the perturbed system (thus, slow–fast Hamiltonian systems with two and a half degrees of freedom are included in our class). Let <span>(varepsilon )</span> be the small parameter of the system, then under certain genericity conditions we prove that the accuracy of averaging is <span>(O(sqrt{varepsilon }|ln varepsilon |))</span> for times of order <span>(varepsilon ^{-1})</span> (such times correspond to a change of slow variables of order 1) for all initial data outside an exceptional set with the measure <span>(O(sqrt{varepsilon }|ln ^5 varepsilon |))</span>. The main novelty of the paper lies in estimating the scattering amplitude and the measure of captured orbits while passing through resonances near separatrices. Our results can also be applied to perturbations of generic two-frequency integrable systems near separatrices, as they can be reduced to periodic perturbations of one-frequency systems.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143430953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
引用次数: 0
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