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Optimal Transport on Null Hypersurfaces and the Null Energy Condition 零超曲面上的最优输运和零能量条件
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-08-01 DOI: 10.1007/s00220-025-05345-y
Fabio Cavalletti, Davide Manini, Andrea Mondino
{"title":"Optimal Transport on Null Hypersurfaces and the Null Energy Condition","authors":"Fabio Cavalletti,&nbsp;Davide Manini,&nbsp;Andrea Mondino","doi":"10.1007/s00220-025-05345-y","DOIUrl":"10.1007/s00220-025-05345-y","url":null,"abstract":"<div><p>The goal of the present work is to study optimal transport on null hypersurfaces inside Lorentzian manifolds. The challenge here is that optimal transport along a null hypersurface is completely degenerate, as the cost takes only the two values 0 and <span>(+infty )</span>. The tools developed in the manuscript enable to give an optimal transport characterization of the null energy condition (namely, non-negative Ricci curvature in the null directions) for Lorentzian manifolds in terms of convexity properties of the Boltzmann–Shannon entropy along null-geodesics of probability measures. We obtain as applications: a stability result under convergence of spacetimes, a comparison result for null-cones, and the Hawking area theorem (both in sharp form, for possibly weighted measures, and with apparently new rigidity statements).</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 9","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05345-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160522","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
Exponential Speedups for Quantum Walks in Random Hierarchical Graphs 随机层次图中量子行走的指数加速
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-08-01 DOI: 10.1007/s00220-025-05370-x
Shankar Balasubramanian, Tongyang Li, Aram W. Harrow
{"title":"Exponential Speedups for Quantum Walks in Random Hierarchical Graphs","authors":"Shankar Balasubramanian,&nbsp;Tongyang Li,&nbsp;Aram W. Harrow","doi":"10.1007/s00220-025-05370-x","DOIUrl":"10.1007/s00220-025-05370-x","url":null,"abstract":"<div><p>There are few known exponential speedups for quantum algorithms and these tend to fall into even fewer families. One speedup that has mostly resisted generalization is the use of quantum walks to traverse the welded-tree graph, due to Childs, Cleve, Deotto, Farhi, Gutmann, and Spielman. We show how to generalize this to a large class of hierarchical graphs in which the vertices are grouped into “supervertices” which are arranged according to a <i>d</i>-dimensional lattice. Supervertices can have different sizes, and edges between supervertices correspond to random connections between their constituent vertices. The hitting times of quantum walks on these graphs are related to the localization properties of zero modes in certain disordered tight binding Hamiltonians. The speedups range from superpolynomial to exponential, depending on the underlying dimension and the random graph model. We also provide concrete realizations of these hierarchical graphs, and introduce a general method for constructing graphs with efficient quantum traversal times using graph sparsification.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 9","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05370-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160525","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 Graphical Calculus for Classical and Quantum Microformal Morphisms 经典和量子微形式态射的图解演算
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-08-01 DOI: 10.1007/s00220-025-05372-9
Andreas Swerdlow
{"title":"A Graphical Calculus for Classical and Quantum Microformal Morphisms","authors":"Andreas Swerdlow","doi":"10.1007/s00220-025-05372-9","DOIUrl":"10.1007/s00220-025-05372-9","url":null,"abstract":"<div><p>We develop a graphical calculus for the microformal or thick morphisms introduced by Th. Voronov. This allows us to write the infinite series arising from pullbacks, compositions, and coordinate transformations of thick morphisms as sums over bipartite trees. The methods are inspired by those employed by Cattaneo-Dherin-Felder in their work on formal symplectic groupoids. We also extend this calculus to quantum thick morphisms, which are special types of Fourier integral operators quantizing classical thick morphisms. The relationship between the calculi for classical and quantum thick morphisms resembles the relationship between the semi-classical and full perturbative expansions over Feynman diagrams in quantum field theory.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 9","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05372-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145154135","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
Approximation of the Thermodynamic Limit of Finite-Gap Solutions to the Focusing NLS Hierarchy by Multisoliton Solutions 用多孤子解逼近聚焦NLS层有限间隙解的热力学极限
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-08-01 DOI: 10.1007/s00220-025-05357-8
Robert Jenkins, Alexander Tovbis
{"title":"Approximation of the Thermodynamic Limit of Finite-Gap Solutions to the Focusing NLS Hierarchy by Multisoliton Solutions","authors":"Robert Jenkins,&nbsp;Alexander Tovbis","doi":"10.1007/s00220-025-05357-8","DOIUrl":"10.1007/s00220-025-05357-8","url":null,"abstract":"<div><p>In this paper we approximate the thermodynamic limit of finite-gap solutions to any integrable equations in the focusing NLS hierarchy (NLS, mKdV, ...) with an associated multisoliton solutions using the Riemann-Hilbert Problem approach. Moreover, we show that both the finite-gap and multisoliton solutions are approximated in the thermodynamic limit by a generalization of the primitive potentials introduced by V. Zakharov and his collaborators in the KdV context. Under certain assumptions on the spectral data for the finite gap potentials, we provide error estimates for the approximation on compact subsets of the (<i>x</i>, <i>t</i>)-plane.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 9","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160636","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
On the Near Soliton Dynamics for the 2D Cubic Zakharov–Kuznetsov Equations 二维三次Zakharov-Kuznetsov方程的近孤子动力学
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-07-29 DOI: 10.1007/s00220-025-05409-z
Gong Chen, Yang Lan, Xu Yuan
{"title":"On the Near Soliton Dynamics for the 2D Cubic Zakharov–Kuznetsov Equations","authors":"Gong Chen,&nbsp;Yang Lan,&nbsp;Xu Yuan","doi":"10.1007/s00220-025-05409-z","DOIUrl":"10.1007/s00220-025-05409-z","url":null,"abstract":"<div><p>In this article, we consider the Cauchy problem for the cubic (mass-critical) Zakharov-Kuznetsov equations in dimension two: </p><div><div><span>$$begin{aligned} partial _tu+partial _{x_1}(Delta u+u^3)=0,quad (t,x)in [0,infty )times {mathbb {R}}^{2}. end{aligned}$$</span></div></div><p>For the initial data in <span>(H^{1})</span> close to the soliton and satisfying a suitable space-decay property, we fully describe the asymptotic behavior of the corresponding solution. More precisely, for such initial data, we show that only three possible behaviors can occur: (1) The solution leaves a tube near soliton in finite time; (2) the solution blows up in finite time; and (3) the solution is global and locally converges to a soliton. In addition, we show that for initial data near a soliton with non-positive energy and above the threshold mass, the corresponding solution will blow up as described in Case 2. Our proof is inspired by the techniques developed for the mass-critical generalized Korteweg de Vries (gKdV) equation in a similar context by Martel-Merle-Raphaël [36]. More precisely, our proof relies on refined modulation estimates and a modified energy-virial Lyapunov functional. The primary challenge in our problem is the lack of coercivity for the Schrödinger operator, which appears in the virial-type estimate. To overcome the difficulty, we apply a transform, which was first introduced in Kenig-Martel [14], to perform the virial computations after converting the original problem into an adjoint one. The coercivity of the Schrödinger operator in the adjoint problem has been numerically verified by Farah-Holmer-Roudenko-Yang [9].</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 8","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171374","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
Arbitrarily Small Spectral Gaps for Random Hyperbolic Surfaces with Many Cusps 多尖随机双曲曲面的任意小谱隙
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-07-02 DOI: 10.1007/s00220-025-05366-7
Yang Shen, Yunhui Wu
{"title":"Arbitrarily Small Spectral Gaps for Random Hyperbolic Surfaces with Many Cusps","authors":"Yang Shen,&nbsp;Yunhui Wu","doi":"10.1007/s00220-025-05366-7","DOIUrl":"10.1007/s00220-025-05366-7","url":null,"abstract":"<div><p>Let <span>(mathcal {M}_{g,n(g)})</span> be the moduli space of hyperbolic surfaces of genus <i>g</i> with <i>n</i>(<i>g</i>) punctures endowed with the Weil–Petersson metric. In this paper we study the asymptotic behavior of the Cheeger constants and spectral gaps of random hyperbolic surfaces in <span>(mathcal {M}_{g,n(g)})</span>, when <i>n</i>(<i>g</i>) grows slower than <i>g</i> as <span>(grightarrow infty )</span>.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 8","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161086","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
Tube Category, Tensor Renormalization and Topological Holography 管范畴、张量重整化与拓扑全息
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-07-02 DOI: 10.1007/s00220-025-05383-6
Tian Lan
{"title":"Tube Category, Tensor Renormalization and Topological Holography","authors":"Tian Lan","doi":"10.1007/s00220-025-05383-6","DOIUrl":"10.1007/s00220-025-05383-6","url":null,"abstract":"<div><p>Ocneanu’s tube algebra provides a finite algorithm to compute the Drinfeld center of a fusion category. In this work we reveal the universal property underlying the tube algebra. Take a base category <span>({mathcal {V}})</span> which is strongly concrete, bicomplete, and closed symmetric monoidal. For physical applications one takes <span>({mathcal {V}}=textbf{Vect})</span> the category of vector spaces. Given a <span>({mathcal {V}})</span>-enriched rigid monoidal category <span>({mathcal {C}})</span> (not necessarily finite or semisimple) we define the tube category <span>({mathbb {X}} {mathcal {C}})</span> using coends valued in <span>({mathcal {V}})</span>. Our main theorem established the relation between (the category of representations of) the tube category <span>({mathbb {X}} {mathcal {C}})</span> and the Drinfeld center <span>(Z({mathcal {C}}))</span>: <span>(Z({mathcal {C}})hookrightarrow textrm{Fun}({mathbb {X}} {mathcal {C}}^{textrm{op}},{mathcal {V}})cong Z({mathcal {C}}hookrightarrow textrm{Fun}({mathcal {C}}^{textrm{op}},{mathcal {V}}))hookrightarrow Z(textrm{Fun}({mathcal {C}}^{textrm{op}},{mathcal {V}})))</span>. Physically, besides viewing the tube category as a version of TFT with domain being the tube, we emphasize the “Wick-rotated” perspective, that the morphisms in <span>({mathbb {X}} {mathcal {C}})</span> are the local tensors of fixed-point matrix product operators which preserves the symmetry <span>({mathcal {C}})</span> in one spatial dimension. We provide a first-principle flavored construction, from microscopic quantum degrees of freedom and operators preserving the symmetry, to the macroscopic universal properties of the symmetry which form the Drinfeld center. Our work is thus a proof to the 1+1D topological holography in a very general setting.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 8","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05383-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161126","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
Regularity for the Boltzmann Equation Conditional to Pressure and Moment Bounds 玻尔兹曼方程受压力和矩限约束的正则性。
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-07-02 DOI: 10.1007/s00220-025-05356-9
Xavier Fernández-Real, Xavier Ros-Oton, Marvin Weidner
{"title":"Regularity for the Boltzmann Equation Conditional to Pressure and Moment Bounds","authors":"Xavier Fernández-Real,&nbsp;Xavier Ros-Oton,&nbsp;Marvin Weidner","doi":"10.1007/s00220-025-05356-9","DOIUrl":"10.1007/s00220-025-05356-9","url":null,"abstract":"<div><p>We prove that solutions to the Boltzmann equation without cut-off satisfying pointwise bounds on some observables (mass, pressure, and suitable moments) enjoy a uniform bound in <span>(L^infty )</span> in the case of hard potentials. As a consequence, we derive <span>(C^{infty })</span> estimates and decay estimates for all derivatives, conditional to these macroscopic bounds. Our <span>(L^infty )</span> estimates are uniform in the limit <span>(s nearrow 1)</span> and hence we recover the same results also for the Landau equation.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 8","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12222422/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144574621","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 Theory of Quantum Jumps 量子跳跃理论
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-07-02 DOI: 10.1007/s00220-025-05352-z
Jürg Fröhlich, Zhou Gang, Alessandro Pizzo
{"title":"A Theory of Quantum Jumps","authors":"Jürg Fröhlich,&nbsp;Zhou Gang,&nbsp;Alessandro Pizzo","doi":"10.1007/s00220-025-05352-z","DOIUrl":"10.1007/s00220-025-05352-z","url":null,"abstract":"<div><p>Using the principles of the so-called <i>ETH</i>-Approach to Quantum Mechanics we describe fluorescence and the phenomenon of “quantum jumps” in idealized models of atoms coupled to the quantized electromagnetic field. In a limiting regime where the orbital motion of the atoms is neglected and the velocity of light tends to <span>(infty )</span> we derive explicit non-linear stochastic differential equations describing the effective time evolution of states of individual atoms. These equations give rise to a measure on state trajectories exhibiting quantum jumps representing a quantum-mechanical analogue of the Wiener measure on Brownian paths in the theory of diffusion.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 8","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161127","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
Hyperspherical Equivariant Slices and Basic Classical Lie Superalgebras 超球面等变片与基本经典李超代数
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-07-02 DOI: 10.1007/s00220-025-05378-3
Michael Finkelberg, Ivan Ukraintsev
{"title":"Hyperspherical Equivariant Slices and Basic Classical Lie Superalgebras","authors":"Michael Finkelberg,&nbsp;Ivan Ukraintsev","doi":"10.1007/s00220-025-05378-3","DOIUrl":"10.1007/s00220-025-05378-3","url":null,"abstract":"<div><p>We classify all the hyperspherical equivariant slices of reductive groups. The classification is essentially <i>S</i>-dual to the one of basic classical Lie superalgebras.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 8","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05378-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161129","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
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