Communications in Mathematical Physics最新文献_第9页

On Single-Frequency Asymptotics for the Maxwell–Bloch Equations: Pure States 关于Maxwell-Bloch方程的单频渐近性：纯态

IF 2.6 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2026-02-05 DOI: 10.1007/s00220-026-05558-9

A. I. Komech, E. A. Kopylova

引用次数: 0

Area Laws and Tensor Networks for Maximally Mixed Ground States 最大混合基态的面积定律和张量网络

IF 2.6 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2026-02-05 DOI: 10.1007/s00220-026-05554-z

Itai Arad, Raz Firanko, Rahul Jain

{"title":"Area Laws and Tensor Networks for Maximally Mixed Ground States","authors":"Itai Arad, Raz Firanko, Rahul Jain","doi":"10.1007/s00220-026-05554-z","DOIUrl":"10.1007/s00220-026-05554-z","url":null,"abstract":"<div>We show an area law in the mutual information for the maximally-mixed state (Omega ) in the ground space of general Hamiltonians, which is independent of the underlying ground space degeneracy. Our result assumes the existence of a ‘good’ approximation to the ground state projector (a good AGSP), a crucial ingredient in previous area-law proofs. Such approximations have been explicitly derived for 1D gapped local Hamiltonians and 2D frustration-free locally-gapped Hamiltonians. As a corollary, we show that in 1D gapped local Hamiltonians, for any (epsilon >0) and any bipartition (Lcup L^c) of the system, <div><div>$$begin{aligned} textrm{I}^epsilon _{max } , ! ! left( L : L^c right) _{Omega } le {textrm{O}}left( log (|L|log (d))+log (1/epsilon )right) , end{aligned}$$</div></div>where |L| represents the number of sites in L, d is the dimension of a site and ( textrm{I}^epsilon _{max } , ! ! left( L : L^c right) _{Omega }) represents the (epsilon )-smoothed maximum mutual information with respect to the (L:L^c) partition in (Omega ). From this bound we then conclude ( textrm{I} , ! ! left( L : L^c right) _Omega le {textrm{O}}left( log (|L|log (d))right) ) – an area law for the mutual information in 1D systems with a logarithmic correction. In addition, we show that (Omega ) can be approximated in trace norm up to (epsilon ) with a state of Schmidt rank of at most (textrm{poly}(|L|log (d)/epsilon )), leading to a good MPO approximation for (Omega ) with polynomial bond dimension. Similar corollaries are derived for the mutual information of 2D frustration-free and locally-gapped local Hamiltonians.</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-026-05554-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337229","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

Semi-Hamiltonian Properties of a Class of Non-diagonalisable Systems of Hydrodynamic Type 一类水动力型非对角系统的半哈密顿性质

IF 2.6 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2026-02-05 DOI: 10.1007/s00220-025-05544-7

Paolo Lorenzoni, Sara Perletti, Karoline van Gemst

引用次数: 0

Approximate Unitary k-Designs from Shallow, Low-Communication Circuits 浅、低通信电路的近似酉k设计

IF 2.6 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2026-02-05 DOI: 10.1007/s00220-025-05542-9

Nicholas LaRacuente, Felix Leditzky

{"title":"Approximate Unitary k-Designs from Shallow, Low-Communication Circuits","authors":"Nicholas LaRacuente, Felix Leditzky","doi":"10.1007/s00220-025-05542-9","DOIUrl":"10.1007/s00220-025-05542-9","url":null,"abstract":"<div>Random unitaries are useful in quantum information and related fields, but hard to generate with limited resources. An approximate unitary k-design is an ensemble of unitaries with an underlying measure over which the average is close to a Haar random ensemble up to the first k moments. A particularly strong notion of approximation bounds the distance from Haar randomness in relative error. Such relative-error approximate designs are secure against queries by an adaptive adversary trying to distinguish it from a Haar ensemble. We construct relative-error approximate unitary k-design ensembles for which communication between subsystems is O(1) in the system size. These constructions use the alternating projection method to analyze overlapping Haar averages, giving a bound on the convergence speed to the full averaging with respect to the 2-norm. Using von Neumann subalgebra indices to replace system dimension, the 2-norm distance converts to relative error without introducing any additional dimension dependence. We use these constructions as the building blocks of a two-step protocol that achieves a relative-error design in (O big ( (log m + log (1/epsilon ) + k log k ) k, text {polylog}(k) big )) depth, where m is the number of qudits in the complete system and (epsilon ) the approximation error. This sublinear depth construction answers a variant of [21, Harrow and Mehraban 2023, Section 1.5, Open Question 1] and [21, Harrow and Mehraban 2023, Section 1.5, Open Question 7]. Moreover, entanglement generated by the sublinear depth scheme follows area laws on spatial lattices up to corrections logarithmic in the full system size.</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05542-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337179","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

Periodic Pitman Transforms and Jointly Invariant Measures 周期Pitman变换与联合不变测度

IF 2.6 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2026-02-05 DOI: 10.1007/s00220-025-05541-w

Ivan Corwin, Yu Gu, Evan Sorensen

{"title":"Periodic Pitman Transforms and Jointly Invariant Measures","authors":"Ivan Corwin, Yu Gu, Evan Sorensen","doi":"10.1007/s00220-025-05541-w","DOIUrl":"10.1007/s00220-025-05541-w","url":null,"abstract":"<div>We construct explicit jointly invariant measures for the periodic KPZ equation (and therefore also the stochastic Burgers’ and stochastic heat equations) for general slope parameters and prove their uniqueness via a one force–one solution principle. The measures are given by polymer-like transforms of independent Brownian bridges. We describe several properties and limits of these measures, including an extension to a continuous process in the slope parameter that we term the periodic KPZ horizon. As an application of our construction, we prove a Gaussian process limit theorem with an explicit covariance function for the long-time height function fluctuations of the periodic KPZ equation when started from varying slopes. In connection with this, we conjecture a formula for the fluctuations of cumulants of the endpoint distribution for the periodic continuum directed random polymer. To prove joint invariance, we address the analogous problem for a semi-discrete system of SDEs related to the periodic O’Connell–Yor polymer model and then perform a scaling limit of the model and jointly invariant measures. For the semi-discrete system, we demonstrate a bijection that maps our systems of SDEs to another system with product invariant measure. Inverting the map on this product measure yields our invariant measures. This map relates to a periodic version of the discrete geometric Pitman transform that we introduce and probe. As a by-product of this, we show that the jointly invariant measures for a periodic version of the inverse-gamma polymer are the same as those for the O’Connell–Yor polymer.</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337175","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

Liouville Type Theorems for the Stationary Navier–Stokes Equations in (mathbb {R}^3) 中平稳Navier-Stokes方程的Liouville型定理 (mathbb {R}^3)

IF 2.6 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2026-02-05 DOI: 10.1007/s00220-026-05555-y

Dongho Chae

引用次数: 0

On Point Spectrum of Jacobi Matrices Generated by Iterations of Quadratic Polynomials 二次多项式迭代生成Jacobi矩阵的点谱

IF 2.6 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2026-02-05 DOI: 10.1007/s00220-025-05549-2

Benjamin Eichinger, Milivoje Lukić, Peter Yuditskii

引用次数: 0

Hypertoric 2-Categories (mathcal {O}) and Symplectic Duality 超曲2范畴(mathcal {O})与辛对偶

IF 2.6 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2026-02-05 DOI: 10.1007/s00220-026-05552-1

Benjamin Gammage, Justin Hilburn

引用次数: 0

Line Operators in U(1|1) Chern–Simons Theory U（1|）中的行算子chen - simons理论

IF 2.6 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2026-02-05 DOI: 10.1007/s00220-025-05546-5

Niklas Garner, Wenjun Niu

{"title":"Line Operators in U(1|1) Chern–Simons Theory","authors":"Niklas Garner, Wenjun Niu","doi":"10.1007/s00220-025-05546-5","DOIUrl":"10.1007/s00220-025-05546-5","url":null,"abstract":"<div>We analyze the non-semisimple category of line operators in Chern–Simons gauge theories based off the Lie superalgebra (mathfrak {gl}(1|1)). Our proposal is that the category of line operators (mathcal {C}) can be identified with the derived category of modules for a boundary vertex operator algebra (mathcal {V}) realized as a certain infinite-order simple current extension of the affine current algebra (V(mathfrak {gl}(1|1))) by boundary monopole operators. By translating this simple current extension of (V(mathfrak {gl}(1|1))) to the unrolled, restricted quantum group (overline{U}^E(mathfrak {gl}(1|1))), we show that our category of line operators admits a second description in terms of a quasi-quantum group (mathcal {A}) realized by uprolling. We also compare our results across an expected physical duality with the cyclic orbifold of a free, B-twisted hypermultiplet and find a slight discrepancy at the level of braiding and associator. We end with a detailed analysis of coupling to background flat (GL(1, {mathbb {C}})) connections and the resulting category of non-genuine line operators.\u0000</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337182","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

Relating Flat Connections and Polylogarithms on Higher Genus Riemann Surfaces 高格黎曼曲面上平面连接与多对数的关系

IF 2.6 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2026-02-05 DOI: 10.1007/s00220-025-05540-x

Eric D’Hoker, Benjamin Enriquez, Oliver Schlotterer, Federico Zerbini

引用次数: 0