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On the TAP Equations via the Cavity Approach in the Generic Mixed p-Spin Models Commun. Math. Phys. (IF 2.4) Pub Date : 2024-03-18 Wei-Kuo Chen, Si Tang
In 1977, Thouless, Anderson, and Palmer (TAP) derived a system of consistent equations in terms of the effective magnetization in order to study the free energy in the Sherrington–Kirkpatrick (SK) spin glass model. The solutions to their equations were predicted to contain vital information about the landscapes in the SK Hamiltonian and the TAP free energy and moreover have direct connections to Parisi’s
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Extrema of 3D Potts Interfaces Commun. Math. Phys. (IF 2.4) Pub Date : 2024-03-16 Joseph Chen, Eyal Lubetzky
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Single-Shot Decoding of Good Quantum LDPC Codes Commun. Math. Phys. (IF 2.4) Pub Date : 2024-03-14 Shouzhen Gu, Eugene Tang, Libor Caha, Shin Ho Choe, Zhiyang He, Aleksander Kubica
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K-theoretic Classification of Inductive Limit Actions of Fusion Categories on AF-algebras Commun. Math. Phys. (IF 2.4) Pub Date : 2024-03-14 Quan Chen, Roberto Hernández Palomares, Corey Jones
We introduce a K-theoretic invariant for actions of unitary fusion categories on unital \({\textrm{C}}^*\)-algebras. We show that for inductive limits of finite dimensional actions of fusion categories on AF-algebras, this is a complete invariant. In particular, this gives a complete invariant for inductive limit actions of finite groups on unital AF-algebras. We apply our results to obtain a classification
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Global Solutions with Asymptotic Self-Similar Behaviour for the Cubic Wave Equation Commun. Math. Phys. (IF 2.4) Pub Date : 2024-03-14 Thomas Duyckaerts, Giuseppe Negro
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$$G_2$$ -instantons on Resolutions of $$G_2$$ -orbifolds Commun. Math. Phys. (IF 2.4) Pub Date : 2024-03-13 Daniel Platt
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Dynamical Localization for Random Band Matrices Up to $$W\ll N^{1/4}$$ Commun. Math. Phys. (IF 2.4) Pub Date : 2024-03-13 Giorgio Cipolloni, Ron Peled, Jeffrey Schenker, Jacob Shapiro
We prove that a large class of \(N\times N\) Gaussian random band matrices with band width W exhibits dynamical Anderson localization at all energies when \(W \ll N^{1/4}\). The proof uses the fractional moment method (Aizenman and Molchanov in Commun Math Phys 157(2):245–278, 1993. https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-157/issue-2/Localizationat-large-di
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Small Data Solutions for the Vlasov–Poisson System with a Repulsive Potential Commun. Math. Phys. (IF 2.4) Pub Date : 2024-03-13 Anibal Velozo Ruiz, Renato Velozo Ruiz
In this paper, we study small data solutions for the Vlasov–Poisson system with the simplest external potential, for which unstable trapping holds for the associated Hamiltonian flow. We prove sharp decay estimates in space and time for small data solutions to the Vlasov–Poisson system with the repulsive potential \(\frac{-|x|^2}{2}\) in dimension two or higher. The proofs are obtained through a commuting
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Random Quantum Circuits Transform Local Noise into Global White Noise Commun. Math. Phys. (IF 2.4) Pub Date : 2024-03-12 Alexander M. Dalzell, Nicholas Hunter-Jones, Fernando G. S. L. Brandão
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The Proper Landau–Ginzburg Potential, Intrinsic Mirror Symmetry and the Relative Mirror Map Commun. Math. Phys. (IF 2.4) Pub Date : 2024-03-12 Fenglong You
Given a smooth log Calabi–Yau pair (X, D), we use the intrinsic mirror symmetry construction to define the mirror proper Landau–Ginzburg potential and show that it is a generating function of two-point relative Gromov–Witten invariants of (X, D). We compute certain relative invariants with several negative contact orders, and then apply the relative mirror theorem of Fan et al. (Sel Math (NS) 25(4):
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Global Finite-Energy Solutions of the Compressible Euler–Poisson Equations for General Pressure Laws with Large Initial Data of Spherical Symmetry Commun. Math. Phys. (IF 2.4) Pub Date : 2024-03-12 Gui-Qiang G. Chen, Feimin Huang, Tianhong Li, Weiqiang Wang, Yong Wang
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Stability of Regularized Hastings–Levitov Aggregation in the Subcritical Regime Commun. Math. Phys. (IF 2.4) Pub Date : 2024-03-06 James Norris, Vittoria Silvestri, Amanda Turner
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Adiabatic Evolution of Low-Temperature Many-Body Systems Commun. Math. Phys. (IF 2.4) Pub Date : 2024-03-06 Rafael L. Greenblatt, Markus Lange, Giovanna Marcelli, Marcello Porta
We consider finite-range, many-body fermionic lattice models and we study the evolution of their thermal equilibrium state after introducing a weak and slowly varying time-dependent perturbation. Under suitable assumptions on the external driving, we derive a representation for the average of the evolution of local observables via a convergent expansion in the perturbation, for small enough temperatures
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Off-shell Partition Functions in 3d Gravity Commun. Math. Phys. (IF 2.4) Pub Date : 2024-03-06 Lorenz Eberhardt
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Geometric Positivity of the Fusion Products of Unitary Vertex Operator Algebra Modules Commun. Math. Phys. (IF 2.4) Pub Date : 2024-03-04 Bin Gui
A unitary and strongly rational vertex operator algebra (VOA) \({\mathbb {V}}\) is called strongly unitary if all irreducible \({\mathbb {V}}\)-modules are unitarizable. A strongly unitary VOA \({\mathbb {V}}\) is called completely unitary if for each unitary \({\mathbb {V}}\)-modules \({\mathbb {W}}_1,{\mathbb {W}}_2\) the canonical non-degenerate Hermitian form on the fusion product \({\mathbb {W}}_1\boxtimes
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The GHP Scaling Limit of Uniform Spanning Trees in High Dimensions Commun. Math. Phys. (IF 2.4) Pub Date : 2024-03-04 Eleanor Archer, Asaf Nachmias, Matan Shalev
We show that the Brownian continuum random tree is the Gromov–Hausdorff–Prohorov scaling limit of the uniform spanning tree on high-dimensional graphs including the d-dimensional torus \({\mathbb {Z}}_n^d\) with \(d>4\), the hypercube \(\{0,1\}^n\), and transitive expander graphs. Several corollaries for associated quantities are then deduced: convergence in distribution of the rescaled diameter, height
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The Irreducibility of the Monodromy Representation Associated with the Dotsenko–Fateev Equation Commun. Math. Phys. (IF 2.4) Pub Date : 2024-03-04 Katsuhisa Mimachi
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Rigid Surface Operator and Symbol Invariant of Partitions Commun. Math. Phys. (IF 2.4) Pub Date : 2024-03-02
Abstract The symbol is used to describe the Springer correspondence for the classical groups by Lusztig. We refine the explanation that the S-duality maps of the rigid surface operators are symbol preserving maps. And we find that the maps \(X_S\) and \(Y_S\) used in the construction of S-duality maps are essentially the same. We clear up cause of the mismatch problem of the total number of the rigid
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Matrix Valued Discrete–Continuous Functions with the Prolate Spheroidal Property and Bispectrality Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-27 W. Riley Casper, F. Alberto Grünbaum, Milen Yakimov, Ignacio Zurrián
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S-Duality and the Universal Isometries of Instanton Corrected q-Map Spaces Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-27
Abstract Given a conical affine special Kähler manifold together with a compatible mutually local variation of BPS structures, one can construct a quaternionic-Kähler (QK) manifold. We call the resulting QK manifold an instanton corrected c-map space. Our main aim is to study the isometries of a subclass of instanton corrected c-map spaces associated to projective special real manifolds with a compatible
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Cyclification of Orbifolds Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-27
Abstract Inertia orbifolds homotopy-quotiented by rotation of geometric loops play a fundamental role not only in ordinary cyclic cohomology, but more recently in constructions of equivariant Tate-elliptic cohomology and generally of transchromatic characters on generalized cohomology theories. Nevertheless, existing discussion of such cyclified stacks has been relying on ad-hoc component presentations
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The Lower Tail of q-pushTASEP Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-26 Ivan Corwin, Milind Hegde
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On the Extensions of the Left Modules for a Meromorphic Open-String Vertex Algebra, I Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-26 Fei Qi
We study the extensions of two left modules \(W_1, W_2\) for a meromorphic open-string vertex algebra V. We show that the extensions satisfying some technical but natural convergence conditions are in bijective correspondence to the first cohomology classes associated to the V-bimodule \({{\mathcal {H}}}_N(W_1, W_2)\) constructed in Huang and Qi (The first cohomology, derivations and the reductivity
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John–Nirenberg Inequalities for Noncommutative Column BMO and Lipschitz Martingales Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-26 Guixiang Hong, Congbian Ma, Yu Wang
In this paper, we continue the study of John–Nirenberg theorems for BMO/Lipschitz spaces in the noncommutative martingale setting. As conjectured from the classical case, a desired noncommutative “stopping time" argument was discovered to obtain the distribution function inequality form of John–Nirenberg theorem. This not only provides another approach without using duality and interpolation to the
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Multifractal Analysis of Measures Arising from Random Substitutions Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-24 Andrew Mitchell, Alex Rutar
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Topological Strings on Non-commutative Resolutions Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-24 Sheldon Katz, Albrecht Klemm, Thorsten Schimannek, Eric Sharpe
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One-Step Replica Symmetry Breaking of Random Regular NAE-SAT II Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-23 Danny Nam, Allan Sly, Youngtak Sohn
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The Wave Maps Equation and Brownian Paths Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-23 Bjoern Bringmann, Jonas Lührmann, Gigliola Staffilani
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Stokes Waves at the Critical Depth are Modulationally Unstable Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-23 Massimiliano Berti, Alberto Maspero, Paolo Ventura
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The Ground State Energy of a Two-Dimensional Bose Gas Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-23 Søren Fournais, Theotime Girardot, Lukas Junge, Leo Morin, Marco Olivieri
We prove the following formula for the ground state energy density of a dilute Bose gas with density \(\rho \) in 2 dimensions in the thermodynamic limit $$\begin{aligned} e^{\text {2D}}(\rho ) = 4\pi \rho ^2 Y\Big (1 - Y \vert \log Y \vert + \Big ( 2\Gamma + \frac{1}{2} + \log (\pi ) \Big ) Y \Big ) + o(\rho ^2 Y^{2}), \end{aligned}$$ as \(\rho a^2 \rightarrow 0\). Here \(Y= |\log (\rho a^2)|^{-1}\)
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On the Distribution of Heat in Fibered Magnetic Fields Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-23 Theodore D. Drivas, Daniel Ginsberg, Hezekiah Grayer
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Wave Propagation on Rotating Cosmic String Spacetimes Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-23 Jared Wunsch, Katrina Morgan
A rotating cosmic string spacetime has a singularity along a timelike curve corresponding to a one-dimensional source of angular momentum. Such spacetimes are not globally hyperbolic: they admit closed timelike curves near the string. This presents challenges to studying the existence of solutions to the wave equation via conventional energy methods. In this work, we show that semi-global forward solutions
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Speiser Meets Misiurewicz Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-22 Magnus Aspenberg, Weiwei Cui
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A Green’s Function Proof of the Positive Mass Theorem Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-20 Virginia Agostiniani, Lorenzo Mazzieri, Francesca Oronzio
In this paper, a new proof of the Positive Mass Theorem is established through a newly discovered monotonicity formula, holding along the level sets of the Green’s function of an asymptotically flat 3-manifolds. In the same context and for \(1
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Quantum Theory in Finite Dimension Cannot Explain Every General Process with Finite Memory Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-20 Marco Fanizza, Josep Lumbreras, Andreas Winter
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Covariant Quantum Combinatorics with Applications to Zero-Error Communication Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-20 Dominic Verdon
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Homological Quantum Rotor Codes: Logical Qubits from Torsion Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-20 Christophe Vuillot, Alessandro Ciani, Barbara M. Terhal
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Exactly Solvable Anharmonic Oscillator, Degenerate Orthogonal Polynomials and Painlevé II Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-20 M. Bertola, E. Chavez-Heredia, T. Grava
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Stability and Invariant Measure Asymptotics in a Model for Heavy Particles in Rough Turbulent Flows Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-19
Abstract We study a system of Skorokhod stochastic differential equations modeling the pairwise dispersion (in spatial dimension \(d=2\) ) of inertial particles transported by a rough turbulent flow with Hölder exponent \(h\in (0,1)\) . Under the assumption that \(h>0\) is sufficiently small, we use Lyapunov methods and control theory to show that the Markovian system is nonexplosive and has a unique
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Modular Transformations of Homological Blocks for Seifert Fibered Homology 3-Spheres Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-19 Toshiki Matsusaka, Yuji Terashima
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Universal Equations for Higher Genus Gromov–Witten Invariants from Hodge Integrals Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-16 Felix Janda, Xin Wang
We establish new universal equations for higher genus Gromov–Witten invariants of target manifolds, by studying both the Chern character and Chern classes of the Hodge bundle on the moduli space of curves. As a consequence, we find new push-forward relations on the moduli space of stable curves.
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Spectral Asymptotic Properties of Semiregular Non-commutative Harmonic Oscillators Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-15 Marcello Malagutti, Alberto Parmeggiani
We study here the spectral Weyl asymptotics for a semiregular system, extending to the vector-valued case results of Helffer and Robert, and more recently of Doll, Gannot and Wunsch. The class of systems considered here contains the important example of the Jaynes–Cummings system that describes light-matter interaction.
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Decay of Multi-point Correlation Functions in $$\mathbb {Z}^d$$ Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-12
Abstract We prove multi-point correlation bounds in \(\mathbb {Z}^d\) for arbitrary \(d\ge 1\) with symmetrized distances, answering open questions proposed by Sims–Warzel (Commun Math Phys 347(3):903–931, 2016) and Aza–Bru–Siqueira Pedra (Commun Math Phys 360(2):715–726, 2018). As applications, we prove multi-point correlation bounds for the Ising model on \(\mathbb {Z}^d\) , and multi-point dynamical
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Entropy Decay for Davies Semigroups of a One Dimensional Quantum Lattice Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-10 Ivan Bardet, Ángela Capel, Li Gao, Angelo Lucia, David Pérez-García, Cambyse Rouzé
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Stochastic Navier–Stokes Equations for Turbulent Flows in Critical Spaces Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-10 Antonio Agresti, Mark Veraar
In this paper we study the stochastic Navier–Stokes equations on the d-dimensional torus with transport noise, which arise in the study of turbulent flows. Under very weak smoothness assumptions on the data we prove local well-posedness in the critical case \(\mathbb {B}^{d/q-1}_{q,p}\) for \(q\in [2,2d)\) and p large enough. Moreover, we obtain new regularization results for solutions, and new blow-up
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3-Manifolds and VOA Characters Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-10 Miranda C. N. Cheng, Sungbong Chun, Boris Feigin, Francesca Ferrari, Sergei Gukov, Sarah M. Harrison, Davide Passaro
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Phase Diagram of the Ashkin–Teller Model Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-09 Yacine Aoun, Moritz Dober, Alexander Glazman
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Freedman’s Theorem for Unitarily Invariant States on the CCR Algebra Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-09 Vitonofrio Crismale, Simone Del Vecchio, Tommaso Monni, Stefano Rossi
The set of states on \(\textrm{CCR}({{\mathcal {H}}})\), the CCR algebra of a separable Hilbert space \({{\mathcal {H}}}\), is here looked at as a natural object to obtain a non-commutative version of Freedman’s theorem for unitarily invariant stochastic processes. In this regard, we provide a complete description of the compact convex set of states of \(\textrm{CCR}({{\mathcal {H}}})\) that are invariant
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Generalised Graph Laplacians and Canonical Feynman Integrals with Kinematics Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-09 Francis Brown
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Localization Theorem for Homological Vector Fields Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-09 Vera Serganova, Alexander Sherman
We present a general theorem which computes the cohomology of a homological vector field on global sections of vector bundles over smooth affine supervarieties. The hypotheses and results have the clear flavor of a localization theorem.
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A Synthetic Null Energy Condition Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-09
Abstract We give a simpler approach to Kunzinger and Sämann’s theory of Lorentzian length spaces in the globally hyperbolic case; these provide a nonsmooth framework for general relativity. We close a gap in the regularly localizable setting, by showing consistency of two potentially different notions of timelike geodesic segments used in the literature. In the smooth pseudo-Riemannian setting, we
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The Inviscid Limit of Navier–Stokes Equations for Locally Near Boundary Analytic Data on an Exterior Circular Domain Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-06 Toan T. Nguyen, Trinh T. Nguyen
In their classical work (Sammartino and Caflisch in Commun Math Phys 192(2):463–491, 1998), Caflisch and Sammartino established the inviscid limit and boundary layer expansions of vanishing viscosity solutions to the incompressible Navier–Stokes equations for analytic data on a half-space. The extension to an exterior domain faces a fundamental difficulty that the corresponding linear semigroup may
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On the 1d Cubic NLS with a Non-generic Potential Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-06 Gong Chen, Fabio Pusateri
We consider the 1d cubic nonlinear Schrödinger equation with an external potential V that is non-generic. Without making any parity assumption on the data, but assuming that the zero energy resonance of the associated Schrödinger operator is either odd or even, we prove global-in-time quantitative bounds and asymptotics for small solutions. First, we use a simple modification of the basis for the distorted
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Co-Dimension One Stable Blowup for the Quadratic Wave Equation Beyond the Light Cone Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-04 Po-Ning Chen, Roland Donninger, Irfan Glogić, Michael McNulty, Birgit Schörkhuber
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Defining Relations for Minimal Unitary Quantum Affine W-Algebras Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-04 Dražen Adamović, Victor G. Kac, Pierluigi Möseneder Frajria, Paolo Papi
We prove that any unitary highest weight module over a universal minimal quantum affine W-algebra at non-critical level descends to its simple quotient. We find the defining relations of the unitary simple minimal quantum affine W-algebras and the list of all their irreducible positive energy modules. We also classify all irreducible highest weight modules for the simple affine vertex algebras in the
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Average-Case Speedup for Product Formulas Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-04
Abstract Quantum simulation is a promising application of future quantum computers. Product formulas, or Trotterization, are the oldest and still remain an appealing method to simulate quantum systems. For an accurate product formula approximation, the state-of-the-art gate complexity depends on the number of terms in the Hamiltonian and a local energy estimate. In this work, we give evidence that
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Entanglement Monogamy via Multivariate Trace Inequalities Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-01
Abstract Entropy is a fundamental concept in quantum information theory that allows to quantify entanglement and investigate its properties, for example its monogamy over multipartite systems. Here, we derive variational formulas for relative entropies based on restricted measurements of multipartite quantum systems. By combining these with multivariate matrix trace inequalities, we recover and sometimes
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Spherically Symmetric Terrestrial Planets with Discontinuities Are Spectrally Rigid Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-01 Joonas Ilmavirta, Maarten V. de Hoop, Vitaly Katsnelson
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Optimal Gevrey Regularity for Supercritical Quasi-Geostrophic Equations Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-01 Dong Li
We consider the two dimensional surface quasi-geostrophic equations with super-critical dissipation. For large initial data in critical Sobolev and Besov spaces, we prove optimal Gevrey regularity endowed with the same decay exponent as the linear part. This settles several open problems in Biswas (J Differ Equ 257(6):1753–1772, 2014), Biswas et al. (J Funct Anal 269(10):3083–3119, 2015).
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Locality Galois Groups of Meromorphic Germs in Several Variables Commun. Math. Phys. (IF 2.4) Pub Date : 2024-02-01 Li Guo, Sylvie Paycha, Bin Zhang
Meromorphic germs in several variables with linear poles naturally arise in mathematics in various disguises. We investigate their rich structures under the prism of locality, including locality subalgebras, locality transformation groups and locality characters. The key technical tool is the dependence subspace for a meromorphic germ with which we define a locality orthogonal relation between two