Mathematical Physics
Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
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Proof that subquadratic growth forces Gibbsian stationary states, while at quadratic growth non-reversible and periodic behavior appears.
· “On the stationary measures of the critical Ornstein--Uhlenbeck process”
Any continuous uniform construction satisfying entailment, contraposition, and falsity must be the nonnegative part of Q−P.
Closed-form Page curves and monotone entanglement bounds give analytic control over classical hardness of Gaussian boson sampling.
· “Anticoncentration and entanglement in Gaussian boson sampling”
Proof uses coarse-graining, geometric linearization, and a (1+1)-dimensional action; fluctuations are superconcentrated.
· “Asymptotics of a planar isoperimetric problem with a white-noise volume term”
New paired Haar theorem bounds critical points by 2m−1, proving the GNS signed line conjecture and the EFO positive conjecture.
· “Critical Points of Line Restrictions of Signed Point-Charge Potentials”
First rigorous justification of time‑dependent density functional theory with Coulomb interactions and a fixed‑point construction of the…
· “The inverse problem of time-dependent density functional theory on the torus”
Proven for Coulomb-interacting electrons, it gives Kohn-Sham theory its first rigorous continuum foundation.
· “Time-Dependent Density Functional Theory with Coulomb Interactions”
At any rate beyond capacity, both entanglement fidelity and decoding success decay to zero.
· “No information transmission through quantum channels above capacity”
A 12-participant study shows the watch-back contact patch alone supports EIT gesture recognition via multi-depth scanning.
· “Algorithmic threshold for high-dimensional projection pursuit I: general theory”
Finite-time bounds on current fluctuations yield confidence intervals from just one trajectory.
· “Concentration of additive functionals of Stratonovich-type”
Enables particle kinematics on spacetimes with both Carrollian and Poisson structures
· “Go Fishing with Alice: Compatible Carrollian and Poisson Structures”
Nonabelian anyon superselection sectors violate Haag duality and its equivalent uniqueness of purifications, as proven by operator…
A drift-plus-diffusion matrix condition separates smoothing from irreducibility, unlike in the classical setting.
· “Irreducibility and regularisation properties of Gaussian quantum Markov semigroups”
Local half-space evolution with oscillatory Poisson kernel enables memory equation well-posedness.
· “An extension theory for fully fractional Schr\"odinger equations with memory”
On hyperbolic surfaces, collective motion begins at α = 5/4 Dκ² and defect dynamics slow with a 1/2-power law.
A 1969 Morse-Cairns conjecture is proved; the number of equilibrium points is bounded by a function exponential in the number of charges.
· “The finiteness conjecture for equilibria of electric fields generated by point charges of one sign”
A universal curve shows late-time chaotic states protect information as well as any engineered code can.
· “Quantum thermalization achieves optimal approximate quantum error correction”
A new mathematical framework justifies heuristic small-coupling methods used in quantum computing and open systems.
· “Non-Closing Double-Commutator Flows and the Small-Coupling Limit of Spin-Boson Models”
New lower bounds meet upper bounds, so position moments cannot spread any faster or slower on the logarithmic scale.
· “Sharp Logarithmic Quantum Dynamics for Quasiperiodic Schr\"odinger Operators”
A theorem uses Householder reflections to show a frustrated zero-field O(n) chain equals a simpler field-driven chain for any length and…
A new representation of the Moore–Tachikawa category recovers L-sheaves and Gaiotto's (BBB)-branes from the same construction.
· “Quasi-algebraic quantization for the B-twist Langlands TQFT”
Renormalization makes the attractive gas well defined for any particle number; slow motion recovers Lieb–Liniger physics.
· “Renormalization of One-Dimensional Semirelativistic Bosons with Contact Interactions”
Review argues that exact solutions should be interpreted as orbits in a reduced phase space and then validated through full PDE simulation…
· “Reduction Based Dynamical Systems Analysis of Nonlinear Wave Equations: A Review”
Truncated correlations now peak at zero field for a whole class of single-spin measures, opening the route to log-Sobolev bounds.
· “The Ding-Song-Sun inequality for a class of even ferromagnets”
A Zeno-like limit emerges without frequent measurements, and the process is resolved on a fine time scale proportional to inverse coupling.
Quenched tree-embedding method proves finite α* and positive u* on irregular Bernoulli percolation clusters
· “Phase transition for strongly correlated percolation models on supercritical Bernoulli clusters”
Covariant phase-space analysis shows the Carroll–Weyl transformation does not reduce the physical phase space, unlike in null strings.
· “Covariant Phase Space and Carroll-Weyl chi Symmetry of Carroll Non-BPS D_p-branes”
The map unifies Brownian bridges, OU relaxation and free diffusion, and the measured restoring force fixes the connection α.
· “Stochastic Processes as Non-Metric Geodesics in Information Geometry”
First norm-resolvent convergence result for the Dirac confinement model on Lipschitz domains without smoothness assumptions.
· “MIT bag model and infinite mass limit in non-smooth domains”
A new proof that relaxes initial conditions and corrects a sign error in prior stationary fluctuation formulas.
Jones and Mueller beam models from simulations give calibration baseline for polarimetry at 5 and 6.7 GHz.
· “Full Characterisation of the Polarisation Primary Beam of the GRAO 32-m Telescope”
In χ(2) optical lattices, sufficiently intense solitons shift exactly one lattice period per pump cycle, matching topological predictions…
· “Quantized transport of two-dimensional multifrequency solitons”
Derives coupled ODEs for all fields including Dirac fermions and Yukawa term, provides solver.
· “Static spherically symmetric electroweak models with fermions and gravity”
Linear transformations from canonical to noncommuting phase space uncover hidden symmetries and momentum correlations.
Explicit closed forms for the Nth power reveal integer triangles and fix a prior error.
· “Arithmetic triangular structures in the transfer-matrix of finite Kronig-Penney models”
Additive rate decomposition preserves accuracy of multiplicative Maxwell-Glen while reducing the local update to one scalar equation
A 1D KPZ-type surface converges to the additive heat equation after only two renormalization terms.
· “Subcritical limits of a 1D KPZ growth surface with finite moments”
Sharp rates for the factorization of atomic ground states when one electron is far from the others, including at ionization threshold.
· “Asymptotics of Ground States for Helium-Like and Bosonic Atoms in a Two-Cluster Region”
Uniform convergence means finite-order channel gains become trustworthy for multi-query EM prediction across all sources.
Two-replica overlaps in the random-field Curie-Weiss model have sub-Gaussian tails whenever beta is below 1, for a Gaussian field whose…
· “On overlap concentration in the Curie-Weiss Random Field model”
Expected energy measures converge to the heat equation under a joint scaling that keeps interactions local on the macroscale.
Refined punctured and normalized orbifold cycles coincide after pushforward, opening the localization toolbox.
· “Negative contacts in genus one: a comparison of punctured and root stack Gromov-Witten theories”
Power-law nonlinear electrodynamics still admits first-order vortex equations; the tension is set by winding number alone.
Exact vector formulas for Foucault pendulum, two-body problem, and Larmor theorem follow from a single algebraic trick: rotate the…
· “New Symbolic Procedures in the Study of Dynamical Systems”
Computer-assisted construction of a Lipschitz domain shows essential spectral radius exceeds 1/2, disproving Kenig's conjecture.
· “A counterexample to Kenig's conjecture for the Laplace double-layer operator”
New formula yields speedups of orders of magnitude for heralded state and gate preparation in linear optics.
Open thermodynamic systems share the same dynamical structure as mass-spring-dampers and RLC circuits.
Training a normalizing flow in one sector and mapping to others yields correct charge distribution where HMC freezes.
· “Sector-Resolved Flow Sampling for Topologically Frozen Lattice Gauge Theories”
A convergent particle discretization solves the Matytsin hydrodynamical problem for generic densities.
· “Efficient computation of the asymptotics of extensive-rank HCIZ integrals”
For the operator ∂_x f ∂_x = 0, C^1 boundary data is necessary and sufficient, and solutions are one order less regular than the data.
· “The Dirichlet problem for a non-commutative elliptic operator in the ball”
A single bound on weighted boundaries yields survival, plus the truncation and large-degree applications.
Learned local stencils beat global neural operators in accuracy, stability, and data use, with no PDE formula needed.
Bach and Eastwood–Singer tensors span all natural weight -2 order ≤4 symmetric 2-tensors in 4 dimensions.
· “Classification of Conformally Covariant 2-Tensors from the Kulkarni--Nomizu Product in Dimension 4”
论文证明：对于非平凡基态丛的哈密顿量族，任何连续纯态模型都存在能量误差至少一个能隙的失败点——算子值表示是唯一出路。
· “Topology Obstructs Pure Foundation Neural Quantum States”
The state is unique and exponentially mixing at every temperature; a floor alone pushes interfaces to infinite height.
A finite-lattice Dirac model on networks reproduces continuous graph spectra as step size tends to zero.
· “Discrete Dirac equation on quantum graphs: A model of a Dirac particle in a branched lattice”
Four fluctuation regimes — sine, Airy, Hermite, and hard-wall sine — from symplectic skew Howe duality
For the deformed logistic map, the periodic points and the preimages of infinity converge to the same finite set of singular points as the…
· “Big Crunch on Julia and Anti-Julia Sets in the Integrable Limit”
PPIM, a Mamba-based network with Pennes-aware initialization, beats PINNs and PINNMamba on a controlled ablation test.
· “PPIM: Pennes Physics-Informed Mamba for Heat-Source-Conditioned 3D Bioheat Simulation”
Direct Gibbs comparison pins down the one-dimensional log-gas scaling limit uniquely.
Explicit formulas for N-dimensional isotropic random walks using a classical special function integral.
· “Random walk and Weber-Schafheitlin integral: generalizations and discussion”
Global strong existence with exponential relaxation is proved for Maxwell-Stefan diffusion with additive friction coefficients on bounded…
· “Global Strong Solutions for Maxwell-Stefan Diffusion with Additive Friction Coefficients”
First efficient algorithms for key tensor parameters, with provable O(1/k) convergence on Gaussian integer inputs.
Recurrences, Maclaurin series, and large-$x$ asymptotics connect Apostol-Bernoulli numbers to Hurwitz-Lerch zeta.
An exponential profile cancels the nonlinear terms, and memory slows decay from exponential to power law.
· “Exact Analytic Solution for the Time-Fractional Hunter-Saxton Equation with Caputo derivative”
Many-body ground states condense onto the Gagliardo-Nirenberg optimizer, with explicit energy expansion.
Proof completes the classification of six-dimensional homogeneous Einstein manifolds, reducing to the product and nearly Kähler metrics.
· “A complete classification of left-invariant Einstein metrics on S³times S³”
A generalised Whiting transform splits frequency regimes and gives the bound needed for full-Kerr stability.
· “Generalized Whiting transform and Flux Estimates for Wave Equations in Subextremal Kerr”
Given a lipschitz shock close to a straight line, the piston speed and flow field are uniquely determined and stable in the BV norm.
· “An Inverse Problem for Determining the Piston Speed from a Given Lipschitz Leading Shock”
Its second cohomology classifies deformations and abelian extensions, and differs from pre-Lie cohomology.
Resulting hyperbolic system models a multiphase fluid with a pressureless final phase.
As the spectral curve degenerates, each ingredient of Fock's formula is governed by its tropical counterpart.
Proving that invertible differential substitutions and conservation-law maps send Darboux-integrable equations onto others of the same kind.
· “On B\"acklund transformations preserving the Darboux integrability of hyperbolic equations”
Every rescaled random walk approaches Brownian motion along the same universal modes, at universal rates.
· “Renormalization Group on Wiener Space: Spectral Theory and Universality”
A Clifford peel leaves only the cubic core, cutting exponential Pauli sums to short formulas.
· “Quantifying Nonstabilizerness of Quantum Codes by Removing the Inert Background”
Small-data proof shows bosons and fermions converge to free solutions with coupled logarithmic phase and spatial offsets.
· “Modified scattering for semiclassical Bose-Fermi mixtures”
A tutorial shows Hamiltonian feedback clears obstacles while measurement sets the convergence rate.
· “Measurement-Based Feedback of Open Quantum Systems: A Control-Theoretic Review and Tutorial”
Higher-dimensional generalization to n variables via tensor product expansion
Explicit formula satisfies both constitutive restrictions, settling a 2024 IUTAM challenge.
For toric Fano surfaces, genus-g Gopakumar-Vafa invariants of the one-point blowup in classes pulled back plus w times the exceptional…