Mathematical Physics
math.MP is an alias for math-ph. 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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Certified interval arithmetic proves a noncircular real-analytic domain with a boundary-constant Neumann eigenfunction.
· “A computer-assisted counterexample to the planar Pompeiu and Schiffer conjectures”
A sharp projection estimate proves the 2-copy threshold matches the 1-copy threshold in every dimension.
Guarantee holds when the ideal circuit gives optimal strings inverse-polynomial weight; noise costs one extra power of n.
· “Polynomial Time Quantum Approximation Schemes for Constrained Optimisation”
The weight is null-critical and fixes the sharp constant for n^{-2σ}.
· “An optimal fractional Hardy inequality on the discrete half-line”
The maps extend the known derivation property to general parameters and determine the automorphism group of the related superalgebra.
· “Derivations on the triplet W-algebras with mathfrak{sl}₂-symmetry”
New formulas let researchers translate familiar heat-equation solutions directly into fractional ones.
Tetrahedral in shear, octahedral in stresslet, icosahedral in quadratic flow: complete census.
· “The Stokes resistance of an arbitrary particle: a classification of hydrodynamic symmetries”
The result unifies known real gauges and predicts them in self-dual Chern-Simons theories.
· “Reality and Complexity of F-symbols in 2+1d Topological Phases”
No Hamiltonian or categorical data needed: six axioms make lattice wave functions string-net ground states.
At fixed pulse energy the optimal stored field is a sech soliton; n-fold overcoupling follows as the design rule.
A rigorous lower bound on Euler speed that matches the extrapolated 0.361 for the species-flipping rule.
Each genus≥2 free energy has one polar term, no logarithms, and a holomorphic remainder across the node.
Weak long-range forces keep a bulk component; strong ones fully confine the gas past an exact wall threshold.
· “Confinement transitions in half-space constrained Riesz gases”
Tuned transport noise yields global classical solutions with probability as close to 1 as desired.
No fitting parameters: the most probable photon counts in a disordered cavity array follow a number-theory distribution.
· “Universal entropic occupation statistics in disordered bosonic resonators”
Two two-by-two tables replace tomography for qubit correlations, entanglement, and channel capacity.
· “Complementary Quantum Correlations Are Universal for Qubits”
Two-replica overlap in Ising and spherical SK models gains a universal N^{-1/3} law; Talagrand's conjecture now follows.
· “Overlap distribution of the critical Sherrington-Kirkpatrick model”
Small equivariant perturbations radiate away; the internal mode drains on the epsilon^-2 time scale and the vortex returns to rest.
· “Asymptotic stability of the degree-one vortex in the abelian Yang-Mills-Higgs model”
Algebra inclusions decide which side can steer which—not tomography.
· “Quantum steering is equivalent to state-preserving conditional expectations”
At four questions, a Klein four-group game wins perfectly under commuting operators yet has no GHZ-equatorial strategy.
· “A Sharp Local-Question Threshold for GHZ-Equatorial Completeness in Four-Player XOR Games”
Up to a continuous remainder, square-wave revivals are log and jump kernels; most irrational times stay continuous.
Proof fixes the 1-RSB interval and shows a full replica symmetry breaking phase with support {0}∪[q,q'] above β2.
· “On the Gardner Transition in the Ising Pure p-Spin Glass II”
A trace-class operator with trace π/2 shows a positive commutator need not fit Kato's sufficient condition.
· “A counterexample to the Kato conjecture for positive commutators”
Even the optimal 1/√n erasure accuracy needs Ω(n²) brickwork cycles under 1D local charge-conserving gates.
· “Diffusive Speed Limits for U(1)-Covariant Quantum Error Correction”
The ladder's critical length switches from log to algebraic to aspect-ratio scaling as couplings become nonlocal.
· “Nonlocality-induced critical-length hierarchy from non-Hermitian competition”
For every small diffusivity, one fixed velocity field produces an exponentially growing magnetic mode at a uniform rate.
An explicit counterexample and an iterable construction push the critical-point ratio to 10.
They replace psi classes while keeping integrability, establish Miura links to Dubrovin-Zhang and ramification hierarchies, and give a short
· “Beyond descendants: integrable observables for cohomological field theories”
Twelve standard forms are obtained, including new quartic and quintic examples, for use in the Painlevé equivalence problem.
· “Modified Painlev\'e systems with meromorphic solutions for polynomial Hamiltonians of all degrees”
For chordal graphs the noncommutative junction-tree formula T(R) produces a valid state exactly when its trace is one, and it is then the un
Rigorous proof for the one-dimensional electron-phonon system shows only the Hamiltonian and fermion number are conserved locally, enabling,
· “Proof of the absence of local conserved quantities in the Holstein model”
Self-overlap correction reduces the quantum SK pressure to a variational problem over classical order parameters.
Nonlinear Koiter energy forces single Leray-Schauder argument on the coupled Galerkin system in periodic channels.
· “Time-periodic solutions for viscous fluids interacting with nonlinear Koiter plates”
The projection leaves the field unchanged in mesoscopic regions and allows conserved densities to be computed from the density of states.
Different orderings and couplings reduce to the same canonical form whose non-escape coordinates are orthogonal and sum to the identity.
Result for Christodoulou's family shows that weak cosmic censorship depends on the regularity class chosen for perturbations
The decomposition into Aharonov-Bohm and fractional statistical terms follows from Grothendieck-Riemann-Roch applied to the symmetric power.
· “Chern classes of Laughlin bundles on the quasihole moduli space”
New long harmonic derivatives with inverse d'Alembertian give the operator and its eigenvalues on analytic superfields.
· “Casimir operators of 4D\,, mathcal{N}=2 supersymmetry in the harmonic approach”
An explicit degenerate mixture refutes the assumption that the convex roof always has one.
· “On supporting affine functionals for Entanglement of Formation”
Optimal transport of quantum states matches classical Lyapunov exponents; OTOCs can only lag.
A Levi-type theorem splits open-system generator wedges; semisimple dynamics carry only Hamiltonian directions.
Lacunary hopping weights make wave packets flatten like |t|^{-N} for every N, with no universal speed limit.
· “Arbitrarily Fast Quantum Dispersion in Long-Range Crystals”
New second-order IMEX method for Cahn-Hilliard-Navier-Stokes needs only linear solves and preserves energy decay.
The paper's construction derandomizes the known counterexample: zero-one permutation tuples make Hmin(Φ⊗Φ) < 2Hmin(Φ)
An explicit finite-dimensional equation describes every stable quasimap to a Nakajima quiver variety.
Scaling depends on how the initial state is averaged, and memory of that state survives at long times
· “Current fluctuations in a gas of active Ornstein-Uhlenbeck particles”
Trust one QKD device, treat the other as a black box: convergent bounds plus finite-size security against general attacks.
· “Computing key rates for one-sided device-independent quantum key distribution”
Rigidity results also separate strong-torsion string backgrounds from special-holonomy spaces.
· “Topology of low-dimensional generalized Ricci solitons and string backgrounds”
Mixed fermion-boson samplers output generalized immanants, beyond pure boson and fermion statistics.
· “Quantum sampling in hybrid light-matter systems with mixed statistics”
A mismatch in band Chern numbers forces every neutral orbital variation to cost positive energy, a soft spectral gap.
Randomized vortices converge in Wasserstein distance to a measure solving the Euler statistical hierarchy.
· “Computing statistical Euler limits of the Navier--Stokes equations in three dimensions”
Chiral kinematics and spatial homogeneity force an affine spectral trajectory; the inverse Cayley transform then sets the couplings.
· “General Construction of Time-Dependent Integrable Chiral Field Theories”
Explicit double-cone observables beat the classical bound and asymptotically saturate the Tsirelson value.
· “Bell-CHSH Violation for a Massless Majorana Field in a Double Cone from Modular Localization”
The bar involution plus quasi-R-matrix gives real F-matrices for every simple Lie algebra and level, but the braiding does not descend.
This basis gives a smooth, local, wormhole-length Hilbert space for a large family of random matrix models.
The walk revisits every site infinitely often, and its visited region converges to a convex limiting shape.
A one-dimensional solvable model proves positive defects trap modes below and negative defects above.
Both inequality branches were numerical checks before; this proof makes them analytic for every dimension.
A five-state network's fixed process cycles through Chern sectors 0, −1, 0, −1, 0 as observation time alone changes.
· “Non-Abelian Spin Counting of Ordered Stochastic Trajectories: Reentrant Finite-Time Chern Numbers”
A new proof gives explicit remainder terms and uniform eigenfunction bounds for every fractional order between 0 and 2.
A new bound pins down when charged scalar collapse can reach extremality; subextremal collapse carries no such limit.
On an exponentially long scale, passages between wells are Poisson(mean N), giving the splitting.
An equivariant index computation on the M9 wall matches the conjectured tensor-branch anomaly eight-form.
Every inter-horizon axis rod attracts, so stationary vacuum spacetimes have a single black hole.
The book's core promise: students can run, verify, and extend every demonstration in Mathematica.
It proves the same number governs conformal field theory anomalies and the Brownian loop measure.
A variational–adjoint reading of the Schrödinger equation makes probability one member of a family of observable kernels.
A universal Hessian bound forces the quantum replica overlap to vanish at strong transverse field.
· “Correlation inequalities for transversal field models with application to quantum glasses”
For the real Ginibre ensemble, the joint counting statistics of real and non-real eigenvalues in a disc have explicit asymptotic cumulants…
Boundary counterterms beyond the usual mass shift are needed, and the cut must be renormalized too.
· “Renormalization, cutoff, and gluing for a quartic model with boundary”
Time labels evolution; position labels measurement outcomes. A teaching map shows why the wavefunction needs no time bra.
· “What do position and time mean in the quantum wavefunction?”
An exact open-system solution ties the mixed-state holonomy to the Gibbs loop, then cooling lands it on the Berry value.
· “Geometric Phases of a Driven Qubit: Comparing Berry and Uhlmann Holonomies”
Photons get a covariant Boltzmann equation in curved spacetime via a non-vanishing volume element on the light cone bundle.
· “Geometric formulation for the relativistic kinetic theory of photons”
For the quasilinear MMT equation with random data, the paper proves long-time smooth solutions and derives the first-order wave kinetic…
The authors show that on any acyclic decay graph with a depth function, the Pauli master equation is exactly a flux conservation law and…
A generalized spectral-averaging identity extends the rank-one spectral-shift phenomenon to infinite rank.
· “Analysis of the Singular Spectrum for General Perturbations”
The intensity's critical mass grows logarithmically and reveals a grating's jump content.
Three recursions—neck, disk, crown—reduce every volume to explicit integrals and closed formulas.
· “Flippered hyperbolic surfaces and renormalized volumes of their moduli spaces I”
Quantitative bounds on Lyapunov exponents imply localization length at most C W^2 for the 1D block Anderson model.
· “Quantitative Furstenberg Theory for Large Random Matrices”
A many-body derivation with O(1/N) error works in dimensions 1–2 and formally 3; only the 3D stochastic objects are missing.
· “A simple derivation of Anderson-Hartree equations with harmonic potential”