Mathematical Physics
Analytic Solution for Suppressed Implosion in 1D Compressible Euler Equations
This paper presents an exact analytic solution to the one-dimensional compressible Euler equations with an initial data cutoff, modifying Kidder's formulation. The solution demonstrates the emergence of a non-centered rarefaction from the cutoff, which effectively suppresses the implosion. The theor…
Generalizing Perron--Frobenius Theory and Eigenvector Centrality for Complex-Valued Network Weights
This paper extends the Perron--Frobenius (PF) theorem and associated eigenvector centrality measures to networks with complex-valued edge weights, which are common in fields like quantum information and machine learning. The authors generalize the PF theorem for complex matrices, establish interconn…
Well-posedness of Kohn-Sham DFT Models for Encapsulated 2D Materials with Yukawa-type Interactions
This paper investigates Kohn-Sham Density Functional Theory (DFT) models for two-dimensional materials encapsulated within a three-dimensional environment between conducting electrodes. The Dirichlet boundary conditions imposed by the electrodes effectively screen the Coulomb interaction, reducing i…
Yang-Baxter Equation for Chiral Potts Model and Integrable Parafermions
This work introduces a new Yang-Baxter equation (YBE) for R-matrices with three spectral parameters, derived from the star-triangle and star-star relations of the chiral Potts model. This construction extends to the Z_N symmetric generalization of the Ising model, where Boltzmann weights depend on t…
Lévy Fields Enable Direct Construction of Exact Scalar Wightman Fields in d≥4 Dimensions
The paper constructs Hermitian scalar quantum fields in d-dimensional spacetime (including d≥4) using stochastic calculus on stationary Lévy random fields, initially within a relaxed Gårding-Wightman framework where field operators are symmetric rather than self-adjoint. By selecting adequate subspa…
KMS Decay Rate Bounds GNS Rate in Quantum Markov Semigroups on Von Neumann Algebras
The paper proves a conjectured inequality: for quantum Markov semigroups with a faithful normal invariant state, the exponential decay rate w.r.t. the KMS inner product lower bounds that of the GNS inner product. This holds beyond Gaussian cases, extending to arbitrary von Neumann algebras. The resu…
New Positive Mass Theorem for Manifolds with Toroidal Ends Without Boundary
This paper introduces new positive mass theorem (PMT) results for asymptotically locally hyperbolic (ALH) manifolds lacking boundaries but possessing general toroidal ends. The methodology extends prior work by incorporating techniques related to μ-bubbles, originally developed for asymptotically fl…