🔢 Category

math-ph

3366 papers

Mathematical physics sits at the fascinating intersection where abstract equations meet the fundamental laws of our universe. This field uses rigorous mathematical tools to model everything from the behavior of subatomic particles to the curvature of spacetime, turning complex theories into testable predictions. It is the language through which physicists describe reality, bridging the gap between pure mathematics and physical observation.

On Gist.Science, we process every new preprint published in this category on arXiv to make these dense studies accessible to everyone. Whether you are a specialist or a curious reader, you will find both plain-language overviews and detailed technical summaries for each paper. Below are the latest mathematical physics papers from arXiv, curated to help you explore the cutting edge of theoretical science.

🔢 mathematics

Gauss Principle in Incompressible Flow: Unified Variational Perspective on Pressure and Projection

This paper clarifies that the Gauss-Appell principle, when applied at a fixed time to incompressible inviscid flow, yields a variational minimization that uniquely determines the reaction pressure as the Lagrange multiplier enforcing kinematic constraints, thereby recovering the Euler equations and the Leray-Hodge projection without inherently selecting global flow features like circulation.

Karthik Duraisamy2026-04-24
🔬 mesoscale physics

Universal scaling of finite-temperature quantum adiabaticity in driven many-body systems

This paper establishes a rigorous, model-independent criterion for finite-temperature quantum adiabaticity in driven many-body systems by deriving bounds on mixed-state fidelity that reveal a universal scaling where the threshold driving rate factorizes into zero-temperature system-size contributions and a temperature-dependent factor that transitions from unity at low temperatures to linear behavior at high temperatures.

Li-Ying Chou, Jyong-Hao Chen2026-04-24
🔢 mathematics

How it cools? Studying the heat flow out of a semi-infinite slab in welding: An analytical approach

This paper presents a novel analytical framework using Laplace transforms and Fourier series to derive closed-form solutions for transient and steady-state heat flow in semi-infinite slabs with Newtonian cooling, offering a computationally efficient and accurate alternative to existing models for optimizing thermal management in welding and additive manufacturing.

Fawzi Aly, Alex Kitt, Luke Mohr2026-04-24
🔢 mathematics

On invariant solutions of linear time-fractional diffusion-wave equations with variable coefficients

This paper employs Lie symmetry analysis to determine infinitesimal symmetries and derive exact invariant solutions for a class of time-fractional diffusion-wave equations with variable coefficients, expressing the results in terms of Mittag-Leffler, generalized Wright, and Fox H-functions.

Sodbaatar Adiya, Khongorzul Dorjgotov, Bayarmagnai Gombodorj, Hiroyuki Ochiai, Uuganbayar Zunderiya2026-04-24
🔢 mathematics

Symplectic symmetry of quadratic-band-touching Hamiltonians in two dimensions

This paper identifies the internal low-energy symmetry of two-dimensional quadratic-band-touching Hamiltonians as the unitary symplectic group USp(2N)USp(2N), constructs the corresponding rotationally invariant interacting theory, and demonstrates that for lattice systems like honeycomb, this symmetry reduces to the unitary group U(N)U(N) through the intersection of symplectic and orthogonal symmetries.

Igor F. Herbut, Samson C. H. Ling2026-04-24
🔢 mathematics

Yang-Baxter Integrability and Exceptional-Point Structure in Pseudo-Hermitian Quantum Impurity Systems

This paper establishes a mathematically controlled framework for Yang-Baxter integrability in periodically driven pseudo-Hermitian quantum impurity systems, demonstrating how a modified RTT structure and biorthogonal Bethe ansatz enable the characterization of exceptional points through defective Gaudin matrices and square-root coalescence of rapidities.

Vinayak M. Kulkarni2026-04-24
🔢 mathematics

Quantum Mixing for Schrödinger eigenfunctions in Benjamini-Schramm limit

This paper establishes quantum mixing for Schrödinger eigenfunctions on a sequence of compact hyperbolic surfaces converging to the hyperbolic plane in the Benjamini-Schramm limit, utilizing the Duhamel formula and exponential mixing of the geodesic flow to apply the results to congruence covers, random high-genus surfaces, and many-body Bose gas models.

Kai Hippi, Félix Lequen, Søren Mikkelsen, Tuomas Sahlsten, Henrik Ueberschär2026-04-24
🔢 mathematics

The KMS and GNS Spectral Gap of Quantum Markov Semigroups

This paper proves that for quantum Markov semigroups with a faithful normal invariant state on arbitrary von Neumann algebras, the exponential decay rate with respect to the KMS inner product (and a broader class of operator monotone induced inner products) is bounded below by the decay rate with respect to the GNS inner product, thereby confirming a conjecture previously limited to the Gaussian case.

Melchior Wirth2026-04-24