🔢 Category

math-ph

2656 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

Derivation of a \PT\PT-Symmetric Sine-Gordon Model from a Nonequilibrium Spin-Boson System via Keldysh Functional Integrals

This paper presents a microscopic derivation of a PT\mathcal{PT}-symmetric non-Hermitian sine-Gordon effective theory from a nonequilibrium spin-boson system using Keldysh functional integrals, establishing a precise dictionary between microscopic parameters and effective couplings to demonstrate that the resulting renormalization group flow, exceptional point physics, and bound-state spectrum align with established non-Hermitian sine-Gordon results.

Vinayak M. Kulkarni2026-04-24
🔢 mathematics

Euler--Poincaré reduction and the Kelvin--Noether theorem for discrete mechanical systems with advected parameters and additional dynamics

This paper develops a discrete Euler-Poincaré reduction framework for mechanical systems with advected parameters and additional dynamics using group difference maps, extends the Kelvin-Noether theorem to this discrete setting, and demonstrates the method's effectiveness in preserving geometric properties through applications to underwater vehicle dynamics and numerical simulations.

Yusuke Ono, Simone Fiori, Linyu Peng2026-04-24
🔢 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