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.
This paper resolves the long-standing questions of uniqueness and weak Gibbsianity for gauge-invariant quasi-free fermionic states by proving that, under specific conditions on their momentum-space two-point functions, these states uniquely maximize entropy among translation-invariant states and are indeed weak Gibbs states, with both properties derived directly from thermodynamic formalism.
This paper proposes an extension of the Alicki-Lindblad-Fannes dynamical entropy to open quantum systems as a measure of information back-flow from the environment, deriving an exact expression for a qubit coupled to a classical spin chain that demonstrates how such information flow can lead to vanishing entropy production.
This paper establishes a general existence theorem for null Force-Free Electrodynamics solutions by proving that any null geodesic congruence admits a transverse basis rotation satisfying the equipartition condition and that shear-free congruences guarantee the existence of field sheet foliations, thereby providing a coordinate-independent geometric criterion for such solutions illustrated through explicit examples in various spacetimes.
This paper establishes a first-principles theory of vacuum Wannier functions that unifies tight-binding and nearly-free-electron models to enable predictive photoemission calculations without semiempirical potentials by constructing dense k-space scattering states at solid-vacuum interfaces.
This paper demonstrates that naively applying stochastic and dissipative terms to nonholonomic systems like the Chaplygin sleigh violates the second law of thermodynamics, but this paradox is resolved by modeling the constraint as a viscous limit that necessitates accompanying stochastic forces, thereby restoring thermodynamic consistency and establishing fundamental limits on the physical realizability of idealized nonholonomic constraints.
This paper investigates the first-return time of random walkers undergoing fractional diffusion with Mittag-Leffler distributed waiting times, demonstrating that for symmetric jump distributions, the return time density depends solely on the waiting-time distribution and providing exact results for both Markovian and non-Markovian settings under different temporal orderings of jumps and waits.
This paper introduces a rigorous and computationally tractable Density Functional Theory (DFT++) framework that extends the cut-and-project method to directly solve the Schrödinger equation for quasicrystals, enabling the ab initio specification of their quantum states without relying on crystalline approximants.
This paper provides sharp, exact characterizations of quantum conditional mutual information and other entropies by transforming their definitions into rapidly converging sums of explicitly constructed terms that inherently demonstrate desired properties like positivity and convexity, thereby offering precise equalities for both small and large values without relying on approximations.
This paper introduces a Gagliardo-type framework for fractional Sobolev spaces on arbitrary time scales using the Lebesgue -measure and off-diagonal interaction energies, establishing their Banach and Hilbert space properties, proving Poincaré-type inequalities that reflect the underlying geometry, and unifying continuous, discrete, and hybrid settings.
This paper investigates the topological content of the Zak phase in one-dimensional topological insulators across all Altland-Zirnbauer-Cartan symmetry classes, demonstrating how to construct a -valued invariant from the Zak phase while revealing that quaternionic structures imposed by specific anti-unitary symmetries force this invariant to vanish.