3190 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 establishes radiation conditions and proves various uniqueness theorems for acoustic and electromagnetic wave-guide networks by utilizing generalizations of Mourre estimates to analyze time-harmonic Maxwell equations.
This paper investigates a modified single-component Abelian-Higgs model with an eighth-order scalar potential and a two-circle vacuum manifold, revealing type-1.5-like vortex behaviors including bound states, clustering of inner-vacuum vortices, and the formation of vortex-filled bubbles confined by domain walls.
This paper introduces the Constraint-Enhanced Quantum Approximate Optimization Algorithm (CE-QAOA), a shallow, ancilla-free hybrid solver that leverages encoded unitary designs and a specialized block-XY mixer to achieve empirical quantum advantages in constrained optimization, including polynomial shot complexity reductions and exponential minimax separations, while successfully finding global optima for small Traveling Salesman Problem instances.
This paper establishes the dynamical conservation of specific entropy, energy, and relative entropy in translation-invariant lattice quantum spin systems using Lieb-Robinson and Araki bounds, thereby providing the analytical foundation for the structural theory of approach to equilibrium.
This paper extends a structural theory for approach to equilibrium in translation-invariant quantum spin systems by demonstrating that dynamical steady states of regular interactions conserve specific energy, are characterized by a dynamical Gibbs variational principle minimizing specific relative entropy, and converge to thermal equilibrium when locality is restored and energy is the sole finite-range constant of motion.
This paper proves that the local eigenvalue statistics of one-dimensional Schrödinger operators with nondegenerate Bernoulli potentials (and certain bounded nonconstant i.i.d. potentials) converge to a Poisson point process of unit intensity after unfolding by the integrated density of states, utilizing a phase coordinate method to establish uniform exponential crossing laws.
This paper utilizes the theory of tangent and cotangent coverings to identify ten previously unknown integrable cases of the ABC-equation, expanding beyond the previously known Veronese web equation case where .
This paper proves that the ground-state energy per unit volume of Jellium coincides with that of the uniform electron gas, extending a previously known classical result to the quantum mechanical case.
This paper introduces a statistical-mechanical framework that treats entire spike trains as microstates within a Boltzmann-like distribution to characterize phase transitions between non-oscillatory and oscillatory neuronal activity regimes, supported by both analytical order parameters and Monte Carlo simulations.
This paper establishes a Landis-type unique continuation theorem at infinity for solutions to the Schrödinger equation with radially growing potentials, proving that solutions decaying faster than an explicitly computable threshold must vanish identically.