3210 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 develops a theory for the exact transmission of finite-dimensional -algebras through quantum channels, revealing that a single dominating algebra often fails to exist even in small dimensions, which necessitates selecting among incomparable maximal algebras and leads to complex phenomena such as algebraic superadditivity and doubly exponential growth in transmittable types at large block-lengths.
This paper investigates the Casimir effect of a massive, self-interacting scalar field in a -dimensional Hořava-Lifshitz theory with rough boundaries, deriving renormalized effective potentials and Casimir energies up to two loops to reveal how anisotropic scaling, boundary roughness, and temperature influence the results, particularly noting infrared divergences in the massless limit for odd scaling exponents .
This paper establishes limit theorems, including pathwise ergodicity, central limit theorems, and Berry–Esseen bounds, for discrete-time quantum trajectories in disordered environments under a quenched Doeblin condition, demonstrating the convergence of posterior states to a unique dynamically stationary state and characterizing the statistical fluctuations of additive functionals for almost every disorder realization.
This paper generalizes the Reimpell-Werner iteration to linear objectives with arbitrary Hermitian cost matrices, proving that it converges to a global optimum under specific initialization conditions with an asymptotic iteration complexity of .
This paper introduces Quantum Markov State Models (QMSMs) to describe the long-time dynamics of open quantum systems by constructing optimal compression and reconstruction channels that preserve both classical metastable phases and quantum coherence, achieving rigorous diamond-norm error bounds that answer Kitaev's exact-rounding question.
This paper establishes a framework comparing covariant quantum state tomography protocols by deriving their large deviation rate functions in terms of a new family of divergences, demonstrating that these rate functions provide a more fine-grained performance metric than traditional sample complexity by revealing strict orderings even among order-optimal protocols.
This paper introduces a pseudo-control protocol that experimentally characterizes the memory dimension of open quantum dynamics by encoding environmental information into an interference matrix, enabling the certification of memory lower bounds without requiring direct access to the environment or full process-tensor tomography.
This paper establishes a connection between the classical limit of the Magnus expansion in quantum field theory and the Malvenuto-Reutenauer Hopf algebra of permutations, demonstrating how cancellations of disconnected diagrams via the adjoint first Eulerian projector allow the derivation of generic Murua coefficients from simpler directed chain coefficients and revealing a link to web-mixing matrices.
This paper introduces a novel ansatz utilizing diagonal phase matrices, Fourier matrices, and real Hadamard matrices to construct new sets of mutually unbiased bases (MUBs) in various dimensions, including specific improvements in dimension 12 and asymptotic extensions that exceed previous tensor product bounds.
This paper establishes a multifaceted hierarchy of quantum channel discrimination strategies for distinguishing non-mixed-unitary channels from mixed-unitary ones, demonstrating that while fully independent and identically distributed (i.i.d.) probes fail without auxiliary memory, introducing block correlations or auxiliary memory enables strictly positive Stein exponents, with auxiliary memory rendering fully i.i.d. probes sufficient for all non-mixed-unitary channels.