Quantum Measurement and Continuous Markov Processes
This paper presents lecture notes from a Perimeter Institute course delivered in late 2025 on diffusive quantum measuring instruments and their connection to continuous Markov processes.
🔢 Category
math-ph
1605 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.
-Deformed Topological Recursion, Weight Vectors and Algebraic Structures
This paper extends the shifted topological recursion to a -deformed framework using highest weight vectors in -algebra representations, thereby deriving -deformed quantum curves and unifying approaches to quantum integrability with insights into -deformed moduli spaces.
Quantization of Contact 3-Manifolds and the Reeb Gravitational Field
This paper proposes a unified geometric framework that canonically quantizes closed contact 3-manifolds via holomorphic embeddings into to define finite-dimensional Hilbert spaces, while demonstrating that the Reeb vector field models Einstein gravity under Sasakian assumptions and providing a novel quantum invariant to distinguish tight contact structures.
Complete Classification and Nondegeneracy of -Component Cubic Nonlinear Schrödinger System in
This paper provides a complete classification of nontrivial solutions, proves the nondegeneracy of the linearized operator, and derives exact -mass identities for the one-dimensional -component cubic nonlinear Schrödinger system, thereby resolving conjectures previously established only for the cases and .
-sectorial discrete Laplacians and recurrence of complex-weighted graphs
This paper establishes that complex-weighted graphs with sectorial edge weights generate -sectorial Dirichlet Laplacians, enabling their extension to electrical networks to prove convergence results and characterize recurrence through functional spaces, capacities, and resolvent properties.
The Algebra of Units: From Buckingham's Pi-grec Theorem to Latent-Variable Learning
This paper presents a data-driven method that automatically discovers dimensionless physical groups from raw measurements using logarithmic transformation, singular value decomposition, and integer-exponent search, thereby recovering classical engineering laws without prior knowledge of the underlying physics.
Exact solution of the Glauber-Ising model on the finite-length semi-open chain
This paper derives the exact time-space correlation function for the finite-length semi-open Glauber-Ising model quenched to zero temperature, enabling the calculation of the dual coagulation-diffusion process's empty-interval probability and confirming consistency with dynamical finite-size scaling theory.
Quantum uniformity norms are pullbacks of matrix-valued uniformity norms
This paper establishes that quantum uniformity norms are pullbacks of matrix-valued uniformity norms under the Weyl orbit embedding, a result that proves their Gowers-Cauchy-Schwarz and triangle inequalities while characterizing Clifford levels via unitary-valued Leibman polynomial maps.
Non-linear stability of the matter dominated universe
This paper numerically demonstrates that the Einstein-de Sitter spacetime is non-linearly stable under small, generic perturbations when modeled with a polytropic fluid, contrasting with its known instability under dust and revealing a new stable regime in cosmological models.
The Optimal Rate Function in Covariant Quantum State Tomography
This paper proves Keyl's conjecture that a specific Schur sampling-based covariant quantum state tomography protocol achieves the optimal rate function, which is an annealed version of quantum relative entropy bounded by the standard quantum relative entropy due to the cost of learning the eigenbasis.