数学物理

We consider classical $O(N)$ vector models in dimension three and higher and investigate the nature of the low-temperature expansions for their multipoint spin correlations. We prove that such expansions define asymptotic series, and derive…

This paper contains a review of the theoretical foundations of Clifford algebras, spinors and spinor bundles in the so-called co-frame formalism. A compact index-free notation is introduced, along with a series of identities useful for…

This paper solves ``The Dry Ten Martini Problem'' for $C^2$ cosine-type quasiperiodic Schr\"odinger operators with large coupling constants and Diophantine frequencies, a model originally introduced by Sinai in 1987 \cite{sinai}. This shows…

We solve the Dry Ten Martini Problem for the unitary almost Mathieu operator with Diophantine frequencies in the non-critical regime.

This paper introduces a Heisenberg picture approach to Matrix Product States (MPS), offering a rigorous yet intuitive framework to explore their structure and classification. MPS efficiently represent ground states of quantum many-body…

This study addresses the often underestimated importance of physical dimensions and units in the formal reconstruction of physical theories, focusing on structuralist approaches that use the concept of ``species of structure" as a…

The existence of edge states is one of the most vital properties of topological insulators. Although tremendous success has been accomplished in describing and explaining edge states associated with PT symmetry breaking, little work has…

Drinfeld classified Poisson homogeneous spaces of a Poisson Lie group in terms of Dirac structures of the Lie bialgebra. In this paper, we study homogeneous spaces of a 2-group and develop Drinfeld theorem in the Poisson 2-group context.

The Vicsek model has long stood as a pivotal framework in exploring collective behavior and self-organization, captivating the scientific community with its compelling dynamics. However, understanding how noise influences synchronization…

We revisit the work of Rieffel and van Daele on pairs of subspaces of a real Hilbert space, while relaxing as much as possible the assumption that all the relevant subspaces are in general positions with respect to each other. We work out,…

Recent work of three of the authors showed that the operator which maps the local density of states of a one-dimensional untwisted bilayer material to the local density of states of the same bilayer material at non-zero twist, known as the…

It is shown that the $\mathfrak{gl}(3)$ polynomial integrable system, introduced by Sokolov-Turbiner in [arXiv:1409.7439], is equivalent to the $\mathfrak{gl}(3)$ quantum Euler-Arnold top in a constant magnetic field. Their Hamiltonian as…

A novel probabilistic framework for modelling anomalous diffusion is presented. The resulting process is Markovian, non-homogeneous, non-stationary, non-ergodic, and state-dependent. The fundamental law governing this process is driven by…

Periods of rational integrals appear in quantum mechanics through asymptotic expansions of traces computed with the semiclassical symbol calculus. We develop a novel formal series expansion for the trace of the Dirac delta of a differential…

We clarify how the elliptic integrable spin chain recently found by Matushko and Zotov (MZ) relates to various other known long-range spin chains. The limit $q\to1$ gives the elliptic spin chain of Sechin and Zotov (SZ), whose trigonometric…

We consider the bounded linear operators with domain in the Hilbert space $L^2(S^n)$, $n=2,3,5$ and describe its symbolic calculus defined by the Berezin quantization. In particular, we derive an explicit formula for the composition of…

A geometric framework, called multicontact geometry, has recently been developed to study action-dependent field theories. In this work, we use this framework to analyze symmetries in action-dependent Lagrangian and Hamiltonian field…

This paper introduces a comprehensive extension of the path integral formalism to model stochastic processes with arbitrary multiplicative noise. To do so, It\^o diffusive process is generalized by incorporating a multiplicative noise term…

A ${\mathbb Z}_2\times{\mathbb Z}_2$-graded Lie algebra $\mathfrak g$ is a ${\mathbb Z}_2\times{\mathbb Z}_2$-graded algebra $\mathfrak g$ with a bracket $[|. , . |]$ that satisfies certain graded versions of the symmetry and Jacobi…

On plain physical grounds localization of relativistic quantum particles is extended to the achronal regions of Minkowski spacetime. Achronal localization fulfills automatically the requirements of causality. It constitutes the frame which…