数学物理
This Ph.D. thesis reports on progress in rigorously establishing hydrodynamic principles from the microscopic Hamiltonian dynamics of quantum many-body systems in a general, non-model-specific manner. Using the C*-algebra framework of…
The twisted product of functions on $R^{2N}$ is extended to a $*$-algebra of tempered distributions which contains the rapidly decreasing smooth functions, the distributions of compact support, and all polynomials, and moreover is invariant…
This paper discusses the modeling of acoustic wave fields in microstructured elastic solids within the framework of Riemann-Cartan geometry. We consider a scenario in which microstructural deformations occur significantly faster than those…
Recently, data-driven methods have shown great promise for discovering governing equations from simulation or experimental data. However, most existing approaches are limited to scalar equations, with few capable of identifying tensor…
In this paper we study the phase diagram of a Sherrington-Kirkpatrick (SK) model where the couplings are forced to thermalize at different time scales. Besides being a challenging generalization of the SK model, such settings may arise…
In a recent paper by G\'erard, H\"afner, and Wrochna, the Unruh state for massless fermions on a Kerr spacetime was constructed and the authors showed its Hadmard property in the case of very slowly rotating black holes $\vert a\vert\ll M$.…
We report partial progress on the weak coupling limit behavior of observables for the periodic quantum Lorentz gas. Our results indicate that for certain observables, the limit behavior is trivial and can be described via a transport…
We investigate the quantum structure of spacetime at fundamental scales via a novel, Lorentz-invariant noncommutative coordinate framework. Building on insights from noncommutative geometry, spectral theory, and algebraic quantum field…
We construct a unified framework of geometrodynamics based on the Finsler geometry to reveal the relationship between spacetime and dynamics.The Lagrangian of electron in electromagnetic field as the Finsler function gives the Finslerian…
This paper presents a PDE approach as an alternative to Monte Carlo simulations for computing the invariant measure of a white-noise-driven bilinear oscillator with hysteresis. This model is widely used in engineering to represent highly…
A third-order operator with periodic coefficients is an L-operator in the Lax pair for the Boussinesq equation on a circle. The projection of the divisor of the Floquet solution poles for this operator coincides with the spectrum of the…
Pure-breakage population balance equations (PBEs) give the standard deterministic description of fragmentation and comminution. They predict mean particle size distributions, but they do not determine fluctuations, size-size correlations,…
We introduce a {\it non-linear} generalization of the classical Dobrushin-Lanford-Ruelle (DLR) framework by developing the concept of a $q$-specification and the associated $q$-equilibrium measures. These objects arise naturally from a…
Diffusion models have recently achieved remarkable success in generative modeling, yet they are commonly formulated as black-box stochastic systems with limited interpretability and few structural guarantees. In this paper, we establish a…
Asymptotic completeness of Rayleigh scattering in models of atoms and molecules of non-relativistic QED is expected, but for a proof we still lack sufficient control on the number of emitted soft photons. So far, this obstacle has only been…
Wahl et al. (2016, 2017) introduced the idea of Granger causality (GC) maps for Langevin systems: dynamics are localised linearly at each point in phase space as vector Ornstein-Uhlenbeck (VOU) processes, for which GCs may in principle be…
We analyze the issue of unitary equivalence within Generalized Uncertainty Principle (GUP) theories in the one-dimensional case. For a deformed Heisenberg algebra, its representation in terms of Hilbert space and conjugate operators is not…
One of the oldest and most common structural engineering issues is the elastic buckling of circular rings under external pressure, which has a fundamental importance in a number of applications in general mechanics, engineering and…
We prove a general version of the crystalline equivalence principle which gives an equivalence of categories between a category of TQFTs defined on a generic space with $G$-symmetry, and a category of TQFTs with internal symmetry. We give a…
Let $(M,g)$ be some smooth, closed, compact Riemannian manifold and $(M_N\mapsto M)_N$ be an increasing sequence of large degree cyclic covers of $M$ that converges when $N\rightarrow +\infty$, in a suitable sense, to some limit…