数学物理
The work is a natural continuation of that published in Stud Appl Math. 2024; 153:e12737. All possible two-components evolutions systems of (1+2)-dimensional second-order PDEs admitting an infinite-dimensional Lie algebra are constructed.…
The Renormalization Group (RG) is a powerful and versatile framework for analyzing complex physical systems. Here, we reinterpret it as a stochastic process that explores physical phase spaces, scale by scale, progressively revealing finer…
Fractal structures generated through nonlinear breather interactions are investigated for the $(2+1)$-dimensional Konopelchenko--Dubrovsky (KD) equation by means of the Hirota bilinear method. The bilinear form of the system is first…
Reflection positivity is one of the Osterwalder--Schrader axioms for Euclidean quantum field theory, ensuring that the reconstructed relativistic Hilbert space carries a positive-definite inner product. For free fermionic theories whose…
Let $(M,g)$ be a smooth orientable $2d$ Riemannian manifold of genus $\mathfrak{g}$ with Riemannian metric $g$ and connected boundary $\Gamma$. Let $\Lambda$ be the Dirichlet-to-Neumann map on $\Gamma$ and let ${\rm det}_\zeta(\Lambda)$ be…
Let $\psi({\mathbf x})$, ${\mathbf x} \in{\mathbb R}^{3N}$, be an eigenfunction of the $N$-particle atomic Schr\"odinger operator. We consider the one-particle density matrix $\gamma(x, y)$ and one-particle kinetic energy density…
The motion of a projectile released from a simple pendulum is analyzed, with particular emphasis on investigating the optimal release angle that maximizes the horizontal range and the corresponding maximum range. This system serves as a…
A differential calculus for causal variational principles is developed, which generalizes the exterior calculus of differential forms and some of the associated differential topological structures to non-smooth spaces. Our calculus includes…
These are detailed expository notes on the staggered optical-lattice hard-core Bose gas of Aizenman, Lieb, Seiringer, Solovej and Yngvason. They restate and expand the arguments and their principal inputs in a common notation, and describe…
We investigate the analyticity of the free energy of the Ising model in the presence of a non-zero external magnetic field, at high temperature, and at low temperature. Using the Fernandez--Procacci convergence criterion for cluster…
A new recursive implementation of the equivariant moving frame method for infinite-dimensional Lie pseudo-group actions is presented. It allows pseudo-group normalizations to be performed before the prolonged action is computed, thereby…
We develop a perturbative framework for time-dependent point interactions in quantum systems with purely discrete unperturbed spectrum. In two and three dimensions the point interaction is described through the renormalized resolvent…
The Lambert $W$ (LW) model for the cosmic fluid equation of state was proposed by S. Saha and K. Bamba in 2019-2020. A recent (early 2026) paper by Dubey, et al, carries out a new fit of the LW model to observational data, in order to…
We develop a one-dimensional theory of dispersive elasticity within Rational Extended Thermodynamics, taking local first-order balance laws rather than higher spatial gradients as the fundamental description. A supplementary…
The quantum-mechanical two-sided Bogoliubov inequality provides upper and lower bounds for the free energy required to separate a system of interacting particles into independent subsystems. The bounds can be calculated straightforwardly…
Topological defects in quantum field theories are believed to assemble into higher categories with extra structure. This has been made precise for defects in $2$- and $3$-dimensional oriented topological quantum field theories by Davydov,…
This article investigates the effective mass density for acoustic and elastic wave propagation in layered media, with emphasis on its transition between these regimes. Conventionally, it is possible to recover the governing equations of…
We present a graphene-assisted MR-DWELL dosimeter governed by electrostatic interface engineering. By adjusting the h-BN spacer, the ratio between graphene's quantum capacitance and the geometric capacitance tunes the screening factor,…
Starting from the Standard Model Lie algebra $\mathfrak{g}_{\mathrm{SM}} = \mathfrak{sl}_3 \oplus \mathfrak{sl}_2 \oplus \mathbb{C}$ sitting inside the complex Lie algebra $\mathfrak{e}_7$, we show how to decompose $\mathfrak{e}_7$ into the…
We introduce a second-order mean-field description of the four-dimensional Euclidean $\phi^4$ model within the Wilson--Polchinski renormalization-group framework. The construction is based on the connected amputated Schwinger functions…