数学物理
In this paper, we review how local potentials arise in the Wu-Yang topological quantization. We also discuss the isomorphism between the de Rham cohomology classes and Cech cohomology classes in such topological quantization. We also…
The paper deals with the semi-Dirac operator in a half-space arising in the description of quasiparticles in quantum mechanics as well as in semi-metals materials and related structures. It completely shows the self-adjointness, computes…
Dynamics generated from Hamiltonians enjoy potential pathways to quantisation, but standard Hamiltonians are only capable of generating conservative forces. Classes of Hamiltonians have been proposed in Berry et al. capable of generating…
Schr\"odinger operators with periodic potential have generally been shown to exhibit ballistic transport. In this work, we investigate if the propagation velocity, while positive, can be made arbitrarily small by a suitable choice of the…
We give a complete and rigorous derivation of the mechanical energy for twisted 2D bilayer heterostructures without any approximation beyond the existence of an empirical many-body site energy. Our results apply to both the continuous and…
In this paper, thermodynamics of a moving medium is considered. Main goal of this paper is to describe thermodynamics state equations and equations of co-existence manifolds of media on two- and three-dimensional manifolds. To this end the…
In this paper, by studying a class of 1-D Sturm-Liouville problems with periodic coefficients, we show and classify the solutions of periodic Schrodinger equations in a multidimensional case, which tells that not all the solutions are Bloch…
One of the approaches to quantum gravity is to formulate it in terms of De Rham algebra, choose a triangulation of space-time, and replace differential forms by cochains (that form a finite dimensional vector space). The key issue of…
In the equivalent single layer theories of anisotropic laminates, the coupling tensor B describes the relation between the in- and out-of plane behavior of the plate. This tensor has some peculiar characteristics and in particular it is not…
We show the representability of density-entropy pairs with canonical and grand-canonical states, and we provide bounds on the kinetic energy of the representing states.
This work is concerned with the study of explicit solutions for generalized coupled reaction-diffusion and Burgers-type systems with variable coefficients. Including nonlinear models with variable coefficients such as diffusive…
In addition to standard and non-standard Lagrangians of classical mechanics, we consider, in this work, null Lagrangians that (i) identically satisfy the Euler-Lagrange equation and at the same time can be expressed as (ii) the total…
The nonstandard Lagrangian representations of Ricatti and Riccati-type equations that exist in the literature cannot be obtained using Helmholtz solution of the inverse problem. In this work we consider Riccati and higher-order Riccati…
In this work we propose and investigate a strategy to prevent consensus in kinetic models for opinion formation. We consider a large interacting agent system, and assume that agent interactions are driven by compromise as well as…
A $(q,t)$-deformation of the 2d Toda integrable hierarchy is introduced by enhancing the underlying symmetry algebra $\mathfrak{gl}(\infty)\simeq \text{q-W}_{1+\infty}$ to the quantum toroidal $\mathfrak{gl}(1)$ algebra. The…
The Dubrovin-Zhang hierarchy is a Hamiltonian infinite-dimensional integrable system associated to a semi-simple cohomological field theory or, alternatively, to a semi-simple Dubrovin-Frobenius manifold. Under an extra assumption of…
We define a hierarchy of Hamiltonian PDEs associated to an arbitrary tau-function in the semi-simple orbit of the Givental group action on genus expansions of Frobenius manifolds. We prove that the equations, the Hamiltonians, and the…
Eigenvectors associated with non-degenerate eigenvalues are shown to correspond to columns of the adjugate of the characteristic matrix. Degenerate eigenvalues are associated with eigenvectors that correspond to reduced complement tensors…
A cylinder will roll down an inclined plane in a straight line. A cone will roll around a circle on that plane and then will stop rolling. We ask the inverse question: For which curves drawn on the inclined plane $\mathbb{R}^2$ can one…
Quantum graphs have become in this century a favorite playground for mathematicians, mathematical physicists, and chemists, due to their manifold applications as models of thin structures, as well as presenting sometimes simpler playground…