相关论文: The ellipse law: Kirchhoff meets dislocations
We consider $\mathbb{S}^2$-valued maps on a domain $\Omega\subset\mathbb{R}^N$ minimizing a perturbation of the Dirichlet energy with vertical penalization in $\Omega$ and horizontal penalization on $\partial\Omega$. We first show the…
Minimal surfaces in $\mathbb{R}^n$ can be locally approximated by graphs of harmonic functions, i.e., functions that are critical points of the Dirichlet energy, but no analogous theorem is known for $H$-minimal surfaces in the…
We study the dynamics of quantized superfluid vortices on axisymmetric compact surfaces with no holes, where the total vortex charge must vanish and the condition of irrotational flow forbids distributed vorticity. A conformal…
We investigate the locality or nonlocality of the energy transfer and of the spectral interactions involved in the cascade for decaying magnetohydrodynamic (MHD) flows in the presence of a uniform magnetic field $\bf B$ at various…
We compute the first-order correction in the quartic coupling $\alpha$ to the entanglement entropy of a massive, non-minimally coupled scalar across the horizon of a four-dimensional Schwarzschild black hole, treating the non-minimal…
In this work we analytically calculate the time-averaged electromagnetic energy stored inside a nondispersive magnetic isotropic cylinder which is obliquely irradiated by an electromagnetic plane wave. An expression for the…
For every $g\in\mathbb{N}_0$ and $\epsilon>0$, we construct a smooth genus $g$ surface embedded into the unit ball with area $8\pi$ and Willmore energy smaller than $8\pi + \epsilon$. From this we deduce that a minimising sequence for…
Various packing problems and simulations of hard and soft interacting particles, such as microscopic models of nematic liquid crystals, reduce to calculations of intersections and pair interactions between ellipsoids. When constrained to a…
This paper examines the properties of the self-energy operator in lattice-matched semiconductor heterostructures, focusing on nonanalytic behavior at small values of the crystal momentum, which gives rise to long-range Coulomb potentials. A…
We investigate a one-parameter family of Coulomb gases in two dimensions, which are confined to an ellipse, due to a hard wall constraint, and are subject to an additional external potential. At inverse temperature $\beta=2$ we can use the…
We study the stationary non-local equation which corresponds to the energy functional of a one-dimensional Ising spin system, in which particles interact via a Kac potential. The boundary conditions share the same sign and both lie above…
This study focuses on microscopic-sized quantum vortex filaments that are shaped like a circle. The model we considered examines loops with different radii and a small but non-zero core diameter. These loops are located in a bounded domain…
The coefficient of the logarithmic term in the entropy on even spheres is re-computed by the local technique of integrating the finite temperature energy density up to the horizon on static d--dimensional de Sitter space and thence finding…
We study the asymptotic behaviour, as a small parameter $\varepsilon$ tends to zero, of minimisers of a Ginzburg-Landau type energy with a nonlinear penalisation potential vanishing on a compact submanifold $\mathcal{N}$ and with a given…
We study a large family of Riesz-type singular interaction potentials with anisotropy in two dimensions. Their associated global energy minimizers are given by explicit formulas whose supports are determined by ellipses under certain…
We study the entropy solution for a class of systems of nonlocal conservation laws in which the convective flux is convoluted with a kernel in both spatial and temporal variables. This formulation models the flux dependence on the solution…
We consider a class of one-dimensional quantum spin systems on the finite lattice $\Lambda\subset\mathbb{Z}$, related to the XXZ spin chain in its Ising phase. It includes in particular the so-called droplet Hamiltonian. The entanglement…
Magnetic fields break time-reversal symmetry, which is leveraged in many settings to enable the nonreciprocal behavior of light. This is the core physics of circulators and other elements used in a variety of microwave and optical settings.…
We investigate the optical and quantum mechanical properties of a charged spinless particle confined in a two-dimensional quantum ring under the simultaneous influence of a spiral dislocation and an external magnetic field. The dislocation…
We consider pure quantum states of $N\gg 1$ spins or qubits and study the average entanglement that can be \emph{localized} between two separated spins by performing local measurements on the other individual spins. We show that all…