Related papers: Planar equilibrium measure problem in the quadrati…
We study two-dimensional (2D) droplets of noninteracting electrons in a strong magnetic field, placed in a confining potential with arbitrary shape. Using semiclassical methods adapted to the lowest Landau level, we obtain near-Gaussian…
The quantum-mechanical problems of a nonrelativistic free particle, a harmonic oscillator and a Coulomb particle on Minkowski plane are discussed. The Schr\"odinger equations for eigenvalues are obtained using the Beltrami-Laplas operator…
This paper deals with the relativistic, quantized electromagnetic and Dirac field equations in the arena of discrete phase space and continuous time. The mathematical formulation involves partial difference equations. In the consequent…
We study the one-dimensional quarter-filled extended Hubbard model with an alternating transfer integral. In the strong-dimerization limit the charge part is described by the quantum Ising model which shows the two-dimensional Ising…
In this paper we analyze a quartic tensor model with one interaction for a tensor of arbitrary rank. This model has a critical point where a continuous limit of infinitely refined random geometries is reached. We show that the critical…
We present a semiclassical analysis of the instability of an electron shuttle composed of three quantum dots: two are fixed and coupled via leads to electron resevoirs at different chemical potentials, while the central dot is mounted on a…
The Schr\"odinger equation for a charged particle in the field of a nonrelativistic electric quadrupole in two dimensions is known to be separable in spherical coordinates. We investigate the occurrence of bound states of negative energy…
Geometrical properties of two-dimensional mixtures near the jamming transition point are numerically investigated using harmonic particles under mechanical training. The configurations generated by the quasi-static compression and…
We consider the complex eigenvalues of a Wishart type random matrix model $X=X_1 X_2^*$, where two rectangular complex Ginibre matrices $X_{1,2}$ of size $N\times (N+\nu)$ are correlated through a non-Hermiticity parameter $\tau\in[0,1]$.…
We consider a constrained minimal energy problem with an external field over noncompact classes of infinite dimensional vector measures on a locally compact space. The components are positive measures (charges) that are constrained from…
Spectral properties of nuclei near the critical point of the quantum phase transition between spherical and axially symmetric shapes are studied in a hybrid collective model which combines the $\gamma$-stable and $\gamma$-rigid collective…
Nonequilibrium steady states of vibrated inelastic frictionless spheres are investigated in quasi-two-dimensional confinement via molecular dynamics simulations. The phase diagram in the density-amplitude plane exhibits a fluidlike…
We study the two-orbital Hubbard model in the limit of vanishing kinetic energy. The phase diagram in the $V-J$ plane, with $V$ and $J$ denoting the interorbital hybridization and exchange coupling respectively, at half filling is obtained.…
We study quantum droplets emerging in a quasi-one-dimensional asymmetric mixture of two atomic species with different intra-component coupling constants. We find that such mixtures support a rich variety of multipole quantum droplets, where…
By solving the Young Laplace equation of capillary hydrostatics one can accurately determine equilibrium shapes of droplets on relatively smooth solid surfaces. The solution, however of the Young Laplace equation becomes tricky when a…
We consider a system of second order non-linear elliptic partial differential equations that models the equilibrium configurations of a two dimensional planar bistable nematic liquid crystal device. Discontinuous Galerkin finite element…
We study the elliptic equation with a line Dirac delta function as the source term subject to the Dirichlet boundary condition in a two-dimensional domain. Such a line Dirac measure causes different types of solution singularities in the…
We study the inverse problem of determining uniquely and stably quasilinear terms appearing in an elliptic equation from boundary excitations and measurements associated with the solutions of the corresponding equation. More precisely, we…
We investigate the critical behavior of continuous phase transitions in the context of Ginzburg Landau models with a double well effective potential. In particular, we show that the recently proposed configurational entropy, a measure of…
The noncommutativity of a four-dimensional phase space is introduced from a purely symplectic point of view. We show that there is always a coordinate map to locally eliminate the gauge fluctuations inducing the deformation of the…