Related papers: Complex potentials and holomorphic differential eq…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support a tridiagonal matrix representation of the wave operator. Doing so results in exactly solvable problems with a…
We define and study a class of finite topological spaces, which model the cell structure of a space obtained by gluing finitely many Euclidean convex polyhedral cells along congruent faces. We call these finite topological spaces,…
This contribution briefly reviews some recent work demonstrating the partial breakdown of the colloidal fluid <--> atomic fluid analogy. The success of liquid state theory for atomic fluids stems in part from the van der Waals picture,…
In this article, we introduce and study the notion of a complete special holonomy manifold $(X,\omega)$ which is given by a global perturbation potential function, i.e., there is a function $f$ on $X$ such that…
We discuss how complex-oxide heterostructures that include high-Tc superconducting cuprates can be used to realize an array of sub-millimeter cavities that support Josephson plasmon polaritons. These cavities have several attractive…
Soliton propagation dynamics under the presence of a complex potential are investigated. A large variety of qualitatively different potentials, including periodic, semi-infinite periodic and localized potentials, is considered. Cases of…
It has recently been realized that fractals may be characterized by complex dimensions, arising from complex poles of the corresponding zeta function, and we show here that these lead to oscillatory behavior in various physical quantities.…
Complex potentials are constructed as Darboux-deformations of short range, radial nonsingular potentials. They behave as optical devices which both refracts and absorbs light waves. The deformation preserves the initial spectrum of energies…
We construct integrable pseudopotentials with an arbitrary number of fields in terms of elliptic generalization of hypergeometric functions in several variables. These pseudopotentials yield some integrable (2+1)-dimensional hydrodynamic…
This is the second part of a work aimed to study complex-phase oscillatory solutions of nonlinear symmetric hyperbolic systems. We consider, in particular, the case of one space dimension. That is a remarkable case, since one can always…
A complex-analytic structure within the unit disk of the complex plane is presented. It can be used to represent and analyze a large class of real functions. It is shown that any integrable real function can be obtained by means of the…
Given two potentials V0 and V1 together with a certain nodeless solution {\phi}0 of V0, we form a composition of these two potentials. If V1 is exactly solvable, the composition is exactly solvable, too. By combining various solvable…
The recently proposed effective potential theory [Phys. Rev. Lett. 110, 235001 (2013)] allows evaluating transport in coupled plasmas with the well-developed formalisms for systems with binary collisions. To facilitate practical…
The closed-form expressions of electric potentials and field lines for a uniformly-charged tube and cylinder are presented using elliptic integrals and Appell's hypergeometric functions, where field lines are depicted by introducing the…
Partition function zeros provide alternative approach to study phase structure of finite density QCD. The structure of the Lee-Yang edge singularities associated with the zeros in the complex chemical potential plane has a strong influence…
The morphometric approach is a powerful ansatz for decomposing the chemical potential for a complex solute into purely geometrical terms. This method has proven accuracy in hard spheres, presenting an alternative to comparatively expensive…
Complex polynomial optimization has recently gained more and more attention in both theory and practice. In this paper, we study the optimization of a real-valued general conjugate complex form over various popular constraint sets including…
We isolate a combinatorial property of capacities leading to a construction of proper forcings. Then we show that many classical capacities such as the Newtonian capacity satisfy the property.
A potential can have features that do not reflect the dynamics of the system it describes but rather arise from the choice of interpolating fields used to define it. This is illustrated using a toy model of scattering with two coupled…
We study discrete complex analysis and potential theory on a large family of planar graphs, the so-called isoradial ones. Along with discrete analogues of several classical results, we prove uniform convergence of discrete harmonic…