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Spatial aspects in quantum mechanics are often difficult to model in geometrically intricate settings that are typical of mesoscopic physics. In such cases, predicting the device behaviors is a vital but difficult challenge. Transverse…
We examine a system of three-bosons confined to two dimensions in the presence of a perpendicular magnetic field within the framework of the adiabatic hyperspherical method. For the case of zero-range, regularized pseudo-potential…
The Laplace operator encodes the behavior of physical systems at vastly different scales, describing heat flow, fluids, as well as electric, gravitational, and quantum fields. A key input for the Laplace equation is the curvature of space.…
A Margulis spacetime is a complete flat Lorentzian 3-manifold M with free fundamental group. Associated to M is a noncompact complete hyperbolic surface S homotopy-equivalent to M. The purpose of this paper is to classify Margulis…
In this work we characterize certain immersed closed hypersurfaces of some ambient manifolds via the second eigenvalue of the Jacobi operator. First, we characterize the Clifford torus as the surface which maximizes the second eigenvalue of…
We continue our investigation of the space of geodesic laminations on a surface, endowed with the Hausdorff topology. We determine the topology of this space for the once-punctured torus and the 4-times-punctured sphere. For these two…
We study surfaces of constant positive Gauss curvature in Euclidean 3-space via the harmonicity of the Gauss map. Using the loop group representation, we solve the regular and the singular geometric Cauchy problems for these surfaces, and…
Based on Lippmann-Schwinger equation approach, we discuss a three-particle system in finite volume. A set of equations which relate the discrete finite-volume energies to the scattering amplitudes are derived under the approximation of the…
A new type of basis functions is proposed to describe a two-electron continuum which arises as a final state in electron-impact ionization and double photoionization of atomic systems. We name these functions, which are calculated in terms…
We propose a technique of compensating the spurious reflections implied by the multiple-scattering (MS) method, commonly used for analyzing finite photonic crystal (PC) systems, to obtain exact values of characteristic parameters, such as…
The possibility that our space is multi - rather than singly - connected has gained a renewed interest after the discovery of the low power for the first multipoles of the CMB by WMAP. To test the possibility that our space is a…
We introduce a simple algorithm which transforms every four-dimensional cubulation into a cusped finite-volume hyperbolic four-manifold. Combinatorially distinct cubulations give rise to topologically distinct manifolds. Using this…
The perturbation method in supersymmetric quantum mechanics (SUSYQM) is used to study the spheroidal wave functions' eigenvalue problem. Expanding the super-potential in series of the parameter alpha, the first order term of ground…
As is well-known, given the complex sphere P^1 minus two points, there exist nonconstant holomorphic maps from the plane into this set, the simplest example of which is given by applying the exponential map and then composing with a…
A generalization of the stochastic wave function method to quantum master equations which are not in Lindblad form is developed. The proposed stochastic unravelling is based on a description of the reduced system in a doubled Hilbert space…
A short-ranged, rotationally symmetric multi-Landau-level model Hamiltonian for strongly interacting electrons in a magnetic field was proposed [A. Anand et al, Phys. Rev. Lett. 126, 136601 (2021)] with the key feature that it allows exact…
A precursor effect on the Fermi surface in the two-dimensional Hubbard model at finite temperatures near the antiferromagnetic instability is studied using three different itinerant approaches: the second order perturbation theory, the…
We probe for statistical and Coulomb induced spin textures among the low-lying states of repulsively-interacting particles confined to potentials that are both rotationally and time-reversal invariant. In particular, we focus on…
We study random elements of subgroups (and cosets) of the mapping class group of a closed hyperbolic surface, in part through the properties of their mapping tori. In particular, we study the distribution of the homology of the mapping…
We study the {\it arc and curve} complex $AC(S)$ of an oriented connected surface $S$ of finite type with punctures. We show that if the surface is not a sphere with one, two or three punctures nor a torus with one puncture, then the…