Related papers: A Solvable Two-Charge Ensemble on the Circle
We study equilibrium configurations of infinitely many identical particles on the real line or finitely many particles on the circle, such that the (repelling) force they exert on each other depends only on their distance. The main question…
I describe a verifiable criterion for the solvability of the 2 by 2 spectral Nevanlinna-Pick problem with two interpolation points, and likewise for three other special cases of the mu-synthesis problem. The problem is to construct an…
We discuss the motion of electrically and magnetically charged particles in the electromagnetic swirling universe. We show that the equations of motion can be decoupled in the Hamilton-Jacobi formalism, revealing the existence of a fourth…
The concept of fractional charge is central to the theory of the fractional quantum Hall effect (FQHE). Here I use exact diagonalization as well as configuration space renormalization (CSR) to study finite clusters which are large enough to…
We propose a one-loop neutrino mass model with several $SU(2)_L$ multiplet fermions and scalar fields in which the inert feature of a scalar to realize the one-loop neutrino mass can be achieved by the cancellation among Higgs couplings…
We discuss the charge distributions across the bulk of a two-dimensional electron gas system which is on an integer or fractional quantum Hall plateau. Our analysis is based on a relation, derived from the long wavelength limit of the bulk…
Starting from a collective description of the incompressible fractional quantum Hall liquid as an elastic medium that supports gapped neutral excitations I show that the one-electron spectral function of this system exhibits a sharp peak at…
We analyze the structure of higher-order radiative corrections for processes with unstable particles. By subsequently integrating out the various scales that are induced by the presence of unstable particles we obtain a hierarchy of…
A modified version of the spinless Anderson model is studied by means of the continuous-time quantum Monte Carlo method. This study is motivated by the peculiar heavy-fermion behavior observed in certain Samarium compounds, which is…
We analyze the process of two-particle scattering with unstable particle in an intermediate state. It was shown that the cross-section can be represented in the universal factorized form for an arbitrary set of particles. Phenomenological…
We propose a simple quantum mechanical equation for $n$ particles in two dimensions, each particle carrying electric charge and magnetic flux. Such particles appear in (2+1)-dimensional Chern-Simons field theories as charged vortex soliton…
Strictly working in the framework of the nonrelativistic quantum mechanics of a spin 1/2 particle coupled to an external electromagnetic field, we show, by explicit construction, the existence of a charge conjugation operator matrix which…
We begin by showing that any $n \times n$ matrix can be decomposed into a sum of $n$ circulant matrices with periodic relaxations on the unit circle. This decomposition is orthogonal with respect to a Frobenius inner product, allowing…
Discretizations of infinite-dimensional variational inequalities lead to linear and nonlinear complementarity problems with many degrees of freedom. To solve these problems in a parallel computing environment, we propose two active-set…
We consider the eigenvalues of symplectic elliptic Ginibre matrices which are known to form a Pfaffian point process whose correlation kernel can be expressed in terms of the skew-orthogonal Hermite polynomials. We derive the scaling limits…
We consider a relativistic charged particle in a background scalar field depending on both space and time. Poincar\'e, dilation and special conformal symmetries of the field generate conserved quantities in the charge motion, and we exploit…
The particle number and energy fluctuations in the system of charged particles are studied in the canonical ensemble for non-zero net values of the conserved charge. In the thermodynamic limit the fluctuations in the canonical ensemble are…
We obtain and investigate explicit analytic solution via universal transform of the diffusion equation in a spherical particles which appears in the so-called single particle model, a popular simple model of an electric battery.
We investigate matrix models in three dimensions where the global $\text{SU}(N)$ symmetry acts via the adjoint map. Analyzing their ground state which is homogeneous in space and can carry either a unique or multiple fixed charges, we show…
We analyze the collective dynamics of an ensemble of globally coupled, externally forced, identical mechanical oscillators with cubic nonlinearity. Focus is put on solutions where the ensemble splits into two internally synchronized…