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We discuss an algebraic treatment of three-body systems in terms of a U(7) spectrum generating algebra. In particular, we develop the formalism for nonlinear configurations and present an algebraic description of vibrational and rotational…
For discrete spectrum of 1D second-order differential/difference operators (with or without potential (killing), with the maximal/minimal domain), a pair of unified dual criteria are presented in terms of two explicit measures and the…
Let $D:\Omega\xrightarrow{}\Omega$ be a differential operator defined in the exterior algebra $\Omega$ of differential forms over the polynomial ring $S$ in $n$ variables. In this work we give conditions for deforming the module structure…
Optical $\chi^{(2)}$ non-linearity can be used for parametric amplification and producing down-converted entangled photon pairs that have broad applications. It is known that weak non-linear media exhibit dispersion and produce a frequency…
For a 2-D coupled PDE-ODE bulk-cell model, we investigate symmetry-breaking bifurcations that can emerge when two bulk diffusing species are coupled to two-component nonlinear intracellular reactions that are restricted to occur only within…
We define U(n) gauge theory on fuzzy S^2_N x S^2_N as a multi-matrix model, which reduces to ordinary Yang-Mills theory on S^2 x S^2 in the commutative limit N -> infinity. The model can be used as a regularization of gauge theory on…
We derive thermodynamically consistent models for diblock copolymer solutions coupled with the electric and magnetic field, respectively. These models satisfy the second law of thermodynamics and therefore are therefore thermodynamically…
A detailed theoretical framework for highly excited Rydberg molecules is developed based on the generalized local frame transformation. Our approach avoids the use of pseudopotentials and yields analytical expressions for the body-frame…
We present several ordering mechanisms in diblock copolymers. For temperatures above the order-disorder temperature and in the weak segregation regime, a linear response theory is presented which gives the polymer density in the vicinity of…
We consider the extension of the Standard electroweak Model through an $SU(2)$ quadruplet of scalars with hypercharge either $3/2$ or $1/2$ (with an additional reflection symmetry in the latter case). We establish, through $\textit{exact…
A numerically solvable two-dimensional (2D) model, employed by the authors to study the dissociative recombination of H$_2^+$ in the ungerade symmetry [Phys. Rev. A $\mathbf{98}$, 062706 (2018)], is extended to describe the collision…
We construct and normalise intertwining operators at the level of Hilbert modules describing the principal series of SL(2). Normalisation is achieved through the use of a Fourier transform defined on some homogenous space and twisted by a…
Budiansky's nonlinear shell theory is particularized to a 2D setting, and thereupon generalized to a fully nonlinear, statically and kinematically exact, theory of strain-gradient elasticity of beams. The governing equations are displayed…
We obtain a U(M) action for supermembranes with central charges in the Light Cone Gauge (LCG). The theory realizes all of the symmetries and constraints of the supermembrane together with the invariance under a U(M) gauge group with M…
This article deals with a nonrelativistic quantum mechanical study of a charge-dyon system with the SU(2)--monopole in five dimensions. The Schr\"odinger equation for this system is separable in the hyperspherical and parabolic coordinates.…
We propose a novel method to describe realistically ionization processes with absorbing boundary conditions in basis expansion within the formalism of the so-called Non-Adiabatic Quantum Molecular Dynamics. This theory couples…
In previous works, an operator was developed for heterotic compactifications on $\mathbb{R}^{2,1}\times G_2$ and $AdS_3 \times G_2$, which preserves $N=1$ $d=3$ supersymmetry and whose kernel is related to the moduli of the…
This work introduces a methodology for the statistical mechanical analysis of polymeric chains under tension controlled by optical or magnetic tweezers at thermal equilibrium with an embedding fluid medium. The response of single bonds…
In this note we consider the set of line operators in theories of class $S$. We show that this set carries the action of a natural discrete dynamical system associated with the BPS spectrum. We discuss several applications of this…
Deconfinement and screening of higher-representation sources in finite-temperature $SU(2)$ lattice gauge theory is investigated by both analytical and numerical means. The effective Polyakov-line action at strong coupling is simulated by an…