Related papers: Computing an orthonormal basis of symmetric or ant…
We address the problem of identifying the (nonstationary) quantum systems that admit supersymmetric dynamical invariants. In particular, we give a general expression for the bosonic and fermionic partner Hamiltonians. Due to the…
We investigate a general system of two coupled harmonic oscillators with cubic nonlinearity. Without damping, the system is Hamiltonian, with the origin as an elliptic equilibrium characterized by two distinct linear frequencies. To…
The ($p=2$) parabose-parafermi supersymmetry is studied in general terms. It is shown that the algebraic structure of the ($p=2$) parastatistical dynamical variables allows for (symmetry) transformations which mix the parabose and parafermi…
One method for the numerical treatment of future null-infinity is to decouple coordinates from the tensor basis and choose each in a careful manner. This dual-frame approach is hampered by logarithmically divergent terms that appear in a…
Four Jacobi settings are considered in the context of Hardy's inequality: the trigonometric polynomials and functions, and the corresponding symmetrized systems. In the polynomial cases sharp Hardy's inequality is proved for the type…
Spherical Harmonic Gaussian type orbitals and Slater functions can be expressed using spherical coordinates or a linear combinations of the appropriate Cartesian functions. General expressions for the transformation coefficients between the…
We present a mechanism to efficiently pre-select the number of intrinsic many-body states that are used to define the many-body wave functions within the discrete Generator Coordinate Method (GCM). This procedure, based on the proper…
Two different approaches are formulated to analyze two-dimensional quantum models which are not amenable to standard separation of variables. Both methods are essentially based on supersymmetrical second order intertwining relations and…
The generalized pseudospectral method is employed for the accurate calculation of eigenvalues, densities and expectation values for the spiked harmonic oscillators. This allows \emph{nonuniform} and \emph{optimal} spatial discretization of…
We carry out a model-theoretic analysis of the Heisenberg algebra. To this end, a geometric structure is associated to the Heisenberg algebra and is shown to be a Zariski geometry. Furthermore, this Zariski geometry is shown to be…
We discuss the necessity of using non-standard boson operators for diagonalizing quadratic bosonic forms which are not positive definite and its convenience for describing the temporal evolution of the system. Such operators correspond to…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
We describe a skeletonization of the spherical harmonic connection problem that reduces the storage and pre-computation to superoptimal complexities at the cost of increasing the execution time by the modest multiplicative factor of…
Gyroscopic alignment of a fluid occurs when flow structures align with the rotation axis. This often gives rise to highly spatially anisotropic columnar structures that in combination with complex domain boundaries pose challenges for…
Traditional computational methods for studying quantum many-body systems are "forward methods," which take quantum models, i.e., Hamiltonians, as input and produce ground states as output. However, such forward methods often limit one's…
This paper introduces and analyzes symmetric and anti-symmetric quantum binary functions. Generally, such functions uniquely convert a given computational basis state into a different basis state, but with either a plus or a minus sign.…
In this paper we are going to build the multiphoton supercoherent states for the supersymmetric harmonic oscillator as eigenstates of the $m$-th power of a special form (but still with a free parameter) of the Kornbluth-Zypman…
A numerical implementation scheme is presented for the recently developed many-body diffusion approach for identical particles, in the case of harmonic potentials. The procedure is free of the sign problem, by the introduction of the…
We consider orthogonal polynomials on the surface of a double cone or a hyperboloid of revolution, either finite or infinite in axis direction, and on the solid domain bounded by such a surface and, when the surface is finite, by…
Classical and quantum mechanical analysis have been carried out on harmonic like oscillator with asymmetric position dependent mass. Phase space analysis are performed both classically and quantum mechanically for a plausible understanding…