Related papers: Deformed Explicitly Correlated Gaussians
Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics.
We develop an innovative numerical technique to describe few-body systems. Correlated Gaussian basis functions are used to expand the channel functions in the hyperspherical representation. The method is proven to be robust and efficient…
Closed-form expressions for all matrix elements required for variational calculation of the electronic structure of periodic solids have been derived using a basis of explicitly correlated Gaussians (ECGs). Periodic basis functions are…
We consider a specific form of explicitly correlated Gaussians -- with tensor pre-factors -- which appear naturally when dealing with certain few-body systems in nuclear and particle physics. We derive analytic matrix elements with these…
A new explicitly correlated functional form for expanding the wave function of an N-particle system with arbitrary angular momentum and parity is presented. We develop the projection-based approach, numerically exploited in our previous…
I show that under certain conditions it is possible to define consistent irrelevant deformations of interacting conformal field theories. The deformations are finite or have a unique running scale ("quasi-finite"). They are made of an…
In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic…
Here, we resume and broaden the results concerned which appeared in math.AG/0101098 and math.AG/0104021. We start from summing up our example of a complex algebraic surface which is not deformation equivalent to its complex conjugate and…
The Gaussian matrix model is known to deform to the $q,t$-matrix model. We consider further deformation to the elliptic $q,t$ matrix model by properly deforming the Gaussian density as well as the Vandermonde factor. Properties of an…
Based on results for real deformation parameter q we introduce a compact non- commutative structure covariant under the quantum group SOq(3) for q being a root of unity. To match the algebra of the q-deformed operators with necesarry…
Numerical projection methods are elaborated for the calculation of eigenstates of the non-relativistic many-particle Coulomb Hamiltonian with selected rotational and parity quantum numbers employing shifted explicitly correlated Gaussian…
We present a simple, robust and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on…
We present an extension of the deformation method applied to self-dual solutions of generalized Abelian Higgs-Chern-Simons models. Starting from a model defined by a potential $V(| \phi |)$ and a non-canonical kinetic term $\omega(| \phi |)…
We derive a formalism, the separation method, for the efficient and accurate calculation of two-body matrix elements for a Gaussian potential in the cylindrical harmonic-oscillator basis. This formalism is of critical importance for…
Within the standard quantum mechanics a q-deformation of the simplest N=2 supersymmetry algebra is suggested. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are…
We study deformations of the quantum conformal mechanics of De Alfaro-Fubini-Furlan with rational additional potential term generated by applying the generalized Darboux-Crum-Krein-Adler transformations to the quantum harmonic oscillator…
Complex Gaussian basis sets are optimized to accurately represent continuum radial wavefunctions over the whole space. First, attention is put on the technical ability of the optimization method to get more flexible series of Gaussian…
Within the Correlated Gaussian Method the parameters of the Gaussian basis functions are often chosen stochastically using pseudo-random sequences. We show that alternative low-discrepancy sequences, also known as quasi-random sequences,…
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional $N=2$ supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra.…
We consider the Friedrichs-Faddeev model in the case where the kernel of the potential operator is holomorphic in both arguments on a certain domain of $\mathbb{C}$. For this model we, first, study the structure of the $T$- and $S$-matrices…