Related papers: Modified group projectors: tight binding method
Using an expansion in powers of an infinitesimally small coupling constant $g$, all generators of the Poincar\'e group in local scalar quantum field theory with interaction term $g \phi^3$ are expressed in terms of annihilation and creation…
Trapped atomic ion qubits or effective spins are a powerful quantum platform for quantum computation and simulation, featuring densely connected and efficiently programmable interactions between the spins. While native interactions between…
The Particle Number Projected Generator Coordinate Method is formulated for the pairing Hamiltonian in a detailed way in the projection after variation and the variation after projection methods. The dependence of the wave functions on the…
We investigate the group contraction method for various space-time groups, including SO(3)->E_2, SO(3,1)->G_3, SO(5-h,h)->P(3,1) (h=1 or 2), and its consequences for representations of these groups. Following strictly quantum mechanical…
We consider generalisations of the elliptic Calogero--Moser systems associated to complex crystallographic groups in accordance to [1]. In our previous work [2], we proposed these systems as candidates for Seiberg--Witten integrable systems…
We develop a quantum mechanical theory to describe the optical response of semiconductor nanostructures with a particular emphasis on higher-order harmonic Generation. Based on a tight-binding approach we take all two-particle correlations…
Symmetry packaging is the phenomenon whereby, upon particle creation, all the internal quantum numbers (IQNs) become locked into a single irreducible representation (irrep) block of the gauge group, as required by locality and gauge…
Extending ideas of twisted equivariant $K$-theory, we construct twisted versions of the representation rings for Lie superalgebras and Lie supergroups, built from projective $\Z_{2}$-graded representations with a given cocycle. We then…
We present a novel platform for the bottom-up construction of itinerant many-body systems: ultracold atoms transferred from a Bose-Einstein condensate into freely configurable arrays of micro-lens generated focused-beam dipole traps. This…
This paper advocates for an innovative approach designed for estimating optoelectronic properties of quantum structures utilizing Tight-Binding (TB) theory. Predicated on the comparative analysis between estimated and actual properties, the…
For general quantum systems the power expansion of the Gibbs potential and consequently the power expansion of the self energy is derived in terms of the interaction strength. Employing a generalization of the projector technique a compact…
An oscillator group $G$ is a semidirect product of a Heisenberg group with a one-parameter group. In this article we construct Olshanski semigroups for infinite-dimensional oscillator groups. These are complex involutive semigroups which…
With the help of a tight-binding (TB) electronic-structure toy model we investigate the matching of parameters across hetero-interfaces . We demonstrate that the virtual crystal approximation, commonly employed for this purpose, may not…
We discuss a fine tuning of the co- and contra-variant transforms through construction of specific fiducial and reconstructing vectors. The technique is illustrated on three different forms of induced representations of the Heisenberg…
Recently, the size-dependence of high-order harmonic generation (HHG) in quantum dots has been investigated experimentally. In particular, for longer driving wavelengths and QDs smaller than 3\,nm, HHG was strongly suppressed, however,…
Path integral-based simulation methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical…
A gauge- and renormalization-group- invariant approach implemented by the pinch technique is formulated for resonant transitions involving the Higgs boson. The lineshape of the Higgs boson is shown to consist of two distinct and physically…
In this paper we introduce a projective invarinat measure on the special unitary group. It is directly related to transition probabilities. It has some interesting connection with convex geometry. Applications to approximation of quantum…
We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This…
We study the representations of the infinite symmetric group induced from the identity representations of Young subgroups. It turns out that such induced representations can be either of type~I or of type~II. Each Young subgroup corresponds…