Related papers: Modified group projectors: tight binding method
In this paper we work with the approximation of unitary groups of operators of the form $e^{-itH}$ where $H\in\mathscr{L}(\mathcal{H})$ is the Hamiltonian of a given quantum dynamical system modeled in the discretizable Hilbert space…
In this paper we explore the method of holomorphic induction for unitary representations of Banach--Lie groups. First we show that the classification of complex bundle structures on homogeneous Banach bundles over complex homogeneous spaces…
Transformation optics offers an unconventional approach to the control of electromagnetic fields. A transformation optical structure is designed by first applying a form-invariant coordinate transform to Maxwell's equations, in which part…
We have developed a symmetry-adapted modeling procedure for molecules and crystals. By using the completeness of multipoles to express spatial and time-reversal parity-specific anisotropic distributions, we can generate systematically the…
This paper introduces a new representation method that is mainly based on chemical bonds among atoms in materials. Each chemical bond and its surrounded atoms are considered as a unified unit or a local structure that is expected to reflect…
The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…
We discuss an application of group theoretical methods to the formulation of the thermodynamics of systems constrained by the conservation laws described by a semi--simple compact Lie group. A general projection method that allows to…
Empirical tight binding(ETB) methods are widely used in atomistic device simulations. Traditional ways of generating the ETB parameters rely on direct fitting to bulk experiments or theoretical electronic bands. However, ETB calculations…
Recently representation theory has been used to provide atomic decompositions for a large collection of classical Banach spaces. In this paper we extend the techniques to also include projective representations. As our main application we…
After summarising the physical approach leading to twisted homotopy and after developing the cohomological approach further with respect to our previous work we propose a third alternative approach to twisted homotopy based on group…
Consider a finite-dimensional real vector space equipped with a finite group acting unitarily on it. We address the general problem of constructing Euclidean stable embeddings of the quotient space of orbits. Our approach is based on…
A quantum group analysis is applied to the Sine-Gordon model (or may be its version) in a strong-coupling regime. Infinitely many bound states are found together with the corresponding S-matrices. These new solutions of the Yang-Baxter…
We have developed an efficient method for quantum number projection from most general HFB type mean-field states, where all the symmetries like axial symmetry, number conservation, parity and time-reversal invariance are broken. Applying…
We present a method of constructing discrete integrable systems with crystallographic reflection group (Weyl) symmetries, thus clarifying the relationship between different discrete integrable systems in terms of their symmetry groups.…
The projector onto gauge invariant physical states was recently constructed for arbitrary constrained systems. This approach, which does not require gauge fixing nor any additional degrees of freedom beyond the original ones---two…
The auxiliary field diffusion Monte Carlo method uses imaginary-time projection techniques to accurately solve the ground-state wave function of atomic nuclei and infinite nuclear matter. In this work, we present a novel representation of…
Space group theory is pivotal in the design of nanophotonics devices, enabling the characterization of periodic optical structures such as photonic crystals. The aim of this study is to extend the application of nonsymmorphic space groups…
Multiport generalizations of beam splitters are the key component in multipath interferometers, which are important in a range of quantum state engineering and precision measurement schemes. Here we propose a straightforward method for…
Braid groups are an important and flexible tool used in several areas of science, such as Knot Theory (Alexander's theorem), Mathematical Physics (Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this note we will…
A multiscale approach was adopted for the calculation of confined states in self-assembled semiconductor quantum dots (QDs). While results close to experimental data have been obtained with a combination of atomistic strain and…