Browsing by Author "Main, Jörg (Apl. Prof. Dr.)"

Now showing 1 - 1 of 1

Open Access
Symmetries and symmetrisation in quantum and electromagnetic multi-mode systems for balancing gain and loss
(2021) Dizdarevic, Daniel; Main, Jörg (Apl. Prof. Dr.)
Losses usually are an undesirable effect in physics. However, in combination with gain, novel and unexpected features occur. This is because gain and loss can effectively be described via an imaginary potential, which renders a Hamiltonian non-Hermitian. Although there are similarities to standard quantum mechanics, non-Hermitian quantum mechanics exhibits unique mathematical features like bi-orthogonal and self-orthogonal states. Such systems can be used to describe open quantum systems efficiently; though, the overall probability is not conserved in general. However, by balancing gain and loss, stable stationary states with intriguing properties can be realised. Balanced gain and loss occurs in combination with anti-unitary symmetries, which are related to time reversal. The simplest and most powerful symmetry in this regard is PT symmetry, which acted as the driving force behind the development of non-Hermitian quantum mechanics in the last two decades. Researchers produced some astounding results involving PT symmetry, like unidirectionally invisible structures and optimal robust wireless power transfer. Due to the generality of the PT operator, PT symmetry is applicable to almost any physical system, though, it is broken even for small perturbations. In the absence of symmetries, balanced gain and loss can still be achieved by means of symmetrisation or semi-symmetrisation, which are introduced in this thesis. Symmetrised non-Hermitian systems show similar features as symmetric ones, but they allow for a broader range of applications. Symmetrisation allows for the description of physical multi-well potentials with gain and loss. Yet, the lack of obvious symmetries or recognisable patterns makes symmetrised systems hard to understand intuitively. The relations between symmetries and symmetrisation are discussed in detail and both concepts are explicitly applied to one-dimensional multi-mode quantum systems, for which a simple matrix model is used as an example. Analytical symmetrised solutions are derived and it is explicitly demonstrated how symmetrisation can be used to systematically find two-mode systems with a stable stationary ground state. Further, it is shown that models with just two modes are only semi-symmetrisable, whereas they can be perfectly PT-symmetric. Semi-symmetrisation is also applied to multi-mode systems for the realisation of multi-mode chains and to spatially extended Gaussian multi-well potentials. Gaussian potentials can be used in experimental realisations with Bose-Einstein condensates involving non-linear contact interactions; these can be used to realise a self-stabilising mechanism of stationary states, thus making the system robust with respect to small perturbations. By deriving a mathematically equivalent model for inductively coupled electric resonant circuits, the concepts of symmetries and symmetrisation can be transferred from the quantum realm to the classical field of electrodynamics. While this provides a simple and, in particular, accessible platform for experiments, the possibility of applications for wireless power transfer are also discussed briefly, which concludes this thesis.