My main area of research is in theoretical condensed matter physics. I specialise in non-Hermitian systems and understanding their behaviour. Hermitian systems have dominated quantum mechanics for the last 100 years but non-hermiticity has opened a vast new territory that harbours new applications in cold atom physics, lasing, sensing and photonics. New and exciting physics such as the non-Hermitian Skin Effect, criticality and universality have emerged. This is coupled together with a broader interest in topological condensed matter systems.

I am also working on various projects in a diversified range of fields within physics:

- Quantum simulation of time-crystal on quantum computers. Composing of both an experimental realisation of time-crystal signatures and a theoretical investigation into the robustness of time-crystals such that they can be recreated in more physically tangible systems.
- The study of percolating quantum systems and their properties. Percolation theory is a classic problem in statistical physics that has applications in material science, network theory and understanding phase transitions. Percolation has yet to be applied to a quantum problem and we do this in the hopes of discovering novel physics.

Non-Hermiticity presents a vast newly opened territory that harbors new physics and applications such as lasing and sensing. However, only non-Hermitian systems with real eigenenergies are stable, and great efforts have been devoted in designing them through enforcing parity-time (PT) symmetry. In this work, we exploit a lesser-known dynamical mechanism for enforcing real-spectra, and develop a comprehensive and versatile approach for designing new classes of parent Hamiltonians with real spectra. Our design approach is based on a novel electrostatics analogy for modified non-Hermitian bulk-boundary correspondence, where electrostatic charge corresponds to density of states and electric fields correspond to complex spectral flow. As such, Hamiltonians of any desired spectra and state localization profile can be reverse-engineered, particularly those without any guiding symmetry principles. By recasting the diagonalization of non-Hermitian Hamiltonians as a Poisson boundary value problem, our electrostatics analogy also transcends the gain/loss-induced compounding of floating-point errors in traditional numerical methods, thereby allowing access to far larger system sizes.

Kirchhoff’s Laws are reformulated so that circuits can be analysed using the powerful tool of topology. This sheds light on the properties of exotic real materials such as graphene. The quantum edge effect in a polyacetylene chain happens only when the edge of the chain is conducting. This was recreated experimentally using electrical circuits. Physical laws govern the properties of the bulk in a material to that of the edge. However, dissipation introduced into circuits using voltage controlled current sources was shown to have broken these laws. Results are attributed to boundary conditions affecting all states in the bulk, not just edge states, implying a new state of matter. Studying Condensed matter systems using electrical circuits gives physicists an accessible, scalable and inexpensive way to study real materials.

I travel 1h 30 min every day amounting to more than 10 hours every week. That's enough to complete a book a week! So here's my book blog to keep myself accountable and share my book recommendations to my friends.

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