Related papers: On the Qualitative Theory of Non-Gamov Decay State…
Excited states of many-body quantum systems play a key role in a wide range of physical and chemical phenomena. Unlike ground states, for which many efficient variational techniques exist, there are few ways to systematically construct…
In part I, the formalism for the description of open quantum systems (that are embedded into a common well-defined environment) by means of a non-Hermitian Hamilton operator $\ch$ is sketched. Eigenvalues and eigenfunctions are…
It is known that the overlap of two energy eigenstates in a decaying quantum system is bounded from above by a function of the energy detuning and the individual decay rates. This is usually traced back to the positive definiteness of an…
A classic no-go theorem in one-dimensional quantum mechanics can be evaded when the potentials are unbounded below, thus allowing for novel parity-paired degenerate energy bound states. We numerically determine the spectrum of one such…
The use of imaginary numbers in modelling quantum mechanical systems encompasses the wave-like nature of quantum states. Here we introduce a resource theoretic framework for imaginarity, where the free states are taken to be those with…
Quantum computers have been widely speculated to offer significant advantages in obtaining the ground state of difficult Hamiltonian in chemistry and physics. In this work, we first propose a Lyapunov control-inspired strategy to accelerate…
Potential wells are employed to constrain quantum particles into forming discrete energy levels, acting as artificial few-level systems. In contrast, an anti-parity-time ($\mathcal{PT}$) symmetric system can have a single pair of real…
Quantum mechanical potentials satisfying the property of shape invariance are well known to be algebraically solvable. Using a scaling ansatz for the change of parameters, we obtain a large class of new shape invariant potentials which are…
Exact solvability (typically, of harmonic oscillators) in quantum mechanics usually implies an elementary form of the spectrum while in all the "next-to-solvable" models, the energies E are only available in an implicit form (typically, as…
We derive the low-energy theory of semi-quantized quantum Hall states, a recently observed class of gapless bilayer fractional quantum Hall states. Our theory shows these states to feature gapless quasiparticles of fractional charge coupled…
The decay of a bound state weakly-coupled to a non-Hermitian tight-binding unstable continuum, i.e. a continuum of states comprising energies with positive imaginary part, is theoretically investigated. As compared to quantum decay in an…
The imaginary-time evolution of quantum states is integral to various fields, ranging from natural sciences to classical optimization or machine learning. Since simulating quantum imaginary-time evolution generally requires storing an…
A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The…
Kato's well known distributional inequality for the magnetic Laplacian holds equally in the more general setting of non-relativistic quantum electrodynamics (QED), where the wave function is vector-valued and the vector potential is…
We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…
The formation of bound states involving multiple particles underlies many interesting quantum physical phenomena, such as Efimov physics or superconductivity. In this work we show the existence of an infinite number of such states for some…
The state of a finite-dimensional quantum system is described by a density matrix that can be decomposed into a real diagonal, a real off-diagonal and and an imaginary off-diagonal part. The latter plays a peculiar role. While it is…
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…
We consider a simple model of an electron moving in a T-shaped confinement potential. This model allows for an analytical solution that explicitly demonstrates the existence of laterally bound electron states in quantum wires obtained by…
We have developed a formalism that includes both quasibound states with real energies and quantum resonances within the same theoretical framework, and that admits a clean and unambiguous distinction between these states and the states of…