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We consider a charged particle, spin 1/2, with relativistic kinetic energy and minimally coupled to the quantized Maxwell field. Since the total momentum is conserved, the Hamiltonian admits a fiber decomposition as $H(P)$, $P\in \BbbR^3$.…
The quantum behavior of electrons in bilayer graphene with applied magnetic fields is addressed. By using second-order supersymmetric quantum mechanics the problem is transformed into two intertwined one dimensional stationary Schr\"odinger…
In quantum electrodynamics, photon--photon scattering can be the result of the exchange of virtual electron--positron pairs. Effectively, this gives rise to self-interaction terms in Maxwell's equations, similar to the nonlinearities due to…
Much of the richness in nature emerges because the same simple constituents can form an endless variety of ordered states. While many such states are fully characterized by their symmetries, interacting quantum systems can also exhibit…
We propose a scheme involving cold atoms trapped in optical lattices to observe different phenomena traditionally linked to quantum-optical systems. The basic idea consists of connecting the trapped atomic state to a non-trapped state…
We study theoretically the electron states in a system of two vertically stacked quantum dots. We investigate the influence of the geometrical symmetry breaking (caused by the displacement as well as the ellipticity of the dots) on the…
We consider a flat lattice of dipoles modeled by harmonic oscillators interacting with the electromagnetic field in dipole approximation. Eliminating the variables from the coupled equations of motion, we come to effective Maxwell…
Many electromagnetic properties of graphene can be described by the Hubbard model on a honeycomb lattice. However, this system suffers strongly from the sign problem if a chemical potential is included. Tensor network methods are not…
Quantum field theory (QFT) on non-stationary spacetimes is well understood from the side of the algebra of observables. The state space, however, is largely unexplored, due to the non-existence of distinguished states (vacuum, scattering…
Non-linear effects in photoemission are shown to open a new access to the band structure of unoccupied states in solids, totally different from hitherto used photoemission spectroscopy. Despite its second-order nature, strong resonant…
We consider the optical properties of finite systems composed of a series of graphene sheets separated by thin dielectric layers. Because these systems respond as conductors to electric fields in the plane of the graphene sheets and as…
We show that two tight binding electrons that repel may form a bounded pair in two dimensions. The paired states form a band with energies that scale like the strength of the interaction potential. By applying an electric field we show that…
We show that two distinct quantum states of the electromagnetic field can be associated to a classical vector X wave or a propagation-invariant solution of Maxwell equations. The difference between the two states is of pure quantum…
Many-body entangled quantum states studied in condensed matter physics can be primary resources for quantum information, allowing any quantum computation to be realized using measurements alone, on the state. Such a universal state would be…
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…
We present a detailed analysis of the dynamics of photon transport in waveguiding systems in the presence of a two-level system. In these systems, quantum interference effects generate a strong effective optical nonlinearity on the…
Cavity enhanced light scattering off an ultracold gas in an optical lattice constitutes a quantum measurement with a controllable form of the measurement back-action. Time-resolved counting of scattered photons alters the state of the atoms…
Modulating macroscopic parameters of materials in time offers innovative avenues for manipulating electromagnetic waves. Due to such enticing prospects, the general research subject of time-varying systems is expanding today in different…
We present a theoretical framework for nonlinear optics of graphene and other 2D materials in layered structures. We derive a key equation to find the effective electric field and the sheet current density in the 2D material for given…
We study three different experiments that involve dry friction and periodic driving, and which employ both single and many-particle systems. These experimental set-ups, besides providing a playground for investigation of frictional effects,…