Related papers: Local Spectral Density and Vacuum Energy near a Qu…
Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…
The density functional theory is used to study the electronic structure of a quantum wire in a magnetic field. The Kohn-Sham equations are solved numerically for different values of electron densities and filling factors. The critical…
In the study of quantum vacuum energy and the Casimir effect, it is desirable to model the conductor by a potential of the form $V(z)=z^\alpha$. This "soft wall" model was proposed so as to avoid the violation of the principle of virtual…
We study the spectrum of a quantum star graph with a non-selfadjoint Robin condition at the central vertex. We first prove that, in the high frequency limit, the spectrum of the Robin Laplacian is close to the usual spectrum corresponding…
We consider a framework in which low energy dynamics of quantum gravity is described preserving locality, and yet taking into account the effects that are not captured by the naive global spacetime picture, e.g. those associated with black…
A density functional theory is developed for fermions in one dimension, interacting via a delta-function. Such systems provide a natural testing ground for questions of principle, as the local density approximation should work well for…
A fundamental problem on graph-structured data is that of quantifying similarity between graphs. Graph kernels are an established technique for such tasks; in particular, those based on random walks and return probabilities have proven to…
We consider local semitransparent Neumann boundary conditions for a quantum scalar field as imposed by a quadratic coupling to a source localized on a flat codimension-one surface. Upon a proper regularization to give meaning to the…
The conformal invariance of the low energy limit theory governing the electronic properties of graphene is explored. In particular, it is noted that the massless Dirac theory in point enjoys local Weyl symmetry, a very large symmetry.…
We report an ab initio evaluation of the surface energy of a simple metal, performed via a coupling-constant integration over the dynamical density-response function. The rapid rate of change of the electron density at the surface is…
We study the energy levels of carriers confined in a magnetic quantum dot of graphene surrounded by a infinite graphene sheet in the presence of energy gap. The eigenspinors are derived for the valleys $K$ and $K'$, while the associated…
We consider the problem of the homogenization of non-local quadratic energies defined on $\delta$-periodic disconnected sets defined by a double integral, depending on a kernel concentrated at scale $\varepsilon$. For kernels with unbounded…
We calculate the local Green function for a quantum-mechanical particle with hopping between nearest and next-nearest neighbors on the Bethe lattice, where the on-site energies may alternate on sublattices. For infinite connectivity the…
The screening effect due to a scanning tunneling microscope tip which is placed in the vicinity of an interacting quantum wire is considered. With the help of a bosonization procedure, we are able to determine non perturbatively the Green's…
A new approach to generalised Casimir type of problems is derived within the context of renormalisable quantum field theory (QFT). We study the simplest case of a massive fluctuating boson field coupled to a time-independent background…
The one-particle Green function of a many-electron system is traditionally formulated within the self-energy picture. A different formalism was recently proposed, in which the self-energy is replaced by a dynamical exchange-correlation…
In a recent series of scanning probe experiments, it became possible to visualize local electron flow in a two-dimensional electron gas. In this paper, a Green's function technique is presented that enables efficient calculation of the…
One of the most important characteristics of a quantum graph is the average density of resonances, $\rho = \frac{\mathcal{L}}{\pi}$, where $\mathcal{L}$ denotes the length of the graph. This is a very robust measure. It does not depend on…
In the full quantum theory, the energy of a many-body quantum system with a given one-body density is described by the Levy-Lieb functional. It is exact, but very complicated to compute. For practical computations, it is useful to introduce…
We suggest a simple approach to calculate the local density of states that effectively applies to any structure created by an axially symmetric potential on a continuous graphene sheet such as circular graphene quantum dots or rings.…