相关论文: Singularities of Dirac-Coulomb propagators

Strong singularities in the electronic density of states amplify correlation effects and play a key role in determining the ordering instabilities in various materials. Recently high order van Hove singularities (VHSs) with diverging…

The Coulomb scattering dynamics in graphene in energetic proximity to the Dirac point is investigated by polarization resolved pump-probe spectroscopy and microscopic theory. Collinear Coulomb scattering rapidly thermalizes the carrier…

This paper is devoted to study the wave propagation and its stability for a class of two-component discrete diffusive systems. We first establish the existence of positive monotone monostable traveling wave fronts. Then, applying the…

We investigate the properties of the set of singularities of semiconcave solutions of Hamilton-Jacobi equations of the form \begin{equation*} u_t(t,x)+H(\nabla u(t,x))=0, \qquad\text{a.e. }(t,x)\in…

Vacuum polarization of charged massless fermions is investigated in the superposition of Coulomb and Aharonov--Bohm (AB) potentials in 2+1 dimensions. For this purpose we construct the Green function of the two-dimensional Dirac equation…

We study gauge invariant states in QED, where states are understood in terms of data living on the boundary of gauge invariant path-integrals. This is done for both scalar and spinor QED, and for boundaries that are either time slices, or…

Topological quantum phase transitions intrinsically intertwine self-similarity and topology of many-electron wave-functions, and divining them is one of the most significant ways to advance understanding in condensed matter physics. Our…

The essentially non-perturbative polarization effects are considered for a planar supercritical Dirac-Coulomb system with strong coupling (similar to graphene and graphene-based heterostructures) in terms of induced charge density…

We consider a Dirac operator in three space dimensions, with an electrostatic (i.e. real-valued) potential $V(x)$, having a strong Coulomb-type singularity at the origin. This operator is not always essentially self-adjoint but admits a…

We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials $\mathbf V$ of Coulomb type: we characterise its…

We characterize the carrier density profile of the ground state of graphene in the presence of particle-particle interaction and random charged impurity for zero gate voltage. We provide detailed analysis on the resulting spatially…

In this paper we propose a definition of quasifree Hadamard states for spinor fields on a curved space-time by specifying the Polarisation Set of the two-point function. We prove that the thermal equilibrium state on an ultrastatic…

At nonzero density the eigenvalues of the Dirac operator move into the complex plane, while its singular values remain real and nonnegative. In QCD-like theories, the singular-value spectrum carries information on the diquark (or pionic)…

An instationary drift-diffusion system for the electron, hole, and oxygen vacancy densities, coupled to the Poisson equation for the electric potential, is analyzed in a bounded domain with mixed Dirichlet-Neumann boundary conditions. The…

We address the problem of an unscreened Coulomb charge in graphene, and calculate the local density of states and displaced charge as a function of energy and distance from the impurity. This is done non-perturbatively in two different…

We establish a novel uniqueness result for an instationary drift-diffusion model for perovskite solar cells. This model for vacancy-assisted charge transport uses Fermi--Dirac statistics for electrons and holes and Blakemore statistics for…

The Dirac equation with the Coulomb potential is studied. It is shown that there exists a new invariant in addition to the known Dirac and Johnson-Lippman ones. The solution of the Dirac equation, using the generalized invariant, and…

We reconsider the strong-coupling expansion for the Hubbard model recently introduced by Sarker and Pairault {\it et al.} By introducing slave particles that act as projection operators onto the empty, singly occupied and doubly occupied…

In the high temperature, chirally invariant phase of QCD, the quark propagator is shown to have two sets of poles with different dispersion relations. A reflection property in momentum space relates all derivatives at zero-momentum of the…

Scattering by charged impurities is known to mainly determine transport properties of electrons in modern quantum materials, but it remains poorly studied for materials with Mexican hat dispersion. Due to such nontrivial features as a…