Related papers: Numerical issues of the two-dimensional Dirac equa…
A fundamental problem regarding the Dirac quantization of a free particle on an $N-1$ curved hypersurface embedded in $N$($\geq 2$) flat space is the impossibility to give the same form of the curvature-induced quantum potential, the…
A key problem in the field of quantum criticality is to understand the nature of quantum phase transitions in systems of interacting itinerant fermions, motivated by experiments on a variety of strongly correlated materials. Much attention…
It is well-known that the tight-binding Hamiltonian of graphene describes the low-energy excitations that appear to be massless chiral Dirac fermions. Thus, in the continuum limit one can analyze the crystal properties using the formalism…
In this note we describe how some objects from generalized geometry appear in the qualitative analysis and numerical simulation of mechanical systems. In particular we discuss double vector bundles and Dirac structures. It turns out that…
The Dirac equation in curved spacetimes is formulated using coordinate-free notation. A Lagrangean density which corresponds to the subject equation is presented. The subject equation is invariant under a local rotation of the coframe. The…
Exact solutions of Dirac equation in two spatial dimensions in the Coulomb field are obtained. Equation which determines the so-called critical charge of the Coulomb field is derived and solved for a simple model.
We discuss the Dirac quantization of two dimensional gravity with bosonic matter fields. After defining the extended Hamiltonian it is possible to fix the gauge completely. The commutators can all be obtained in closed form; nevertheless,…
The recent discovery of Dirac semimetals represents a new achievement in our fundamental understanding of topological states of matter. Due to their topological surface states, high mobility, and exotic properties associated with bulk Dirac…
There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in Riemannian space of constant negative curvature, hyperbolic Lobachevsky space, in presence of an external magnetic field, analogue…
The spectrum of bound and scattering states of the one dimensional Dirac Hamiltonian describing fermions distorted by a static background built from two Dirac delta potentials is studied. A distinction will be made between mass-spike and…
In a Dirac semimetal, the conduction and valence bands contact only at discrete (Dirac) points in the Brillouin zone (BZ) and disperse linearly in all directions around these critical points. Including spin, the low energy effective theory…
It is shown that the calculation of Dirac operator for the spherical coordinate system with spherical Dirac matrices and using the spin connection formalism is in the contradiction with the definition of standard Dirac operator in the…
Geometric phase in the wave function is important with regard to quantum non-locality and adiabatic evolution. We study the confinement of a particle by three-dimensional isotropically moving walls, of relevance to experimental trapping…
When aiming to apply mathematical results of non-commutative geometry to physical problems the question arises how they translate to a context in which only a part of the spectrum is known. In this article we aim to detect when a…
In this paper, we show, by using the approach of effective mass, that the model of a two-dimensional Dirac oscillator can be used to describe the thermal properties of graphene under an uniform magnetic field. All thermal quantities of…
Graphene, a two-dimensional crystal made of carbon atoms, provides a new and unexpected bridge between low and high-energy physics. The field has evolved very fast and very good reviews are already available in the literature. Graphene…
This work analyzes monolayer graphene in external electromagnetic fields, which is described by the Dirac equation with minimal coupling. Supersymmetric quantum mechanics allows building new Dirac equations with modified magnetic fields.…
The behavior of electrons in strained graphene is usually described using effective pseudomagnetic fields in a Dirac equation. Here we consider the particular case of a spatially constant strain. Our results indicate that lattice…
A relativistic equation is deduced for the bound state of two particles, by assuming a proper boundary condition for the propagation of the negative-energy states. It reduces to the (one-body)Dirac equation in the infinite limit of one of…
The stationary Dirac equation $(p\cdot\sigma)\psi=E\psi$, confined to a two-dimensional (2D) region, supports states propagating along the boundary and decaying exponentially away from the boundary. These edge states appear on the 2D…