We study the spectrum of the 1D Dirac Hamiltonian encompassing the bound and scattering states of a fermion distorted by a static background built from $delta$-function potentials. We distinguish between mass-spike and electrostatic $delta$-potentials. Differences in the spectra arising depending on the type of $delta$-potential studied are thoroughly explored.
The problem of electron scattering on the one-dimensional complexes is considered. We propose a novel theoretical approach to solution of the transport problem for a quantum graph. In the frame of the developed approach the solution of the transport
problem is equivalent to the solution of a linear system of equations for the emph{vertex amplitudes} $mathbf{Psi}$. All major properties, such as transmission and reflection amplitudes, wave function on the graph, probability current, are expressed in terms of one $mathbf{Gamma}$-matrix that determines the transport through the graph. The transmission resonances are analyzed in detail and comparative analysis with known results is carried out.
We proposed an action of neutral fermions interacting with external electromagnetic fields to construct a 3+1 dimensional topological field theory as the effective action attained by integrating out the fermionic fields in the related path integral.
These neutral quasiparticles are assumed to emerge from the collective behavior of the original physical particles and holes (antiparticles). Although our construction is general it is particularly useful to formulate effective actions of the time reversal invariant topological insulators.
In this contribution to the study of one dimensional point potentials, we prove that if we take the limit $qto 0$ on a potential of the type $v_0delta({y})+{2}v_1delta({y})+w_0delta({y}-q)+ {2} w_1delta({y}-q)$, we obtain a new point potential of the
type ${u_0} delta({y})+{2 u_1} delta({y})$, when $ u_0$ and $ u_1$ are related to $v_0$, $v_1$, $w_0$ and $w_1$ by a law having the structure of a group. This is the Borel subgroup of $SL_2({mathbb R})$. We also obtain the non-abelian addition law from the scattering data. The spectra of the Hamiltonian in the exceptional cases emerging in the study are also described in full detail. It is shown that for the $v_1=pm 1$, $w_1=pm 1$ values of the $delta^prime$ couplings the singular Kurasov matrices become equivalent to Dirichlet at one side of the point interaction and Robin boundary conditions at the other side.
We study the spectral and scattering theory of light transmission in a system consisting of two asymptotically periodic waveguides, also known as one-dimensional photonic crystals, coupled by a junction. Using analyticity techniques and commutator me
thods in a two-Hilbert spaces setting, we determine the nature of the spectrum and prove the existence and completeness of the wave operators of the system.
We investigate the thermodynamic limit of the exact solution, which is given by an inhomogeneous $T-Q$ relation, of the one-dimensional supersymmetric $t-J$ model with unparallel boundary magnetic fields. It is shown that the contribution of the inho
mogeneous term at the ground state satisfies the $L^{-1}$ scaling law, where $L$ is the system-size. This fact enables us to calculate the surface (or boundary) energy of the system. The method used in this paper can be generalized to study the thermodynamic limit and surface energy of other models related to rational R-matrices.
J. Mateos Guilarte
,Jose M. Munoz-Castaneda
,Irina Pirozhenko andn Lucia Santamaria-Sanz
.
(2019)
.
"One-dimensional scattering of fermions on $delta$-impurities"
.
Jose M Munoz-Castaneda
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