相关论文: Contact interactions and Kronig-Penney Models in H…

We introduced some contact potentials that can be written as a linear combination of the Dirac delta and its first derivative, the $\delta$-$\delta'$ interaction. After a simple general presentation in one dimension, we briefly discuss a…

We construct a family of hermitian potentials in 1D quantum mechanics that converges in the zero-range limit to a $\delta$ interaction with an energy-dependent coupling. It falls out of the standard four-parameter family of pointlike…

We consider a quantum mechanical particle living on a graph and discuss the behaviour of its wavefunction at graph vertices. In addition to the standard (or delta type) boundary conditions with continuous wavefunctions, we investigate two…

We propose a new method to construct a four parameter family of quantum-mechanical point interactions in one dimension, which is known as all possible self-adjoint extensions of the symmetric operator $T=-\Delta \lceil C^{\infty}_{0}({\bf…

The transmission T and conductance G through one or multiple one-dimensional, delta-function barriers of two-dimensional fermions with a linear energy spectrum are studied. T and G are periodic functions of the strength P of the…

We present a detailed study of a generalised one-dimensional Kronig-Penney model using $\delta\text{-}\delta'$ potentials. We analyse the band structure and the density of states in two situations. In the first case we consider an infinite…

We show that and how point interactions offer one of the most suitable guides towards a quantitative analysis of properties of certain specific non-Hermitian (usually called PT-symmetric) quantum-mechanical systems. A double-well model is…

The theory of interaction at one point is developed for the one-dimensional Schrodinger equation. In analog with the three-dimensional case, the resulting interaction is referred to as the Fermi pseudo-potential. The dominant feature of…

We consider the interaction between the Hermitian world, represented by a real delta-function potential $-\alpha\delta(x)$, and the non-Hermitian world, represented by a PT-symmetric pair of delta functions with imaginary coefficients…

We study a non-relativistic particle subject to a three-dimensional spherical potential consisting of a finite well and a radial $\delta$-$\delta'$ contact interaction at the well edge. This contact potential is defined by appropriate…

Relativistic PT-symmetric fermionic interacting systems are studied in 1+1 and 3+1 dimensions. The objective is to include non-Hermitian PT-symmetric interaction terms that give {\it real} spectra. Such interacting systems could describe…

Recently developed methods for PT-symmetric models can be applied to quantum-mechanical matrix and vector models. In matrix models, the calculation of all singlet wave functions can be reduced to the solution a one-dimensional PT-symmetric…

Non-Hermitian systems having parity-time ($\mathcal {PT}$) symmetry can undergo a transition, spontaneously breaking the symmetry. Ultracold atomic gases provide an ideal platform to study interaction effects on the transition. We consider…

At the limit of an infinite confinement strength $\omega$, the ground state of a system that comprises two fermions or bosons in a harmonic confinement interacting through the Fermi--Huang pseudopotential remains strongly correlated. A…

Considering the recent advances, the weak correlation between the massive Kalb-Ramond and the Proca interacting models is investigated by means of a set of complementary quantum field techniques beyond the semi-classical approach. A…

Generalized PT symmetry provides crucial insight into the sign problem for two classes of models. In the case of quantum statistical models at non-zero chemical potential, the free energy density is directly related to the ground state…

We construct PT-symmetric quantum mechanical models with an O(N)-symmetric interaction term of the form $-g(\vec{x}^{2})^{2}/N$. Using functional integral methods, we find the equivalent Hermitian model, which has several unusual features.…

The paradigm of electrons interacting with a periodic lattice potential is central to solid-state physics. Semiconductor heterostructures and ultracold neutral atomic lattices capture many of the essential properties of 1D electronic…

PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside of the conventional equilibrium…

The configuration interaction (CI) method for calculating the exact eigenstates of a quantum-mechanical few-body system is problematic when applied to particles interacting through contact forces. In dimensions higher than one the approach…