Related papers: Super Periodic Potential
For complex one-dimensional potentials, we propose the asymmetry of both reflectivity and transmitivity under time-reversal: $R(-k)\ne R(k)$ and $T(-k) \ne T(k)$, unless the potentials are real or PT-symmetric. For complex PT-symmetric…
A large number of symmetry-protected topological (SPT) phases have been hypothesized for strongly interacting spin-1/2 systems in one dimension. Realizing these SPT phases, however, often demands fine-tunings hard to reach experimentally.…
A theory of electromagnetic (EM) wave scattering by many small particles of an arbitrary shape is developed. The particles are perfectly conducting or impedance. For a small impedance particle of an arbitrary shape an explicit analytical…
Using the formalism of supersymmetric quantum mechanics, we obtain a large number of new analytically solvable one-dimensional periodic potentials and study their properties. More specifically, the supersymmetric partners of the Lame…
The subwavelength focusing based on surface plasmon polaritons (SPP) has been widely explored in tapered metallic structures. However, the efficiency of energy localization is relatively weak, largely due to high propagation loss and strong…
Bloch wave functions of electrons have properties called quantum geometry, which has recently attracted much attention as the origin of intriguing physical phenomena. In this paper, we introduce the notion of the quantum-geometric pair…
We analyze the supersymmetry and the shape invariance of the potentials of the (1+1) relativistic oscillators we have recently proposed.
Currently there is no general theory of quantum tunnelling of a particle through a potential barrier which is compatible with QFT. We present a complete calculation of tunnelling amplitudes for a scalar field for some simple potentials…
We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are given as solutions of a set of dynamical…
We analyze the behavior of a non-Hermitian opened one-dimensional quantum system with $\mathcal{PT}$ symmetry. This system is built by a dimer, with balanced gains and losses described by a parameter $\gamma$. By varying $\gamma$ the system…
In order to clarify whether the odd-frequency superconductivity can be realized or not, we study a quasi-one-dimensional triangular lattice in the Hubbard model using the random phase approximation (RPA) and the fluctuation exchange (FLEX)…
We analyse a system in which, due to entanglement between the spin and spatial degrees of freedom, the reduced transmitted state has the shape of the freely propagating pulse translated in the complex co-ordinate plane. In the case an…
Scattering a quantum particle by a self-similar fractal potential on a Cantor set is investigated. We present a new type of solution of the functional equation for the transfer matrix of this potential, which was derived earlier from the…
We demonstrate theoretically the existence of one-way Tamm plasmon-polaritons on the interface between magnetophotonic crystals and conducting metal oxides. In contrast to conventional surface plasmon-polaritons (SPPs), Tamm…
We study the scattering off a time-periodic zero-range potential in one spatial dimension. We focus on the parameter regions that lead to zero-transmission probability (ZTP). For static potentials, ZTP leads to fermionization of…
It is shown that in the case of the one-particle one-dimensional scattering problem for a given time-independent potential, for each state of the whole quantum ensemble of identically prepared particles, there is an unique pair of…
Surface plasmon polaritons (SPPs) are central to application areas such as sensing, energy harvesting, and nanoscale optics, and are typically excited via spatial structuring -- an approach lacking dynamic control. We demonstrate that…
We present a semi-analytical model that predicts the excitation of surface-plasmon polaritons (SPP) on a graphene sheet located in front of a sub-wavelength slit drilled in thick metal screen. We identify the signature of the SPP in the…
We formulate and study the set of coupled nonlinear differential equations which define a series of shape invariant potentials which repeats after a cycle of $p$ iterations. These cyclic shape invariant potentials enlarge the limited…
A new variational method for studying the equilibrium states of an interacting particles system has been proposed. The statistical description of the system is realized by means of a density matrix. This method is used for description of…