相关论文: The band-gap structure and the singular character …
Numerical analysis indicates that there exists an unexpected new ordered chaos for the bounded one-dimensional multibarrier potential. For certain values of the number of barriers, repeated identical forms (periods) of the wavepackets…
We investigate the transmission properties of a quantum one-dimensional periodic system of fixed length $L$, with $N$ barriers of constant height $V$ and width $\lambda$, and $N$ wells of width $\delta$. In particular, we study the…
The spectrum of the self-adjoint Schr\"odinger operator associated with the Kronig-Penney model on the half-line has a band-gap structure: its absolutely continuous spectrum consists of intervals (bands) separated by gaps. We show that if…
We have previously discussed the classical diffusive system of the bounded one-dimensional multitrap using the transfer-matrix method which is generally applied for studying the energy spectrum of the unbounded quantum Kronig-Penney…
We show that the transmission through single and double {\delta}-function potential barriers of strength P in bilayer graphene is periodic in P with period {\pi}. For a certain range of P values we find states that are bound to the…
We discuss the properties of a large number N of one-dimensional (bounded) locally periodic potential barriers in a finite interval. We show that the transmission coefficient, the scattering cross section $\sigma$, and the resonances of…
We describe a broad class of bounded non-periodic potentials in one-dimensional stationary quantum mechanics having the same spectral properties as periodic potentials. The spectrum of the corresponding Schroedinger operator consists of a…
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…
In this work, we investigate the bound states in the continuum (BIC) of a one-dimensional spin-1 flat band system. It is found that, when the potential is sufficiently strong, there exists an effective attractive potential well surrounded…
The momentum spectrum of a periodic network (quantum graph) has a band-gap structure. We investigate the relative density of the bands or, equivalently, the probability that a randomly chosen momentum belongs to the spectrum of the periodic…
The Kronig-Penney model is used to Study the effect of nonlinear interaction on the transmissive properties of both ordered and disordered chains. In the ordered case, the nonlinearity can either localize or delocalize the electronic states…
The energy spectrum for a system of atoms in a periodic potential can exhibit a gap in the band structure. We describe a system in which a laser is used to produce a mechanical potential for the atoms, and a standing wave light field is…
Applying certain known theorems about one-dimensional periodic potentials, we show that the energy spectrum of the associated Lam\'{e} potentials $$a(a+1)m~{\rm sn}^2(x,m)+b(b+1)m~{\rm cn}^2(x,m)/{\rm dn}^2(x,m)$$ consists of a finite…
For an ideal Bose-gas within a multi-slab periodic structure, we discuss the effect of the spatial distribution of the gas on its Bose-Einstein condensation critical temperature $T_c$, as well as on the origin of its dimensional crossover…
We study the properties of the quantum states in the one-dimensional system with a shifted periodic potential in both the discrete model and the continuous model. With open boundary conditions, the edge states appear in the energy gaps…
We investigate a one-dimensional quantum system with a self-similar arrangement of delta-function potential barriers, exhibiting discrete scale invariance. The singular potential induces kinematically enforced symmetry breaking at $x=0$,…
Complex periodic structures inherit spectral properties from the constituent parts of their unit cells, chiefly their spectral band gaps. Exploiting this intuitive principle, which is made precise in this work, means spectral features of…
The spectrum of excitations a two-dimensional, planar honeycomb lattice of two-level atoms coupled by the in-plane electromagnetic field may exhibit band gaps that can be opened either by applying an external magnetic field or by breaking…
The origin of spectral singularities in finite-gap singly periodic PT-symmetric quantum systems is investigated. We show that they emerge from a limit of band-edge states in a doubly periodic finite gap system when the imaginary period…
A transmission phenomenon for a quantal particle scattered through a multi-well potential in one dimension is observed by means of an amplitude-phase method. The potential model consists of $N$ identical potential cells, each containing a…