scholarly journals (1+1)-Dirac bound states in one dimension, with position-dependent Fermi velocity and mass

Open Physics ◽  
2013 ◽  
Vol 11 (4) ◽  
Author(s):  
Omar Mustafa

AbstractWe extend Panella and Roy’s [17] work for massless Dirac particles with position-dependent (PD) velocity. We consider Dirac particles where the mass and velocity are both position-dependent. Bound states in the continuum (BIC)-like and discrete bound state solutions are reported. It is observed that BIC-like solutions are not only feasible for the ultra-relativistic (massless) Dirac particles but also for Dirac particles with PDmass and PD-velocity that satisfy the condition m(x) v F2 (x) = A, where A ≥ 0 is constant. Dirac Pöschl-Teller and harmonic oscillator models are also reported.

2007 ◽  
Vol 16 (01) ◽  
pp. 189-198 ◽  
Author(s):  
SHI-HAI DONG ◽  
D. MORALES ◽  
J. GARCÍA-RAVELO

By using the exact quantization rule, we present analytical solutions of the Schrödinger equation for the deformed harmonic oscillator in one dimension, the Kratzer potential and pseudoharmonic oscillator in three dimensions. The energy levels of all the bound states are easily calculated from this quantization rule. The normalized wavefunctions are also obtained. It is found that the present approach can simplify the calculations.


Nanophotonics ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Shereena Joseph ◽  
Saurabh Pandey ◽  
Swagato Sarkar ◽  
Joby Joseph

Abstract From theoretical model to experimental realization, the bound state in the continuum (BIC) is an emerging area of research interest in the last decade. In the initial years, well-established theoretical frameworks explained the underlying physics for optical BIC modes excited in various symmetrical configurations. Eventually, in the last couple of years, optical-BICs were exploited as a promising tool for experimental realization with advanced nanofabrication techniques for numerous breakthrough applications. Here, we present a review of the evolution of BIC modes in various symmetry and functioning mediums along with their application. More specifically, depending upon the nature of the interacting medium, the excitations of BIC modes are classified into the pure dielectric and lossy plasmonic BICs. The dielectric constituents are again classified as photonic crystal functioning in the subwavelength regime, influenced by the diffraction modes and metasurfaces for interactions far from the diffraction regime. More importantly, engineered functional materials evolved with the pure dielectric medium are explored for hybrid-quasi-BIC modes with huge-quality factors, exhibiting a promising approach to trigger the nanoscale phenomena more efficiently. Similarly, hybrid modes instigated by the photonic and plasmonic constituents can replace the high dissipative losses of metallic components, sustaining the high localization of field and high figure of merit. Further, the discussions are based on the applications of the localized BIC modes and high-quality quasi-BIC resonance traits in the nonlinear harmonic generation, refractometric sensing, imaging, lasing, nanocavities, low loss on-chip communication, and as a photodetector. The topology-controlled beam steering and, chiral sensing has also been briefly discussed.


2021 ◽  
Vol 13 (1) ◽  
pp. 22-38
Author(s):  
Yu.D. Golovaty

The threshold behaviour of negative eigenvalues for Schr\"{o}dinger operators of the type \[ H_\lambda=-\frac{d^2}{dx^2}+U+ \lambda\alpha_\lambda V(\alpha_\lambda \cdot) \] is considered. The potentials $U$ and $V$ are real-valued bounded functions of compact support, $\lambda$ is a positive parameter, and positive sequence $\alpha_\lambda$ has a finite or infinite limit as $\lambda\to 0$. Under certain conditions on the potentials there exists a bound state of $H_\lambda$ which is absorbed at the bottom of the continuous spectrum. For several cases of the limiting behaviour of sequence $\alpha_\lambda$, asymptotic formulas for the bound states are proved and the first order terms are computed explicitly.


Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 372
Author(s):  
Nir Hacker ◽  
Boris A. Malomed

We consider a two-component linearly coupled system with the intrinsic cubic nonlinearity and the harmonic-oscillator (HO) confining potential. The system models binary settings in BEC and optics. In the symmetric system, with the HO trap acting in both components, we consider Josephson oscillations (JO) initiated by an input in the form of the HO’s ground state (GS) or dipole mode (DM), placed in one component. With the increase of the strength of the self-focusing nonlinearity, spontaneous symmetry breaking (SSB) between the components takes place in the dynamical JO state. Under still stronger nonlinearity, the regular JO initiated by the GS input carries over into a chaotic dynamical state. For the DM input, the chaotization happens at smaller powers than for the GS, which is followed by SSB at a slightly stronger nonlinearity. In the system with the defocusing nonlinearity, SSB does not take place, and dynamical chaos occurs in a small area of the parameter space. In the asymmetric half-trapped system, with the HO potential applied to a single component, we first focus on the spectrum of confined binary modes in the linearized system. The spectrum is found analytically in the limits of weak and strong inter-component coupling, and numerically in the general case. Under the action of the coupling, the existence region of the confined modes shrinks for GSs and expands for DMs. In the full nonlinear system, the existence region for confined modes is identified in the numerical form. They are constructed too by means of the Thomas–Fermi approximation, in the case of the defocusing nonlinearity. Lastly, particular (non-generic) exact analytical solutions for confined modes, including vortices, in one- and two-dimensional asymmetric linearized systems are found. They represent bound states in the continuum.


2019 ◽  
Vol 94 (10) ◽  
pp. 105214
Author(s):  
Zafar Ahmed ◽  
Sachin Kumar ◽  
Dona Ghosh ◽  
Tarit Goswami

1993 ◽  
Vol 328 ◽  
Author(s):  
N. Peyghambarian ◽  
K. Meissner ◽  
B. Fluegel ◽  
S. Mazumdar ◽  
F. Guo ◽  
...  

ABSTRACTCollective excitations, such as plasmons, rotons, electron-hole liquid, and excitonic Molecules, have been extensively studied in condensed Matter.1 Wannier excitons in inorganic semiconductors are bound by the exchange interactions between two electrons of the exciton, and the bound state of More than two excitons is not possible. We demonstrate here a new type of collective excitations,2 bound states of Multiple charge-transfer (CT) excitons. Coulomb interactions in one dimension are shown to bind a train of several (More than two) CT excitons. Experimental evidence for these new type of elementary excitations is reported in a quasi-one-dimensional CT crystal of anthracene PMDA. High density excitation by femtosecond light pulses generates Multi-exciton chains, which we refer to as excitonic n-strings with n = 1, 2, 3, etc., along the stack axis of the crystal. Both the n = 2 excitonic string (biexciton) and the n = 3 string (tri-exciton) are observed. This report provides evidence for an n > 2 exciton chain in this system.2 The stability of the n-string exciton is supported by our theoretical calculations based on the extended Hubbard Hamiltonian in one dimension.


2018 ◽  
Vol 64 (5) ◽  
pp. 464 ◽  
Author(s):  
David Lohr ◽  
Enriqueta Hernandez ◽  
Antonio Jauregui ◽  
Alfonso Mondragon

We study the Jost solutions for the scattering problem of a von Neumann-Wigner type potential, constructed by means of a two times iterated and completely degenerated Darboux transformation. We show that for a particular energy the unnormalizedJost solutions coalesce to give rise to a Jordan cycle of rank two. Performing a pole decomposition of the normalized Jost solutions we find the generalized eigenfunctions: one is a normalizable function corresponding to the bound state in the continuum and the other is a bounded, non-normalizable function. We obtain the time evolution of these functions as pseudo-unitary, characteristic of a pseudo-Hermitian system.


Nanophotonics ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Haoran Zhang ◽  
Tao Wang ◽  
Jingyi Tian ◽  
Jiacheng Sun ◽  
Shaoxian Li ◽  
...  

Abstract In this work, we propose and numerically investigate a two-dimensional microlaser based on the concept of bound states in the continuum (BIC). The device consists of a thin gain layer (Rhodamine 6G dye-doped silica) sandwiched between two high-contrast-grating layers. The structure supports various BIC modes upon a proper choice of topological parameters; in particular it supports a high-Q quasi-BIC mode when partially breaking a bound state in the continuum at Γ point. The optically-pumped gain medium provides sufficient optical gain to compensate the quasi-BIC mode losses, enabling lasing with ultra-low pump threshold (fluence of 17 μJ/cm2) and very narrow optical linewidth in the visible range. This innovative device displays distinguished sensing performance for gas detection, and the emission wavelength sensitively shifts to the longer wavelength with the changing of environment refractive index (in order of 5 × 10−4). The achieved bulk sensitivity is 221 nm/RIU with a high signal to noise ratio, and a record-high figure of merit reaches to 4420 RIU−1. This ultracompact and low threshold quasi-BIC laser facilitated by the ultra-narrow resonance can serve as formidable candidate for on-chip gas sensor.


2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Zejie Yu ◽  
Xiankai Sun

AbstractPhotonic bound states in the continuum (BICs) have recently been studied in various systems and have found wide applications in sensors, lasers, and filters. Applying BICs in photonic integrated circuits enables low-loss light guidance and routing in low-refractive-index waveguides on high-refractive-index substrates, which opens a new avenue for integrated photonics with functional single-crystal materials. Here, we demonstrate high-quality integrated lithium niobate microcavities inside which the photonic BIC modes circulate and further modulate these BIC modes acousto-optically by using piezoelectrically actuated surface acoustic waves at microwave frequencies. With a high acousto-optic modulation frequency, the acousto-optic coupling is well situated in the resolved-sideband regime. This leads to coherent coupling between microwave and optical photons, which is exhibited by the observed electro-acousto-optically induced transparency and absorption. Therefore, our devices serve as a paradigm for manipulating and controlling photonic BICs on a chip, which will enable many other applications of photonic BICs in the areas of microwave photonics and quantum information processing.


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