Bound States in Continuum Generated by Point Interaction and Supersymmetric Quantum Mechanics

Kočinac, S.; Milanović, V.

doi:10.1142/s0217984912501771

Cited by 9 publications

(5 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In some cases, this SUSY method is equivalent to von Neumann and Wigner's approach and the Gel'fand-Levitan approach 192 . The SUSY method has been applied to generate BICs in point interaction systems 193 , periodic Lamé potentials 194 , and photonic crystals 195 . The SUSY method has also been extended to non-Hermitian systems with material gain and loss, where BICs are found below, above, and at the exceptional point [196][197][198][199][200][201][202][203][204] .…”

Section: Potential Engineeringmentioning

confidence: 99%

Bound states in the continuum

et al. 2016

View full text Add to dashboard Cite

Bound states in the continuum are waves that, defying conventional wisdom, remain localized even though they coexist with a continuous spectrum of radiating waves that can carry energy away. Their existence was first proposed in quantum mechanics and, being a general wave phenomenon, later identified in electromagnetic, acoustic, and water waves. They have been studied in a wide variety of material systems such as photonic crystals, optical waveguides and fibers, piezoelectric materials, quantum dots, graphene, and topological insulators. This Review describes recent developments in this field with an emphasis on the physical mechanisms that lead to these unusual states across the seemingly very different platforms. We discuss recent experimental realizations, existing applications, and directions for future work.

show abstract

Section: Potential Engineeringmentioning

confidence: 99%

Bound states in the continuum

et al. 2016

View full text Add to dashboard Cite

show abstract

“…The corresponding supersymmetric wave functions for all the states of energies E n ≠ε is somewhat lengthy to be written down so we''ll skip it. More details can be found in (Kočinac & Milanović, 2012b). We state that constants λ and C in Eqs.…”

Section: Supersymmetric Quantum Mechanicsmentioning

confidence: 99%

“…In the previous section we have considered particle on the halfline with zero transmission (T R(L) =0). For the more general case of finite transmission probability, rather then employing equations (34), we use the parameterized representation of the transmission and reflection coefficients (Kočinac et al, 2012b):…”

Section: Susy and General Point Interactionmentioning

confidence: 99%

See 1 more Smart Citation

Some properties of one-dimensional point interactions

Kočinac¹

2016

Univ Thought

View full text Add to dashboard Cite

In this review paper we shall give a brief account of some properties of so called point interactions that describe a potentials spatially localized. A different families of one-dimensional point interactions are investigated and then relevant tunneling times are calculated. Than we demonstrate how a bound state in the continuum may be generated applying supersymmetric quantum mechanics. Finally, it is shown how the latter method may be used to tailor phase rigidity of one-dimensional point interactions.

show abstract

“…Thereby, identifying which fermionic zero modes are trapped in the submanifold Σ, simultaneously determines which bosonic zero modes are localized. In this paper the focus is on exactly these fermionic zero modes that are trapped on the complex dimension one curve Σ, with Σ being considered as a defect of the theory on S. We establish the result that these fermionic zero modes are associated to an one dimensional N = 2 supersymmetric quantum mechanics (SUSY QM hereafter) algebra [26][27][28][29][30][31][32][33][34][35][36][37][38][39]. Particularly, the zero modes localized on Σ are in bijective correspondence with the vectors of the graded Hilbert space that describes the SUSY QM vector space of quantum states (for an similar case related to superconducting strings and to Chern-Simons gauge theories in (2 + 1)-dimensions, see [40,41]).…”

Section: Introductionmentioning

confidence: 99%

Graded Geometric Structures Underlying F-Theory Related Defect Theories

Oikonomou

2013

Int. J. Mod. Phys. A

View full text Add to dashboard Cite

In the context of F-theory, we study the related eight dimensional super-YangMills theory and reveal the underlying supersymmetric quantum mechanics algebra that the fermionic fields localized on the corresponding defect theory are related to. Particularly, the localized fermionic fields constitute a graded vector space, and in turn this graded space enriches the geometric structures that can be built on the initial eight-dimensional space. We construct the implied composite fibre bundles, which include the graded affine vector space and demonstrate that the composite sections of this fibre bundle are in one-to-one correspondence to the sections of the square root of the canonical bundle corresponding to the submanifold on which the zero modes are localized. IntroductionString theory has proven to be the most promising theory towards the unified description of all forces and matter in nature. Particularly, it encompasses in its theoretical framework gravity and a large number of field theoretic features such as, supersymmetry, chiral matter and spontaneous symmetry breaking. The appealing attribute of string theory is that it can provide consistent UV completion of many field theoretic models because it can accommodate quite successfully supersymmetric grand unified theories. M-theory embodies all the different string theories that describe independently various features of the UV completions of the Standard Model (SM hereafter), with the various branches of M-theory being connected with dualities, a strong tool towards a non-perturbative description. However, certain branches of M-theory prove to be more efficient in realizing SM phenomenological features, than others. Particularly, type IIB string theory and the strongly coupled version of it, F-theory (for an important stream of papers on F-theory see and for reviews on F-theory see [4][5][6]) embody many phenomenological features of the SM. The most appealing feature of these theories is that these allow gauge * voiko@physics.auth.gr

show abstract

Bound States in Continuum Generated by Point Interaction and Supersymmetric Quantum Mechanics

Cited by 9 publications

References 34 publications

Bound states in the continuum

Bound states in the continuum

Some properties of one-dimensional point interactions

Graded Geometric Structures Underlying F-Theory Related Defect Theories

Contact Info

Product

Resources

About