Tunneling theory without the transfer-Hamiltonian formalism. II. Resonant and inelastic tunneling across a junction of finite width

Quantum tunneling, wherein a quanject has a non-zero probability of tunneling into and then exiting a barrier of finite width and height, is the subject of Chapter 13. The description for the one-dimensional case is extended to the barrier being inverted, which forms an attractive potential well. The first application of this analysis is to the emission of alpha particles from the decay of radioactive nuclei, where the alpha-nucleus attraction is modeled by a potential well and the barrier is the repulsive Coulomb potential. Excellent results are obtained. Ditto for the similar analysis of proton burning in stars and yet a different analysis that explains tunneling through a Josephson junction, the connector between two superconductors. The final application is to the scanning tunneling microscope, a device that allows the microscopic surfaces of solids to be mapped via electrons from the surface molecules tunneling into the tip of the STM probe.

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Hamiltonian Aspects of Three-Layer Stratified Fluids

Journal of Nonlinear Science ◽

10.1007/s00332-021-09726-0 ◽

2021 ◽

Vol 31 (4) ◽

Author(s):

R. Camassa ◽

G. Falqui ◽

G. Ortenzi ◽

M. Pedroni ◽

T. T. Vu Ho

Keyword(s):

Hamiltonian Structure ◽

Linear Equations ◽

Hamiltonian Formalism ◽

Reduction Process ◽

Ideal Fluids ◽

Upper Lid ◽

Stratification Structure ◽

Special Solutions ◽

Dispersionless Limit ◽

Unbounded Fluid

AbstractThe theory of three-layer density-stratified ideal fluids is examined with a view toward its generalization to the n-layer case. The focus is on structural properties, especially for the case of a rigid upper lid constraint. We show that the long-wave dispersionless limit is a system of quasi-linear equations that do not admit Riemann invariants. We equip the layer-averaged one-dimensional model with a natural Hamiltonian structure, obtained with a suitable reduction process from the continuous density stratification structure of the full two-dimensional equations proposed by Benjamin. For a laterally unbounded fluid between horizontal rigid boundaries, the paradox about the non-conservation of horizontal total momentum is revisited, and it is shown that the pressure imbalances causing it can be intensified by three-layer setups with respect to their two-layer counterparts. The generator of the x-translational symmetry in the n-layer setup is also identified by the appropriate Hamiltonian formalism. The Boussinesq limit and a family of special solutions recently introduced by de Melo Viríssimo and Milewski are also discussed.

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Finite-width waveguide and waveguide intersections for self-collimated beams in photonic crystals

Applied Physics Letters ◽

10.1063/1.1828577 ◽

2004 ◽

Vol 85 (21) ◽

pp. 4834-4836 ◽

Cited By ~ 25

Author(s):

Zhaofeng Li ◽

Haibo Chen ◽

Zhitang Song ◽

Fuhua Yang ◽

Songlin Feng

Keyword(s):

Photonic Crystals ◽

Finite Width

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