Taksu Cheon, Research Field

The single particle quantum mechanics with 1-dimenional Dirac's delta potential which is in every introductory textbook has very interesting non-trivial analogues in 2 and 3 dimensions. One has to introduce renormalization to deal with the divergences. Mathematically rigoorous treatment of the problem requires self-adjoint extension theory of functional analysis. Once this is done, the system can be thought of as a 'solvable' idealization of generic potential model in 2 and 3 dimensions.

As such, it can be used, for example, to probe the multidimensional tunneling (resonance tunneling or 'chaotic' tunneling). Berry phase, which is thought to be an esoteric phenomena in high mathematical physics could be realized and even utilized in relatively simple settings.

2 and 3 dimensional systems with pointlike potential are among the simplest non-integrable systems. They serve as the "experimental ground" for the "quantum chaos", namely, the study quantum mechanical properties of classically chaotic systems.

Moreover, even in 1 dimension, delta potential (which causes discontinuity in the derivative of wave function while keeping the wave function itself continuous) has a non-trivial partner which induces discontinuity in the wave function itself. This object, ocasionally termed delta-prime potential, can be realized as a singular but renormalized limit of three deltas of canceling infite strength pushed into a single point. Experimental realization would enable the production of nano-device whose electrons will have the maximum existence probability at the edge of the device while their node come at the center.

Here's a presentation for some "official" ocasion: [PDF] [MOV]

Research Field Outline

Taksu Cheon

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[Japanese]

[Research Page] [TC Home] [Theory Group]

[Japanese]

Quantum mechanics of pointlike potentials and its applications

Evolutionary Game Theory and Ecosystem

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	Quantum mechanics of pointlike potentials and its applications The single particle quantum mechanics with 1-dimenional Dirac's delta potential which is in every introductory textbook has very interesting non-trivial analogues in 2 and 3 dimensions. One has to introduce renormalization to deal with the divergences. Mathematically rigoorous treatment of the problem requires self-adjoint extension theory of functional analysis. Once this is done, the system can be thought of as a 'solvable' idealization of generic potential model in 2 and 3 dimensions. As such, it can be used, for example, to probe the multidimensional tunneling (resonance tunneling or 'chaotic' tunneling). Berry phase, which is thought to be an esoteric phenomena in high mathematical physics could be realized and even utilized in relatively simple settings. 2 and 3 dimensional systems with pointlike potential are among the simplest non-integrable systems. They serve as the "experimental ground" for the "quantum chaos", namely, the study quantum mechanical properties of classically chaotic systems. Moreover, even in 1 dimension, delta potential (which causes discontinuity in the derivative of wave function while keeping the wave function itself continuous) has a non-trivial partner which induces discontinuity in the wave function itself. This object, ocasionally termed delta-prime potential, can be realized as a singular but renormalized limit of three deltas of canceling infite strength pushed into a single point. Experimental realization would enable the production of nano-device whose electrons will have the maximum existence probability at the edge of the device while their node come at the center. Here's a presentation for some "official" ocasion: [PDF] [MOV]
	Evolutionary Game Theory and Ecosystem To be posted Link to a seminar slide covering altruism in game theory [PDF] [MOV] Click here for more