We present a calculation of single-charge tunneling in a semiconductor quantum dot based on a full self-consistent tight-binding calculation of. It's simply the most general kind of interaction Hamiltonian you can write down in this simplified two-level system. On the 2D Hilbert space. The characteristics of tunnel junctions formed between n- and p-doped graphene are investigated theoretically. The single-particle tunnel current that flows.


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The tunnelling problem[ edit ] The wave function single particle tunneling a particle summarises everything that can single particle tunneling known about a physical system. This is directly related to the probability density of the particle's position, which describes the probability that the particle is at any given place.

In the limit of large barriers, the probability of tunnelling decreases for taller and wider barriers. For simple tunnelling-barrier models, such as the rectangular barrieran analytic solution exists.

Phys. Rev. B 64, - Single-particle tunneling in semiconductor quantum dots

Problems in real life often do not have one, so "semiclassical" or "quasiclassical" methods have been developed to give approximate solutions to these problems, like the WKB approximation.

Probabilities may be derived with arbitrary precision, constrained by computational resources, via Feynman 's single particle tunneling integral method; such precision is seldom required in engineering practice.

Examples include the tunnelling of a classical wave-particle association, [17] evanescent wave coupling the application of Maxwell's wave-equation to light and the application of the non-dispersive wave-equation from acoustics applied to "waves on strings".

Evanescent wave coupling, until recently, was only called "tunnelling" in quantum mechanics; now it is used in other contexts. Single particle tunneling effects are modelled similarly to the rectangular potential barrier.

In these cases, there is one transmission medium through which the wave propagates that is the same or nearly the same throughout, and a second medium through which the single particle tunneling travels differently.

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This can be described as a thin region of medium B between two regions of medium A. In opticsmedium A is a vacuum while medium B is glass.

In acoustics, medium A may be a liquid or gas and medium B a solid. For both cases, medium A is a region of space where the particle's total energy is greater than its potential energy and medium B is the potential barrier.

These have single particle tunneling incoming wave and resultant waves in both directions.

Quantum tunnelling - Wikipedia

There can be more mediums and barriers, and the barriers need not be discrete; approximations are useful in this case. For instance, tunnelling is a source of current leakage in very-large-scale integration VLSI electronics single particle tunneling results in the single particle tunneling power drain and heating effects that plague high-speed and mobile technology; it is considered the lower limit on how small computer chips can be made.

Nuclear fusion in stars[ edit ] Main article: Nuclear fusion Quantum tunnelling is essential for nuclear fusion in stars.


Temperature and pressure in the core of stars are insufficient for nuclei to overcome the Coulomb single particle tunneling in order to achieve a thermonuclear fusion. However, there is some probability to penetrate the barrier due to quantum tunnelling.

Though the probability is very low, the extreme number of nuclei in a star generates a steady fusion reaction over millions or even billions of years - single particle tunneling precondition for the evolution of life in insolation habitable zones.

Radioactive decay Radioactive decay is the process of emission of single particle tunneling and energy from the unstable nucleus of an atom to form a stable product. This is done via the tunnelling of a particle out of the nucleus an electron tunnelling into the nucleus is electron capture.


This was the first application of quantum tunnelling and led to the first approximations. Radioactive decay is also a relevant issue for astrobiology as this consequence of quantum tunnelling is creating a constant source of energy over a large period of time for environments outside the circumstellar habitable zone where insolation would not be possible subsurface oceans single particle tunneling effective.

  • Quantum mechanics - Single particle tunneling Hamiltonian - Physics Stack Exchange
  • Quantum tunnelling

Here it is important both as electron tunnelling and proton tunnelling. Electron tunnelling is a key factor in many biochemical redox reactions photosynthesis, cellular respiration as well as enzymatic catalysis while proton tunnelling is a key factor in spontaneous mutation single particle tunneling DNA.


A hydrogen bond joins normal base pairs of DNA. There exists a double well potential along a hydrogen bond separated by a potential energy barrier.

It is believed single particle tunneling the double well potential is asymmetric with one well deeper than the other so the proton normally rests in the deeper well.

For a mutation to occur, the proton must have tunnelled into the shallower of the two potential wells. The movement of the proton from its regular position is called a tautomeric transition. Other instances of quantum tunnelling-induced mutations in biology are believed to single particle tunneling a cause of ageing and cancer.

Semiconductor devices Cold emission of electrons is relevant to semiconductors and superconductor physics.