Quantum tunnelling
[2][3] Tunneling plays an essential role in physical phenomena such as nuclear fusion[4] and alpha radioactive decay of atomic nuclei.
To understand the phenomenon, particles attempting to travel across a potential barrier can be compared to a ball trying to roll over a hill.
The wave packet becomes more de-localized: it is now on both sides of the barrier and lower in maximum amplitude, but equal in integrated square-magnitude, meaning that the probability the particle is somewhere remains unity.
The first person to apply the Schrödinger equation to a problem that involved tunneling between two classically allowed regions through a potential barrier was Friedrich Hund in a series of articles published in 1927.
[11] In 1927, Lothar Nordheim, assisted by Ralph Fowler, published a paper that discussed thermionic emission and reflection of electrons from metals.
Nordheim and Fowler simplified Oppenheimer's derivation and found values for the emitted currents and work functions that agreed with experiments.
[10] A great success of the tunnelling theory was the mathematical explanation for alpha decay, which was developed in 1928 by George Gamow and independently by Ronald Gurney and Edward Condon.
[12][13][14][15] The latter researchers simultaneously solved the Schrödinger equation for a model nuclear potential and derived a relationship between the half-life of the particle and the energy of emission that depended directly on the mathematical probability of tunneling.
Esaki, Giaever and Josephson shared the 1973 Nobel Prize in Physics for their works on quantum tunneling in solids.
Tunnelling is a source of current leakage in very-large-scale integration (VLSI) electronics and results in a substantial power drain and heating effects that plague such devices.
This peculiar property is used in some applications, such as high speed devices where the characteristic tunnelling probability changes as rapidly as the bias voltage.
[21] The scanning tunnelling microscope (STM), invented by Gerd Binnig and Heinrich Rohrer, may allow imaging of individual atoms on the surface of a material.
By using piezoelectric rods that change in size when voltage is applied, the height of the tip can be adjusted to keep the tunnelling current constant.
The temperature in stellar cores is generally insufficient to allow atomic nuclei to overcome the Coulomb barrier and achieve thermonuclear fusion.
Though this probability is still low, the extremely large number of nuclei in the core of a star is sufficient to sustain a steady fusion reaction.
[27] Radioactive decay is the process of emission of particles and energy from the unstable nucleus of an atom to form a stable product.
Radioactive decay is a relevant issue for astrobiology as this consequence of quantum tunnelling creates a constant energy source over a large time interval for environments outside the circumstellar habitable zone where insolation would not be possible (subsurface oceans) or effective.
The quantum mechanical tunnelling rate for the same reaction using the hydrogen isotope deuterium, D− + H2 → H− + HD, has been measured experimentally in an ion trap.
[30] In chemical kinetics, the substitution of a light isotope of an element with a heavier one typically results in a slower reaction rate.
However, in certain cases, large isotopic effects are observed that cannot be accounted for by a semi-classical treatment, and quantum tunnelling is required.
[31] By including quantum tunnelling, the astrochemical syntheses of various molecules in interstellar clouds can be explained, such as the synthesis of molecular hydrogen, water (ice) and the prebiotic important formaldehyde.
Electron tunnelling is a key factor in many biochemical redox reactions (photosynthesis, cellular respiration) as well as enzymatic catalysis.
[27] Spontaneous mutation occurs when normal DNA replication takes place after a particularly significant proton has tunnelled.
to satisfy the real part of the equation; for a good classical limit starting with the highest power of the Planck constant possible is preferable, which leads to
[37] More recently, experimental tunnelling time data of phonons, photons, and electrons was published by Günter Nimtz.
Moreover, if quantum tunneling is modeled with the relativistic Dirac equation, well established mathematical theorems imply that the process is completely subluminal.
The existence of the chaotic sea, where transport is classically allowed, between the two symmetric tori then assists the quantum tunnelling between them.
is small in front of the size of the regular islands, the fine structure of the classical phase space plays a key role in tunnelling.
In particular the two symmetric tori are coupled "via a succession of classically forbidden transitions across nonlinear resonances" surrounding the two islands.
A classical wave-particle association was originally analyzed as analogous to quantum tunneling,[50] but subsequent analysis found a fluid dynamics cause related to the vertical momentum imparted to particles near the barrier.
