effect

tunnel effect

The tunnel effect is a quantum phenomenon where particles pass through potential barriers.
28 related articles · 3 formulas · 2 who worked here

Description

In 1928, George Gamow, Ronald Gurney and Edward Condon independently explained alpha decay: a particle inside the nucleus does not have enough energy to escape according to classical laws, but thanks to the wave properties of matter, there is a small probability of finding it outside — as if it passed through a wall without breaking it. Later, the effect found application in electronics: in 1957, Leo Esaki created the tunnel diode, where current flows through the forbidden zone of a semiconductor.

History

In 1927, Friedrich Hund first discovered tunneling while analyzing a double potential well. In 1928, George Gamow, and independently Ronald Gurney and Edward Condon, applied the concept to explain alpha decay. Later, in 1957, Leo Esaki invented the tunnel diode, demonstrating practical use of the effect in semiconductors, for which he received the Nobel Prize.

How it works

The tunnel effect manifests at scales on the order of the de Broglie wavelength of the particle. As the particle mass and barrier width decrease, the tunneling probability increases. It is used in scanning tunneling microscopes, tunnel diodes, flash memory cells, and in nuclear fusion in stars (overcoming the Coulomb barrier). Limits of applicability: requires quantum description; not observed in the macroscopic world due to exponential suppression for large masses and thicknesses.

In practice

Tunnel diodes, flash memory, scanning tunneling microscopes, radioactive alpha decay, quantum computers.

Fun fact

In a USB flash drive, electrons tunnel through an oxide layer just a few nanometers thick, changing the cell charge — that's how your files are stored.

Concept graph →

Formulas

$$B = S_E[\phi_b] - S_E[\phi_{\text{vacuum}}]$$
Tunneling rate depends on action difference.
What is in the formula
BvariableEuclidean action difference — action difference
S_EvariableEuclidean action of a field configuration — action
\phi_bvariableField configuration of the bounce (instanton) — field configuration
\phi_{\text{vacuum}}variableField configuration of the vacuum state — field configuration
b=s_e[φ_b(x)]-s_e[φ_{{fv}}] · 2607.06680
$$T \approx \exp\left(-2\int_{z_1}^{z_2} \sqrt{\frac{2m}{\hbar^2}(V(z)-E)}\, dz\right)$$
Approximate quantum tunneling probability through a barrier.
What is in the formula
Tvariabletunneling probability — transmission probability
z1variableleft turning point of the barrier — position metre
z2variableright turning point of the barrier — position metre
mvariablemass of the tunneling particle — mass kilogram
Vvariablepotential energy as a function of position — potential energy joule
Evariableenergy of the particle — energy joule
ħconstantfundamental quantum of action divided by 2π — reduced planck constant = 1.054571817e-34 joule second
∫operatorsums the integrand over the interval — integral
√operatortakes the non-negative root — square root
expoperatorraises e to the given power — exponential
d\approx\exp[-\sqrt{\frac{8m_{e}}{ħ^{2}}}\int_{z_{1}}^{z_{2}}m^{1/2}(φ,f,z)dz] · 2505.00872v4
$$\Gamma \propto e^{-S}$$
Quantum tunneling rates are exponentially suppressed by the bounce action.
What is in the formula
\GammavariableTunneling rate (probability per unit time) — rate per second
SvariableEuclidean action of the bounce solution — action joule second
\proptooperatorIndicates proportionality — proportional to
e^{-S}operatorExponential function with exponent -S — exponential
\gamma/v=m^4e^{-s} · 2606.06587v1

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