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In this model the conduction is supposed to be carried by a free electron system moving in a self-consistent periodic potential. On the contrary, Frenkel derived his formula describing the dielectric (or the semiconductor) as simply composed by neutral atoms acting as positively charged trap states (when empty, i.e. when the atoms are ionized).
By Newton's laws of motion, the above equation represents the force on the ion. This equation can be exactly solved using the Floquet theorem or the standard techniques of multiple scale analysis. [8] The particle dynamics and time averaged density of charged particles in a Paul trap can also be obtained by the concept of ponderomotive force.
In the case where the electron/hole transport is limited by trap states in the form of exponential tails extending from the conduction/valence band edges, = (), the drift current density is given by the Mark-Helfrich equation, [10] = ((+)) (+ +) + + + where is the elementary charge, = / with being the thermal energy, is the effective ...
An ion trap mass spectrometer may incorporate a Penning trap (Fourier-transform ion cyclotron resonance), [12] Paul trap [13] or the Kingdon trap. [14] The Orbitrap, introduced in 2005, is based on the Kingdon trap. [15] Other types of mass spectrometers may also use a linear quadrupole ion trap as a selective mass filter.
Trap emission is a multistep process wherein a carrier falls into defect-related wave states in the middle of the bandgap. A trap is a defect capable of holding a carrier. The trap emission process recombines electrons with holes and emits photons to conserve energy. Due to the multistep nature of trap emission, a phonon is also often emitted.
The Gross–Pitaevskii equation can also be derived as the semi-classical limit of the many body theory of s-wave interacting identical bosons represented in terms of coherent states. [24] The semi-classical limit is reached for a large number of quanta, expressing the field theory either in the positive-P representation (generalised Glauber ...
[6] [7] This generic equation plays a central role in the theory of critical dynamics, [8] and other areas of nonequilibrium statistical mechanics. The equation for Brownian motion above is a special case. An essential step in the derivation is the division of the degrees of freedom into the categories slow and fast. For example, local ...
Quantity (common name/s) (Common) symbol/s SI units Dimension Number of wave cycles N: dimensionless dimensionless (Oscillatory) displacement Symbol of any quantity which varies periodically, such as h, x, y (mechanical waves), x, s, η (longitudinal waves) I, V, E, B, H, D (electromagnetism), u, U (luminal waves), ψ, Ψ, Φ (quantum mechanics).