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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 ...
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.
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).
In ion trapping and atomic physics experiments, the Lamb Dicke regime (or Lamb Dicke limit) is a quantum regime in which the coupling (induced by an external light field) between an ion or atom's internal qubit states and its motional states is sufficiently small so that transitions that change the motional quantum number by more than one are strongly suppressed.
In many practical partial differential equations, one has a term that involves derivatives (such as a kinetic energy contribution), and a multiplication with a function (for example, a potential). In the spectral method, the solution ψ {\displaystyle \psi } is expanded in a suitable set of basis functions, for example plane waves,
The electron mobility is defined by the equation: =. where: E is the magnitude of the electric field applied to a material,; v d is the magnitude of the electron drift velocity (in other words, the electron drift speed) caused by the electric field, and
[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 ...
Informally, the Kolmogorov forward equation addresses the following problem. We have information about the state x of the system at time t (namely a probability distribution p t ( x ) {\displaystyle p_{t}(x)} ); we want to know the probability distribution of the state at a later time s > t {\displaystyle s>t} .