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A quantity undergoing exponential decay. Larger decay constants make the quantity vanish much more rapidly. This plot shows decay for decay constant (λ) of 25, 5, 1, 1/5, and 1/25 for x from 0 to 5. A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.
Solving this equation for V yields the formula for exponential decay: =, where V 0 is the capacitor voltage at time t = 0. The time required for the voltage to fall to V 0 / e is called the RC time constant and is given by, [1] =.
In semiconductor lasers, the carrier lifetime is the time it takes an electron before recombining via non-radiative processes in the laser cavity. In the frame of the rate equations model, carrier lifetime is used in the charge conservation equation as the time constant of the exponential decay of carriers.
In phenomenological applications, it is often not clear whether the stretched exponential function should be used to describe the differential or the integral distribution function—or neither. In each case, one gets the same asymptotic decay, but a different power law prefactor, which makes fits more ambiguous than for simple exponentials.
There is a half-life describing any exponential-decay process. For example: As noted above, in radioactive decay the half-life is the length of time after which there is a 50% chance that an atom will have undergone nuclear decay. It varies depending on the atom type and isotope, and is usually determined experimentally. See List of nuclides.
Although the term skin effect is most often associated with applications involving transmission of electric currents, skin depth also describes the exponential decay of the electric and magnetic fields, as well as the density of induced currents, inside a bulk material when a plane wave impinges on it at normal incidence.
The constant decay rate of the golden rule follows. [8] As a constant, it underlies the exponential particle decay laws of radioactivity. (For excessively long times, however, the secular growth of the a k (t) terms invalidates lowest-order perturbation theory, which requires a k ≪ a i.)
First order LTI systems are characterized by the differential equation + = where τ represents the exponential decay constant and V is a function of time t = (). The right-hand side is the forcing function f(t) describing an external driving function of time, which can be regarded as the system input, to which V(t) is the response, or system output.
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