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A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where N is the quantity and λ is a positive rate called the exponential decay constant, disintegration constant, [1] rate constant, [2] or transformation ...
In quantum many-body systems, ground states of gapped Hamiltonians have exponential decay of correlations. [3] [4] [5] In 2015, it was shown that the problem of determining the existence of a spectral gap is undecidable in two or more dimensions.
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.
It is a complex number with two pieces of information: real part is the temporal oscillation; imaginary part is the temporal, exponential decay. In certain cases the amplitude of the wave decays quickly, to follow the decay for a longer time one may plot log | ψ ( t ) | {\displaystyle \log \left|\psi (t)\right|}
This exponential decay is related to the motion of the particles, specifically to the diffusion coefficient. To fit the decay (i.e., the autocorrelation function), numerical methods are used, based on calculations of assumed distributions. If the sample is monodisperse (uniform) then the decay is
Fluorescence-lifetime imaging microscopy or FLIM is an imaging technique based on the differences in the exponential decay rate of the photon emission of a fluorophore from a sample. It can be used as an imaging technique in confocal microscopy , two-photon excitation microscopy , and multiphoton tomography.
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.
Rutherford applied the principle of a radioactive element's half-life in studies of age determination of rocks by measuring the decay period of radium to lead-206. Half-life is constant over the lifetime of an exponentially decaying quantity, and it is a characteristic unit for the exponential decay equation. The accompanying table shows the ...
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