A smooth decline in signal intensity over time, characteristic of many dissipative quantum processes.Exponential decay describes a process where a quantity decreases at a rate proportional to its current value, producing a characteristic curve that drops quickly at first and then tails off gradually. In physics, it appears in radioactive decay, the damping of oscillations, and the loss of coherence in quantum systems. The concept is fundamental because it provides a simple mathematical model for many dissipative processes, where the 'memory' of the initial state fades over a characteristic timescale.
The concept was formalized in the 17th century, but its application to radioactive decay was established by Ernest Rutherford and Frederick Soddy in 1902, who showed that the rate of decay is proportional to the number of atoms present.
Mathematically, exponential decay follows the equation N(t) = N₀ e^(-t/τ), where τ is the time constant. The key property is that the quantity decreases by the same fraction in each equal time interval — for example, half of the remaining amount decays every half-life. This arises when the rate of decay is directly proportional to the amount present, which happens in many physical systems where each particle or excitation decays independently with a constant probability per unit time.
Exponential decay is used in radiocarbon dating, in modeling the discharge of capacitors in electronics, and in medical imaging where radioactive tracers decay exponentially to produce signals.
In quantum mechanics, exponential decay is not strictly universal — certain systems can exhibit deviations, such as the 'quantum Zeno effect' where frequent measurements can slow down or even halt the decay.
