Uses of The Wigner Function Outside Quantum Mechanics
- In the modelling of optical systems such as telescopes or fibre telecommunications devices, the Wigner function is used to bridge the gap between simple ray tracing and the full wave analysis of the system. Here p/ħ is replaced with k = |k|sinθ ≈ |k|θ in the small angle (paraxial) approximation. In this context, the Wigner function is the closest one can get to describing the system in terms of rays at position x and angle θ while still including the effects of interference. If it becomes negative at any point then simple ray-tracing will not suffice to model the system.
- In signal analysis, a time-varying electrical signal, mechanical vibration, or sound wave are represented by a Wigner function. Here, x is replaced with the time and p/ħ is replaced with the angular frequency ω = 2πf, where f is the regular frequency.
- In ultrafast optics, short laser pulses are characterized with the Wigner function using the same f and t substitutions as above. Pulse defects such as chirp (the change in frequency with time) can be visualized with the Wigner function. See Figure 4.
- In quantum optics, x and p/ħ are replaced with the X and P quadratures, the real and imaginary components of the electric field (see coherent state). The plots in Figure 1 are of quantum states of light.
Read more about this topic: Wigner Quasiprobability Distribution
Famous quotes containing the words function, quantum and/or mechanics:
“The press and politicians. A delicate relationship. Too close, and danger ensues. Too far apart and democracy itself cannot function without the essential exchange of information. Creative leaks, a discreet lunch, interchange in the Lobby, the art of the unattributable telephone call, late at night.”
—Howard Brenton (b. 1942)
“The receipt to make a speaker, and an applauded one too, is short and easy.Take of common sense quantum sufficit, add a little application to the rules and orders of the House, throw obvious thoughts in a new light, and make up the whole with a large quantity of purity, correctness, and elegancy of style.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (16941773)
“the moderate Aristotelian city
Of darning and the Eight-Fifteen, where Euclids geometry
And Newtons mechanics would account for our experience,
And the kitchen table exists because I scrub it.”
—W.H. (Wystan Hugh)