The sound of quantum drums

Nanoscale drums provide insight into math, quantum physics and microelectronics

Forty years ago, mathematician Mark Kac asked the theoretical question, "Can one hear the shape of a drum?"

If drums of different shapes always produce their own unique sound spectrum, then it should be possible to identify the shape of a specific drum merely by studying its spectrum, thus "hearing" the drum's shape (a procedure analogous to spectroscopy, the way scientists detect the composition of a faraway star by studying its light spectrum).

But what if two drums of different shapes could emit exactly the same sound? If so, it would be impossible to work backward from the spectrum and uniquely surmise the physical structure of the drum, because there would be more than one correct answer to the question.

It took until the 1990s for mathematicians to prove that, in fact, two drums of different shapes could produce the same sound. In other words, you can't hear the shape of a drum. That outcome, which was physically verified in one instance with vibrations on the surface of soap bubbles, raised theoretical questions about spectroscopy. READ THE FULL ARTICLE http://nanotechnologytoday.blogspot.com/2008/02/stanford-researchers-hear-sou...

Category:

Science & Technology

Tags:

• nanotechnology
• quantum
• drums
• math
• physics
• microelectronics
• nanostructures

[cochinorrea]

any ways, on your case you have the different shapes sharing the same set of egien values (energies). but i was wondering in what extend the properties of the different shapes are identically? Nice work by the way

[cochinorrea]

Hi, you guys mentioned two drums (classical wave equation) that have the same sound..... thats not tottaly true.... yes yes i know that mark cak in 1966 talked about it and then in 1992 gordon and webber (i don know if i spell that right) show 2 different shapes (drums) with the same set of eigen values (for the laplasian operator). but thats not enought to assure that the two drums will have the same sound because the intensity of the eigen states is different even for the same initial condit,,

[looonger]

very cool!

[dogyoda]

pretty cool!