Following my recent work on stochastic processes and quantum mechanics (see here and here), after I showed its existence with numerical computation (see here), this time I moved one step forward with an experimental setup. The idea come out from my son Giorgio. He is a teen with a lot of ideas and was of real help to assemble all the apparatus.

In order to try to see how my mathematics for stochastic processes could be applied to a real stochastic motion I needed a natural source to start with. The best and easier to manage of this is Johnson-Nyquist thermal noise in a resistance. This effect is really small being of the order of nV and so we were in need for some significant instrumentation. To buy it was impossible as this is generally very highly priced and not affordable for amateur efforts. There is some hope from ebay to find some old apparatus but one is not granted to have it in fully order and, in any case, this should come from US and so one have to incur in a lot of problems, not least time to deliver, that make us desist. The next step was to find in the known literature a possible circuit for a very low noise and high gain preamaplier that we could realize just buying components. Looking around with google I have found this paper by Graziella Scandurra, Gianluca Cannatà, and Carmine Ciofi of University of Messina in Italy. I wrote to Dr. Scandurra to ask some clarifications and she was so kind to pointing me out toward another circuit that fitted better my needs, similar to the one I have found, published in this paper. The circuit given by the same authors in the latter is used in the former but in a differential topology. For my aims, a differential preamplifier was not needed and so I followed the advice by Dr. Scandurra and opted for the simplest circuital solution. Unfortunately, this circuit used a IF3602 by Interfet. This is a dual N-channel jfet in a single package having a very low noise figure and high gain. This component is practically impossible to find and the only way to get is to order it through some reseller with a large number of items at a high price. Not the best for me. So, I was in need for a substitute. A colleague of mine, Massimiliano Rossi (former researcher at Tor Vergata University in Rome) pointed me out the Toshiba jfet 2SK170BL normally used in audio applications. Looking at the datasheet this appears well suited to substitute the IF3602 but this comes singly packaged. I solved this issue by buying a matched quad on ebay and using a pair of them.

Last week-end, with the help of my son, I have built the circuit as given in the paper and provided the given substitution. This was the result with the circuit perfectly working

and here with the output given an input signal from a BF generator

As you can see it is up and running. This circuit, as designed by the researchers of University of Messina, proved to be robust and reliable. So, here is my first measurement using as a device under test a potentiometer with a maximum of 1 MOhm:

and this is the final proof that this is indeed Johnson noise

giving the experimental proof of existence for the square root of a stochastic process.

As a final aside, I give here the circuit of the preamplifier with the list of components for those aiming to realize it:

and

As said above, you can substitute the IF3602 with a matched pair of 2SK170BL by Toshiba at very low cost.

So, we can conclude that the square root of a stochastic process, as given in my paper, exists and is meaningful both numerically and experimentally.

Marco Frasca (2012). Quantum mechanics is the square root of a stochastic process arXiv arXiv: 1201.5091v2

Scandurra, G., Cannatà, G., & Ciofi, C. (2011). Differential ultra low noise amplifier for low frequency noise measurements AIP Advances, 1 (2) DOI: 10.1063/1.3605716

Cannatà, G., Scandurra, G., & Ciofi, C. (2009). An ultralow noise preamplifier for low frequency noise measurements Review of Scientific Instruments, 80 (11) DOI: 10.1063/1.3258197

Marco, how do you finance your researches? Are you employed somewhere?

Dear Vladimir,

this was done with my money for my son that have had the idea. Yes, I am regularly employed.

Cheers,

Marco

[…] got its square root (see here) that proved to be in agreement with my theoretical expectations (see here). We built up the main instrument, the low-noise high-gain amplifier but my aim has always been to […]

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