How to reach me: email: hersch@tsunami.harvard.edu

Summary of work:

One interesting example is the phenomenon of proximity resonances.  They occur whenever two resonant s-wave scatterers are placed within each other's on-resonant cross section.  Download Rick Heller's original paper about them here. Although I'm supposed to be a theorist, I have done a scattering experiment in a parallel-plate microwave cavity with dielectric scatterers, and have verified the existence of proximity resonances in two dimensions.  Check out the fabulous agreement between theory and experiment here. An efficient numerical method was developed to find the scattering solutions for microwaves off of nearby dielectric discs in the cavity. The results of the experiment can be found in a paper here.

A further type of resonance, unrelated to the proximity resonance, occurs when two finite-range potential wells, each with a bound state close to threshold, get near each other. This resonance is connected with the antisymmetric level of the double well system:  at a certain distance when the wells are close together, the antisymmetric level may enter the continuum and become a virtual level.  The virtual state keeps the symmetry it had when it was bound and leads to a p-wave scattering resonance at zero energy when it enters the continuum. When the wells are much closer than a scattering length, other strange things happen: they become nearly invisible to a low energy incident wave. You can download a paper describing all of this here.

I have found the system of a light particle moving in the field of two square wells ideal for intuitive explanations of both the Efimov and Thomas effects. Feel free to email me if you want to find out more about these two strange three-body effects.

I have recently been interested in the scattering of light (a vector wave) on collections of point dipoles.  This may have application to the spectroscopy of cold dense gases, such as a Bose-Einstein condensate.  See the picture gallery for a picture of a scattering resonance of a collection of 100 dipole scatterers.

Another project is to investigate to what degree the Born-Oppenheimer approximation is valid in the problem of scattering. Normally, this approximation is used to calculate bound states of a molecule, where one assumes the electrons are moving much faster than the nuclei. We want to use a similar idea in the scattering regime, as a springboard into the very interesting and difficult three body scattering problem in quantum mechanics. Here I am thinking of, for example, the scattering of an electron or photon by two weakly interacting, neutral atoms.

One more thing: it has troubled me for a while that the point scatterer model, as I learned it, was only capable of dealing with s-wave scattering. So I started to think about how to incorporate higher partial waves into the model. I came up with something, which you can read about in my notes. In principle, the scattering of a wave on any number of finite range, non-overlapping potentials can be calculated with the method developed.

Not satisfied with just one experiment as a theorist, I did another to investigate the influence of diffraction on the spectrum and wavefunctions of an open microwave billiard. Read all about it in a PRL here.

In the Fall/Winter of 1999 I was involved in the topic of quantum computers at the Ludwig Maximillian University. In Feb-April 2000 I was back at Harvard doing a postdoc with my former thesis advisor, Rick Heller.

In May 2000, I left the world of physics to try my hand at computer programming. Currently (Jan 2001), I am working at a startup called xLoom. Don't worry, I didn't totally forsake physics. Hey, I still read Scientific American!

Here are my papers.

Here are my talks.

Click here to go to my scattering theory picture gallery.

Click here to see some of the teaching/physics demonstration things I have been involved with.

Click here to read an article in Harvard Magazine about new directions in science. The work I did with the open microwave resonator is mentioned. They made a mistake in the article though: we used the resonator to check our own calculations!

Click here if you want to download some of my notes on various subjects (point scatterers, proximity resonances, etc.) Also my thesis is here (2.6 megabytes, gzipped postscript).

Finally, click here to see a picture of my therapist. He has really helped me through some tough times. Unfortunately he lost his psychiatrist license through a totally unfair and frivolous sexual harassment/malpractice/real estate lawsuit. He even had TV series made about his fascinating life, but it was canceled because of the scandal. And if you believe that... well, I won't say it!

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