Sunday, February 26, 2012

Extreme Physics

In our culture, the word "extreme" has taken on a new meaning because of its use in naming new sports that are dangerous. By "extreme physics," I mean the physics of a phenomena when one of its defining parameters is at an extrema; that is, a minimum, maximum, or point of inflection. Mathematically, an extrema of a function is defined as the point were the first derivative is zero. In many ways, extreme physics can be just as exciting as extreme sports.

It interesting to me that the underpinnings of physics are based on extremes. Surely I am not unique in thinking this way; but, I am excited by the topic because one of my projects is based on the theme of using the limits of the nonlinear-optical response to discover new things about light-matter interactions that in the end may lead to a deeper understanding.

As we have been digging deeper and deeper, new patterns are emerging. This regularity, however, is only observed at the extremes of the nonlinear-optical response. Given how all of known physics manifests itself by an extrema, it is pretty exciting to think that we may be on the verge of discovering truly new physics.

There are other projects that are going well and have potentially very exciting ramifications. For example, we are in the process of fine-tuning a new model of the self-healing process. But this is not just a model in the form of an equation that we use to fit our our data (which we are indeed doing), but the parameters represent new phenomena. If the model fits, we are potentially looking at new theory that may be generally applicable to many things. The more general the applicability of our work, the happier my mood.

I end here by lifting an excerpt from a review article we are writing for Physics Reports. It is a more detailed description of what I have written above.

The extremes of physics are characterized by unique behavior. For example, the second law of thermodynamics states that entropy cannot decrease in a closed system. The special case when entropy change is minimized (i.e. it remains unchanged) defines reversible thermodynamic processes. The maximum efficiency of a heat engine requires a reversible process. Calculations of reversible heat engine efficiencies led to the definition of entropy. While motivated by practical applications, entropy has become one of the most important fundamental concepts in physics.

Quantum mechanics is based on the fact that certain quantities cannot be simultaneously measured to arbitrary precision. To accommodate this observation, variables such as momentum and position are generalized to become operators that do not commute. The mathematical formalism naturally leads to the uncertainty principle, which states that there is a lower bound to the product of the position and momentum uncertainties. The fact that uncertainties are constrained by a lower bound is the basis of quantum mechanics, which describes a vast richness of new phenomena that is inexplicable using classical mechanics.

The principal of energy conservation originates from the more general concept of a Hamiltonian, which yields the equations of motion through a process of finding the extrema of the action. These ideas carry over into the quantum realm in the formulation of path integrals, which bring out the wave nature of matter. The absolute maximum speed limit defined by the speed of light, on the other, leads to non-absolute time, where observers in different coordinate systems view the same phenomena but from the perspective of a rotation in four-dimensional space-time. The marriage of relativity with quantum mechanics as embodied by the Dirac equation led to a natural way of accounting for the electron spin, and as a bonus unexpectedly predicted the existence of antimatter.

Clearly, the extremes are fertile soil from which the most fundamental concepts in physics grow. As we later show, the fact there there is a fundamental limit to the nonlinear-optical response of a quantum system defines an extreme that is characterized by several features. For example, while many states of a quantum system contribute to the nonlinear-optical response, at the upper bound only three states are found to contribute. This was originally postulated as a hypothesis and later confirmed to be true for many quantum systems, though it has not yet been rigorously proven. As such, it is referred to as the three-level ansatz.

We will show that systems with a nonlinear response near the fundamental limit share other properties. Why this is true is not yet understood; but, the fact that certain universal properties appear to be associated with the extremes of the nonlinear response hints at fundamental causes, perhaps grounded in new physics, which become apparent only under scaling rules that follow naturally from these limits.

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