As the study of physics becomes increasingly specialised, the profession risks being divided into an endless series of subfields. Russian-born Vladimir Kravtsov calls on the physics community to rededicate itself to the study of broad issues to avoid intellectual fragmentation.

Connected Clusters

In physics, disorder is often a state of mind. The reality is that physical systems are in perfect harmony. It's our limited knowledge that prevents us from seeing the true elegance of a system's structure and behaviour. In fact, the primary task of physicists is to discover the order that exists under the veil of disorder.

In the physics of disordered systems, researchers have developed the concept of 'connected clusters'--parts of systems that are linked together to enable the continual transfer of mass, charge and energy.

Think of an endless sea where the only recognisable point of reference is the horizon. Now think of a sea dotted with islands. The larger and more numerous the islands, the more likely you are to be able to navigate the sea. Now think of the islands being connected by bridges. Navigation can take place continuously without being hampered by the unpredictability of weather. In brief, bridges not only shorten the journey but alter the means of travel in ways that fundamentally change the islands' relationship to one another.

The latter transformation is what comes to my mind each time I think about physics as a whole, a profession to which I have devoted many years of study. I am convinced that physics can progress only when it enjoys an environment marked by many islands connected by many bridges. Such connected clusters of intellect, tied together by research and education, offer endless opportunities for the transfer of data, ideas and insights.

Today, my profession, I am sorry to say, is heading in the opposite direction: decomposing connected clusters into small, isolated islands of research and study. The major force behind this process is the increasing complexity of physics itself, which requires physicists to study narrower and narrower subject areas to gain deeper and deeper understanding.

As a result of such trends, some members of the physics community believe that it has become impossible to explore physics as a whole. What does the field of optics have to do with the study of disordered solids? And how can a better understanding of both enhance our understanding of computational algorithms? These fields seem completely disconnected. Right? Below I will try to convince you that such a notion is wrong.

Let us consider the development of mesoscopics--a branch of condensed matter physics that surfaced about 15 years ago. Before then, condensed matter physicists believed that to predict the behaviour of a large disordered system, it sufficed to examine the average behaviour of many analogous disordered systems. Researchers refer to this as the law of self-averaging, a fundamental principle of physics for more than a century.

For this law to work, the subsets of the system must operate as independent entities. Conversely, when the subsets are correlated (that is, not independent but related to one another), the law of self-averaging fails, and fluctuations between the average and specific become significant. That's exactly what happens to impure metals at low temperatures.

According to quantum mechanics, in the absence of interaction, electrons in metals behave like light waves and will follow a self-replicating pattern forever. Such behaviour allows us to predict the amplitude of the wave at one point if we know the amplitude of the wave at another point. In short, it means that the electron waves within the metals are correlated or coherent.

This coherence collapses when the temperature rises above absolute zero due to the interaction of the electrons. However, if the temperature is low and the sample size is small enough, the coherence is preserved over the whole sample.

Here we enter the fascinating world of mesoscopic physics in which a system's physical quantities may visibly fluctuate from sample to sample. Such mesoscopic fluctuations, which defy the law of self-averaging, were so surprising that it took about 3 years for most condensed matter physicists to be convinced that the perceived phenomenon was neither a theoretical miscalculation nor experimental mistake.

Yet, a similar phenomenon had been known in optics for decades. So-called 'speckles'--bright dark spots--can be observed when coherent monochromatic light passes through a scattering medium (such as milky glass) that possesses many scattering points. Although the positions of the speckles are random, they do not change over time. In fact, the positions can be changed only by altering the frequency of light or shifting the scattering medium.

The origins of both speckles and mesoscopic fluctuations in electronic systems are one and the same. Both are created by interferences in the coherent waves. Only when this connection was understood, however, did the new field of mesoscopic physics become widely accepted.

Such an example shows that 'understanding' physical phenomena largely involves establishing connections between different subfields of knowledge--in this case, between condensed matter physics and optical physics. These intricate ties can only take place in an intellectual environment that nurtures the development of connected clusters through research and educational systems designed to encourage and reward a broad understanding of physics.

But the story does not end here. New ideas and methods developed in condensed matter physics have prompted advances in the optics of disordered media, which involve the search for the localisation of light and the restoration of images using statistical methods. By applying these methods it's possible to see through such strongly scattering media as 'milky glass' or human tissue.

Here we have an example of the relationship between fundamental and applied science. Abstract knowledge dealing with self-averaging leads to knowledge pertaining to mesoscopic fluctuations in condensed matter and analogous insights in optics of disordered media. It turns out that these insights could prove useful in screening cancerous tumours in humans, which would make applied science a by-product of fundamental science.

Connections like these again illustrate that we should not bother fundamental scientists with such questions as "How will your research improve our lives?" Researchers never know. Let them follow their instincts. That's the best way to achieve breakthroughs that may ultimately improve our lives.

Here's another example of a story with the same conclusion. In mesoscopic physics, the dephasing of the electron wave function limits the phase coherence length and thus sets the upper boundary for sizes of mesoscopic systems. The existence of mesoscopics is based on the fact that dephasing is effectively switched off at very low temperatures. That is why mesoscopic phenomena can happen only at temperatures as low as 0.01-0.1 degrees Kelvin and for samples of micrometer size.

During 15 years of development, mesoscopic physicists have acquired a lot of 'know-how' in dealing with very low temperatures and very small samples. In the process, they have gained vast knowledge of the fundamentals of dephasing in different systems. Your response may be: So what? Haven't these efforts been a waste of money and talent?

The answer is no. Several years ago, computer scientists launched an effort to build a 'quantum computer' relying on quantum interference instead of classical 0-1 bit sequences. If realised, this effort could revolutionise computational physics because tasks requiring exponentially long computation time with conventional 0-1 bit sequences would require much less time with quantum algorithms.

A critical aspect of success in this effort depends on the ability to preserve quantum phase coherence for sufficient periods. Such knowledge will also be crucial for the creation of small but macroscopic (and thus technological) quantum devices. That's where 'abstract experience' earned in the field of mesoscopic physics can be put to work for improving our lives. Yet it's important to keep in mind that a physicist's understanding of such abstractions is derived largely from an ability to place his or her research into the larger intellectual currents within the discipline.

Examples like these illustrate how misguided it is for physicists to box themselves into narrow research fields. All physicists belong to the larger physics community and all should seek to transfer ideas from their own subfields to others as integral parts of their work. This requires a broad understanding of the basic fields of physics and an ability to generalise results. Such integration is the only way to overcome the intellectual fragmentation that now threatens the future of physics.

Vladimir Kravtsov
ICTP Condensed Matter Group

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