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How a theoretical physicist’s passionate approach to simple math got him the Padma Bhushan

First Indian to get Boltzmann Medal, Dhar equated his approach to statistical mechanics to art & said it is wrong to 'propagate idea that everyone should do only applied work'.

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New Delhi: As a college student, Deepak Dhar enjoyed solving simple math problems he stumbled upon in magazines. Years later, he would go on to become one of India’s foremost theoretical physicists, making waves in the field of statistical mechanics. 

In an interview with ThePrint, Dhar (71) — whose contribution to theoretical physics brought him many laurels, including the Padma Bhushan this year — says, “Many problems in mathematics have been stated in the form of simple puzzles. But when you go on to solve them, sometimes the solutions mark the beginning of solving deeper problems.” 

“You don’t know what relevance such solutions may have at the beginning of the journey,” he says. Adding, “We take the name of Ramanujan and cite him as one of the greatest mathematicians, but his work was not immediately applicable at that time. Even now, there are very few direct technological applications of his work.”

Last year, Dhar became the first-ever Indian scientist to be chosen for the Boltzmann Medal, one of the highest international recognitions in statistical physics awarded once every three years.

In 2002, he was awarded the TWAS (The World Academy of Sciences) prize — conferred on scientists from developing countries for outstanding contribution to scientific knowledge. He is also a recipient of the 1991 Shanti Swarup Bhatnagar Prize for Science and Technology — one of the highest Indian science awards — for his contributions to physical sciences.

At present, he is a distinguished professor at the department of physics of Indian Institute of Science Education and Research (IISER), Pune.

For Dhar, his journey into statistical mechanics began with his work on recreational mathematical problems that would be published in the Sunday supplement pages of magazines. Dhar says solving the puzzles taught him new mathematical techniques, and led him to the answers of a number of complex mathematical questions.

His research revolves around understanding how macroscopic properties emerge from a large collection of simpler objects. For example, how a simple rule that a few sand particles topple when piled together, determines what happens in a large pile of sand. These simple models are templates to understand how complex properties appear in everyday objects.

Dhar explains it thus, “Suppose some dry sand is poured on a flat table slowly. We know that it will form a conical shaped pile on the table. Now, if you drop another grain of sand on it, sometimes the grain will just sit on one point. Other times, it will slip down, and knock off other particles and cause a mini avalanche. 

“If you keep dropping one grain of sand at a time, sometimes nothing will happen, while other times grains will slip down in bursts.”

This is a simple example of a system in which a steady perturbation is added from outside, but the release or relaxation happens in jerky bursts,” he adds.

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‘TIFR school of statistical physics’

While his research often deals with abstract mathematical concepts, Dhar has been widely recognised for his rare ability to break down complex concepts in very simple terms.

Srikanth Sastry, a theoretical physicist at the Jawaharlal Nehru Centre for Advanced Scientific Research in Bengaluru, tells ThePrint, “Dhar is well-known for developing ingenious ways to obtain exact solutions in a number of problems in statistical physics.”

“He is also well-known for training and influencing a large number of students and colleagues in pursuing this style of theoretical statistical physics. He and Professor Mustansir Barma are credited with bringing into being and nurturing a ‘TIFR school of statistical physics’, in the sense of an informal group of people pursuing a certain style of research,” he adds.

Sastry says that this was not a conscious effort but something that emerged from the environment of excellence that prevailed as a result of Dhar’s high-quality research.

Spenta Wadia, a theoretical physicist who set up the International Centre for Theoretical Sciences at Mumbai’s Tata Institute of Fundamental Research (TIFR), tells ThePrint, “The solution of the sandpile model set the paradigm for the explanation of many natural phenomena like the magnitudes of earthquakes and frequency of aftershocks, fluctuations in the financial market, and forest fires etc.”

The sandpile model was introduced by three physicists, namely Per Bak, Chao Tang and Kurt Wiesenfeld in a 1987 paper. It was eventually solved by Dhar three years later.

Dhar showed that the sequence in which the sand grains were placed on a pile did not matter. After an avalanche stopped, the final result was the same. For instance, if two sand grains are added to a stable pile in two different orders, first at site A and then at site B, the final pile of sand grains turns out to be exactly the same.   

“The model had a very interesting solution. And was connected to other problems in statistical mechanics,” says Dhar. 

Another mathematical problem Dhar has been credited with solving is the ‘directed site animals enumeration problem’. Let us say there is a two-dimensional lattice, like a square chess board. The board has a rule on how the chess pieces can be set: if one piece is put down, the next piece can only be placed in two other adjacent boxes. 

In such a set up, how many different shapes can one generate with a finite number of pieces? Dhar was the one to derive the solution to this problem.

A mathematical solution to such problems can also be used to understand the structure of molecules. As Dhar puts it, “If there is a solution of potassium and sodium chloride and that undergoes crystallisation, at what concentration will the atoms of sodium and potassium occur?”

‘His desk would self-organise into a state of chaos’

Dhar’s colleague Sreejith G.J., associate professor of physics at IISER, tells ThePrint, “One thing that describes Professor Dhar is that he is very sharp. Sometimes I discuss aspects of my work with him. He is able to understand what I want to know even before I finish posing my questions. It is as if by the time you finish asking your question, he already knows where the problem is, and can often promptly point me in the right direction.”

Wadia, who worked with Dhar for nearly thirty years, quipped that his colleague’s desk was always a mess. “Only he would know where to find which paper. Once in a while, his wife would come in and organise the desk, but soon the desk would ‘self-organise’ into a state of chaos.”

Adding that Dhar had a sense of precisely articulating his thoughts, Wadia says, “Even while giving grades, Dhar had a system of giving grades with decimal digits. He wouldn’t just give a grade 8 for example, he’d give an 8.2 or an 8.53.”

He also points out that Dhar’s teaching style produced outstanding students, some of who are now a part of the ICTS (International Centre for Theoretical Sciences in Bengaluru). His students have turned out to be some of the best known researchers in the field of theoretical physics, who are globally recognised for their work, says Wadia.

Meanwhile, Dhar says the central government is currently giving “higher priority to applied research”, adding that the “funds for theoretical research are more difficult to get”. While emphasising the importance of applied work, he cautions that it is “wrong” to propagate the idea that “everyone should only do applied work”.

He also remarks that top researchers are asked about the relevance of theoretical research all the time. “Even Michael Faraday was asked this question when he was studying the flow of current through complicated circuits and wires,” he says. Dhar explains that back then, it was just some strange phenomena that Faraday seemed to be chasing, but his research became relevant with time as power grids became more complex. 

“I think much of the new ideas in research start out with these kinds of setups, but these ideas can grow and be used in various fields. I think one should have a healthy mix of relevant and not-so-relevant research,” he says. Equating his approach to the discipline to art, he adds, “An accounting-minded person may question the use of paintings, but a wider set of people understand that paintings can be useful in a bigger set of contexts.”

(Edited by Amrtansh Arora)

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