PROVIDENCE, R.I. [Brown University] — Michael Kosterlitz freely admits it — when he first started working in condensed matter physics in the early 1970s, he wasn’t quite sure what he was doing. But then his very first paper in the field wound up answering a question that had puzzled physicists for years.

“I suppose you could take a lesson from this and say that sometimes ignorance is a good thing,” Kosterlitz said. “You don’t know the problem is insoluble, so you go ahead and do it.”

His research, co-authored with colleague David Thouless and published in 1973, drew on a branch of mathematics called topology to show how phase transitions could occur in very thin, two-dimensional materials. The work laid the groundwork for decades of subsequent research in ultra-thin materials and exotic phases of matter. In the past decade, the Kosterlitz-Thouless theory has informed the development of materials that could be helpful in making next-generation electronic devices and quantum computers.

Today — Saturday, Dec. 10 — Kosterlitz received an honor he had never envisioned when he embarked on this research more than 40 years ago. With his wife, two daughters and son in a crowd of luminaries from all over the world, Kosterlitz stood on the stage at the Stockholm Concert Hall as King Carl XVI Gustaf of Sweden handed him his diploma and gold medal as winner of the 2016 Nobel Prize in Physics. He shares the award with Thouless and Duncan Haldane.

"Not only have this year's Laureates made important special discoveries, but in addition — and perhaps most importantly — they have set the stage for a new way of describing matter," said Thors Hans Hansson, member of the Nobel Committee for physics, in his introduction of Kosterlitz, Thouless and Haldane. Their theory, he added, "combines truth with beauty. This is theoretical physics at its best."

The humble theorist

His colleagues in the Brown Physics Department, where Kosterlitz has worked since 1982, describe him as not only a brilliant theorist with a deep love of physics, but also as a kind, caring and humble man who has never been one to seek the limelight. Instead, the limelight sought him — beginning with a surprise phone call from the Nobel committee on Oct. 4, when the Royal Swedish Academy of Sciences announced the prize.

Kosterlitz responded to the news in his typically understated fashion.

“I’m quite pleased about the whole thing,” he said at a news conference following the October announcement.

“At the moment I feel like I’m in some alternate universe, where reality has taken a long vacation,” he added. “But everything seems to be real, so I guess I will have to assume that it is and proceed accordingly.”

Kosterlitz was born in Aberdeen, Scotland, in 1943. His father, Hans Kosterlitz, who was Jewish, fled Germany in 1934 during the rise of the Nazis. The elder Kosterlitz had dreamed of becoming a theoretical physicist, but his father refused to pay for his studies if he went into physics. So Hans Kosterlitz went into medicine. After traveling to the U.K., he established himself as a prominent researcher in brain physiology. He’s credited as one of the discoverers of endorphins and enkephalins, brain chemicals that modulate the body’s response to pain.

“I got very interested in science because of him,” Michael Kosterlitz said, “but I decided that it’s not a good idea to go into medicine. I could see people saying something like: ‘Young Kosterlitz is quite good, but he’s not a patch on his old man.’ I thought I’d better not go into competition with my father.”

So the younger Kosterlitz chose physics instead, fulfilling his father’s own dream. After earning his Ph.D. from Oxford University in 1969, Michael Kosterlitz took a job as a postdoctoral research at Torino University in Italy.

It was during his time at Torino that a bit of a blunder put Kosterlitz on a path that would eventually lead to the Nobel Prize. He had been studying high-energy physics, a branch dealing with elementary particles and forces that govern their behavior. The top destination in Europe for a young high-energy physicist was CERN — the European Organization for Nuclear Research — and that’s where he wanted to be.

But Kosterlitz, who admits to being a bit disorganized at times, flubbed the opportunity. “As is my wont, I failed to get my paperwork in on time,” he said. “So I couldn’t go.”

The mistake left him scrambling for a job, which he eventually found at the University of Birmingham in the U.K. He was deeply disappointed to have missed his shot at CERN, “but you could say the rest is history because that’s where I met David Thouless,” Kosterlitz said.

That meeting came at a time when Kosterlitz was increasingly frustrated with his high-energy work.

“I had been doing long tedious calculations for very little return, and I was getting a bit fed up,” he said. “So I started walking from office to office asking if anybody had a tractable problem I could work on. I found myself in David Thouless’s office where he was telling me all about superfluid helium films, crystals, dislocations, vortices — all concepts that were completely new to me. But somehow what he was saying made sense. So I started working on some of the ideas he was throwing out, and basically things worked out.”

Groundbreaking theory

Phase transitions in bulk materials — like a block of ice melting to water, or water evaporating to a gas — were fairly well understood. But how phase transitions could work in two dimensions was a mystery. In fact, Kosterlitz says, there were rigorous theorems that suggested these transitions shouldn’t happen at all.

Those theorems stated that two-dimension systems had no long-range order. Lacking order, a phase change that affected the whole of a two-dimensional system would be impossible. However, there were experiments that suggested otherwise. Experimentalists had shown that below a certain critical temperature, thin films of helium underwent a phase transition to a superfluid, a state in which it flows without friction.

“Those experiments were staring us in the face,” Kosterlitz said. “We said there must be a definite phase transition here, which is outside the rigorous theorem.”

Kosterlitz and Thouless showed that while two-dimensional systems did lack the kind of long-range order dictated by the theorem, they had a different kind of order enforced by the arrangement of tiny vortices that form within a system. In a liquid system, these vortices are like the swirls that form when water goes down a bathtub drain. But analogous structures could form in solid systems, in the arrangement of electron spins.

At very low temperature, each vortex circulating one way is coupled in an orderly fashion with an anti-vortex circulating in the opposite way. The tight coupling of vortices and anti-vortices gives the system a long-range “quasi-order.” But if the temperature of the system were to rise past a critical point, the vortices and anti-vortices would decouple and drift apart, disrupting the quasi-order of the system. The phenomenon became known as the Kosterlitz-Thouless transition.

The understanding of how phase changes happen in two dimensions has led to an avalanche of new research of different matter states in ultra-thin materials. These kinds of materials could revolutionize electronics and computing in the coming years.

Happy colleagues

It took the Nobel committee more than 40 years to finally recognize the work done by Kosterlitz and Thouless.

“It was really long overdue,” said Vesna Mitrović, one of Kosterlitz’s colleagues in the Brown Physics Department. “I think the paper was so ahead of its time, and that’s why it took so long to be appreciated. On a personal level, I could not imagine having anyone better get the Nobel Prize. He’s just a wonderful colleague, smart and very humble.”

Kosterlitz joins Leon Cooper, who won the Nobel in physics in 1972, as the second Nobel Laureate currently on the University’s physics faculty. Cooper won for his theory explaining the nature of superconductivity.

“It takes some of the pressure off me,” Cooper joked.

“I’m absolutely delighted,” he added. “He really deserves it. He’s a terrifically nice guy and very unassuming.”

Mitrović said the fact that there are two Nobel Laureates on the faculty speaks volumes about the quality of Brown’s Physics Department.

“One Nobel Prize, you could say it’s a statistical error maybe, but two Nobel Prizes... it’s amazing,” she said, echoing a joke that's been floating around the department. “We all dream about working in an environment like this. It’s really great to have people like that next to you that you can discuss and talk about physics.”

Jim Valles, another Brown physicist, relishes the chance to work side-by-side with a man whose work inspired him at a formative period in his career, when he first started graduate school.

“I walked into this lab where there was a student who was three years ahead of me... and he was working on experiments to test the Kosterlitz-Thouless theory of phase transitions,” Valles said. “I watched them trying to fit the data and get all the wrinkles out of the experiment, and it was fitting. Everybody was talking about the K-T theory, and I just wanted more of that as I went through my graduate career.”

Now at Brown, Valles works on superconductivity in two-dimensional materials, an area in which the Kosterlitz-Thouless transition is important. Valles and Kosterlitz talk often about how the theory applies to these exotic systems.

“We’re doing some work currently where we’re citing Mike again and one of his former Ph.D. students,” Valles said. “The theory seems to fit our data pretty well, and we’re very excited about it.”

It's been just as exciting for students. Evan Coleman, a junior studying mathematical physics, said he was learning about the Kosterlitz-Thouless transition in one of his classes when the prize was announced.

"I ran down to my friend's room in the same dorm and woke him up and we had a bit of a celebration," Coleman said. "Then we went to class and had a lecture on the material. I think these coincidences are the privilege of coming to Brown and being at a place where so many things are happening that are at the cutting edge."

Adjusting to the limelight

While Kosterlitz says he’s appreciative of the attention that comes with the Nobel, it’s all been a bit much for the quiet theorist. The life of the man who helped explain the physics of phase changes has undergone a phase change of its own.

“Life has become a bit of a circus,” he said.

One of the first messages of congratulations Kosterlitz received came from another Nobel Laureate, who tried to prepare him for what’s to come. “His final sentence was, ‘Life as you know it is now over,’” Kosterlitz said. “That sentence is certainly true.”

Since the prize announcement in October, Kosterlitz says he’s been inundated with requests for lectures, public appearances and interviews with the press. Before the Nobel festivities began officially this past week in Sweden, Kosterlitz was feted by the Swedish Embassy in Washington, D.C., and met with President Obama in the Oval Office.

Kosterlitz concedes that his organizational skills haven’t improved much since he flubbed his application to CERN, so his wife, Berit, has been managing his schedule, and she’s been by his side throughout.

For her, the trip to Stockholm for the Nobel event was a homecoming. She was born there and was thrilled to be returning home to celebrate with the whole Kosterlitz family. Their daughters, Karin and Elisabeth, and their son, Jonathan, all made the trip Stockholm.

“I will enjoy being back in Sweden,” Berit Kosterlitz said in an interview prior to Nobel Week, “especially because it’s close to Christmas time and it’s magical.”

Cooper, who has firsthand experience in navigating the Nobel Week festivities, encouraged Kosterlitz to relax and take it all in. The week is packed full of lectures, news conferences, banquets and dinners with the King of Sweden and government officials. It all culminates today — on Saturday, Dec. 10. The new Laureates received their Nobel medals earlier, with the Nobel Prize Banquet following at Stockholm City Hall.

“It’s incredible because the whole country participates,” Cooper said. “That’s one of the things that makes it so special. It’s not something that’s hidden in a dark room.”

But Kosterlitz says he’ll be just as happy when all the hoopla subsides.

“I still have the odd problem I’d like to look at,” he said. “There’s no way I can do anything like that now — not until all this hype and excitement is over. I need time to sit and think again.”

Lately, he’s thinking about problems in nonequilibrium physics.

“If you drive a system out of equilibrium and you keep the driving force absolutely fixed, many systems are known to go into some stationary state,” Kosterlitz said. He’s trying to develop a theory of how those dynamics work.

“I’ve been working on that… for a few years,” he said. “To tell the truth, I’m beginning to think that my hypothesis is wrong. Maybe it is and maybe it’s not. I’m not sure.”

That uncertainty is inherent in exploring the unknown. Four decades ago, when Kosterlitz started investigating the idea of phase changes, he had no idea where it might lead. As it turns out, it led to Stockholm, and the highest honor in physics.