Complex optimization problems are part of basically every aspect of our world. For example, making the most efficient public transport schedule or finding the best route for parcel deliveries can be very challenging. The complexity of similar issues are often illustrated with the ‘Traveling Salesman’: a salesman that is planning to visit a number of cities by using the shortest route possible faces an unexpected challenge. When the number of cities is small, this task is relatively easy, but the complexity increases dramatically when more and more cities are included in the salesman’s trip. For example, when visiting just 10 cities, almost 400.000 possible tours are possible. When more cities are to be visited, a normal computer can easily be busy for days or even years to calculate all these routes and select the shortest one.
Spin glass problem
The optimization problem of the Traveling Salesman is mathematically very similar to many scientific questions, for example, in the so-called Spin glass problem in physics. A spin glass can be seen as a material, containing many tiny magnets that each act as a compass needle pointing North. But besides the magnetic field of the earth, they are influenced by each other as well, while also other external factors, like temperature, may influence their direction continuously. As a result, their compass needles basically move all the time and point randomly to all directions. It is very complicated to find out at which direction the small magnets should point to achieve their optimum and best configuration: this is what physicists call ‘The Spin glass problem.’
However, if these moving magnets are cooled down to absolute zero, i.e. -273 degrees Celsius or zero Kelvin, their random movements stop, and they are arranged in a seemingly chaotic way, like the messy structure of glass. ‘This arrangement is the most stable, preferred configuration of the magnets,’ Klärs explains. ‘Mathematically, it is similar to the optimal route of the Traveling Salesman.’
So, if scientists measure this arrangement at zero Kelvin, they have found the solution to the spin glass problem. By mathematically describing and analyzing the structure of this optimal solution in a spin glass, scientists can apply these formulas to many other problems, including the one of the Travelling Salesman. But applications can also be found in chemistry, biologically, computer science and everyday issues in logistics. So, studying or experimenting with spin glass problems may provide mathematical tools to analyze some interesting and hard to solve real-world problems.
More efficient and effective
To study the spin glass problem, scientists usually build magnets, that are subsequently cooled down. The optimal orientation of the tiny magnets at zero Kelvin is studied by measuring the orientation of their magnetic field. But Klärs wants to perform this research in a more efficient and effective way: he plans to build an optical computer system that replaces the traditional magnets to study the spin glass problem in a different way.
‘We are designing a computer where several dozens of tiny lasers replace the tiny magnets present in a spin glass,’ he explains. ‘The lasers behave similarly to the tiny magnets: we can measure their ideal ‘orientation’, similar to measuring the direction of the magnetic field of the small magnets in the cooled down spin glass. In addition, this optimal orientation is influenced by other lasers, when they exchange little bits of light, similar to magnets influencing each other with their individual magnetic fields.’ If the experiments go well and the system can be controlled and manipulated, the scientist aims to increase the number of lasers to several thousands. The advantage of Klärs’ new design is its speed: cooling down a spin glass magnet until it reaches its optimum orientation takes seconds, while lasers respond orders of magnitude faster. In addition, it is a more effective procedure, with less practical problems.
Although the spin glass studies may seem very theoretical and mainly a toy for smart physicians and mathematicians, it is much more than that. In many situations there is a big need to find the best solution to a complicated problem. Mathematical formulas, derived from spin glass research, may provide these solutions to not only daily life problems, but also to optimize industrial processes.
‘It may clarify the biological patterns that often exist in nature’
In addition, these algorithms may help explaining observations in other scientific fields. For example, it may clarify the biological patterns that often exist in nature, like the orderly structure of tissues or the stripe pattern in zebras. Even the regularly spaced ripples formed in sand can be better understood and explained using the knowledge and mathematical description of the spin glass problem. Therefore, in a later stage of his research, Klärs aims to use his mathematical formulas derived from his complicated laser studies to explain and understand a variety of problems in other scientific fields as well as in real practical life.
It is clear that this fundamental research serves a lot more than a few dedicated scientists. Spin glass research boosts the development of new mathematical techniques and algorithms that can be applied to many other scientific as well as real-life questions. Therefore, it may dramatically increase our understanding of the natural world around us and improve the efficiency of many aspects of our daily life.