Why is the dynamic changing
Erratic dynamics in the quantum world
Research Report 2018 - Max Planck Institute for the Physics of Complex Systems
Physical systems show amazing cooperative properties that result from the joint interaction of many particles. These include, for example, the loss-free flow of current in a superconductor or magnetic materials that can arise from the interaction between electrons at low temperatures. The general understanding of such phases is based on the fact that these systems are in equilibrium, a balanced state in which the system no longer changes over time. In recent years a novel architecture of experiments has opened the door to a new area of research. So-called quantum simulators now allow insights into quantum physics beyond equilibrium, which were previously not possible. In this way, for example, the purely quantum mechanical time evolution of many-particle systems can be experimentally realized and measured to a previously unthinkable extent. However, the fundamental question arises of how matter can be characterized in such states and, in particular, how general principles can be understood and worked out.
Collapse of a quantum magnet
In the following, let us consider a paradigmatic example of a quantum magnet for many-particle physics and disturb it in such a way that its strength - measured by the magnetization - is reduced. If you suddenly impose this disturbance on the magnet, you force it out of balance. Because the magnet cannot immediately adapt to the changed framework conditions. Instead, its magnetization only approaches the expected lower value after a certain time (see Fig. 1). If the disturbance is increased, the magnet continues to disintegrate as expected. However, if you exceed a certain threshold, the behavior changes fundamentally. Initially, the magnetization is reduced to a point where it even disappears completely; the system has completely lost its magnetic properties. However, if you wait a little longer, the magnet will appear to be revived from nowhere at a later point in time and it will regain its magnetization, albeit at a lower strength. This pattern repeats itself periodically.
Now it turns out that similar sequences of collapse and resuscitation can also be observed in completely different quantum materials. This raises the question of the extent to which a more general underlying principle exists that can explain such a dynamic across systems. This leads to the theory of the so-called dynamic quantum phase transitions  .
Dynamic quantum phase transitions
In quantum mechanics, states are described as vectors and the dynamics correspond to a rotation of this vector. Instead of studying the decay of the magnet by means of its magnetization, it is just as obvious to characterize the dynamics by how far this rotated initial vector (as a measure of the magnetization) deviates from the initial one. This is called the Loschmidt amplitude. If the magnetization changes only slightly, then this deviation of the vectors is expected to be small, whereas if the magnet collapses, the deviation will be large. It turns out that this deviation in quantum mechanics bears a surprising similarity to another central quantity in physics, the so-called partition function.
This similarity has decisive consequences that are closely linked to phase transitions and thus to a central concept for understanding general principles and properties of physical systems in equilibrium. While we regularly encounter phase transitions in everyday life, such as when melting ice or boiling water, they are so important in physics because they can show the universal behavior of a system and thus its macroscopic properties, surprisingly, regardless of the details at the atomic level.
Phase transitions are expressed in sharp changes and structures in sums of state if they are viewed as a function of the so-called control parameter, in the case of melting ice, for example, this would be the temperature. Correspondingly, due to the similarity between sums of state and Loschmid amplitudes, the latter can now also show sharp structures and thus show sudden changes in time. These special points in time are called dynamic quantum phase transitions  .
In the case of the magnet, as well as for a large class of other quantum materials that show sequences of collapse and resuscitation, it turns out that the times for the collapse are associated with those dynamic quantum phase transitions  (see Fig. 2). This allows the observations in a large number of different systems to be traced back to one and the same dynamic principle, and in addition one can even infer the concept of universal behavior analogous to equilibrium . As a consequence, we can understand the dynamics of entire classes of systems at once without having to do this anew for each individual problem. This can not only provide insights into the fundamental laws of physical systems, but also be of importance for future quantum information technologies that are also based on quantum dynamics, such as quantum computers.
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