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Studying the Emergence of Generalized Thermal Ensembles in Quantum Systems

A research team from Skoltech, under the guidance of Professor Anatoly Dymarsky, has analyzed the occurrence of generalized thermal ensembles in quantum systems that have additional symmetries.

Image credit: Skolkovo Institute of Science and Technology

Eventually, it was discovered that black holes thermalize in a manner similar to ordinary matter. The study outcomes have been reported in Physical Review Letters.

In modern physics, the physics behind black holes still remains an elusive topic. It is the most acute point of tension between the theory of general relativity and quantum mechanics. The theory of quantum mechanics proposes the behavior of black holes to be similar to ordinary quantum systems. However, in many ways, this is complicated from the perspective of Einstein’s theory of general relativity.

Hence, the subject of gaining insights into the black holes quantum mechanically is still a persistent source of physical paradoxes. By carefully resolving such paradoxes, one can obtain clues regarding the way quantum gravity works. This is precisely why the physics behind black holes is a topic of active study in the field of theoretical physics.

A specifically important subject is how black holes thermalize. Recent research by a team of researchers from Skoltech discovered that black holes are not much different from ordinary matter in this context. In other words, the occurrence of equilibrium can be elucidated in terms of the same mechanism as in the traditional case.

Black holes could be analytically studied only using the fast-developing theoretical tools of what is called holographic duality. Using this duality, specific types of traditional quantum systems can be mapped to certain cases of quantum gravity systems.

More research work is needed to extend this similarity to thermalization dynamics, but this study offers additional support for the model that significant features of black holes and quantum gravity, overall, can be elucidated in terms of the collective dynamics of traditional quantum many-body systems.

Moreover, the study throws new light on the way traditional many-body quantum systems thermalize. In general, it is mostly accepted that individual quantum mechanical systems can be characterized precisely using equilibrium statistical mechanics.

The accurate mathematical statement that offers such a description is known as the Eigenstate Thermalization Hypothesis. However, a proof for this theory was lacking. The authors of this study claim that they have closed this gap partially.

To the best of our knowledge, our work is the very first analytic proof of the Eigenstate Thermalization Hypothesis in spatially-extended systems, with all previous works on the subject (with very few exceptions) being numerical. We believe that the conceptual and technical novelty of our paper is of broad interest.

Anatoly Dymarsky, Professor, Skoltech Center for Energy Science and Technology


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