Analog Systems for Gravity Duals

• Applicant: Dr. Sabine Hossenfelder
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields ; Theoretical Condensed Matter Physics
• Term: from 2016 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 286641560

• Final Report Year: 2020

Final Report Abstract

For all we currently know, nature on its most fundamental level is described by quantum field theories. However, many quantum field theories which describe physical systems are intractable with the existing mathematical methods. We can write down the equations but do not know how to solve them. In the past two decades, physicists have therefore developed new ways of handling such mathematically difficult situations, the most powerful of which are quantum simulations. The idea of quantum simulations is that instead of attempting to calculate the behavior of a system, one creates a second system that can be controlled in the laboratory and that has, to a certain accuracy, the same behavior as the first system. This is basically a custom-made simulation; a “quantum simulation” because the systems of interest have quantum properties. The systems studied in this project are examples of such quantum simulations. We are trying to understand the behavior of one system, a strongly coupled condensed matter system, like the quark gluon plasma or high-temperature superconductors, whose equations we cannot solve. Therefore, instead of solving the equations, we derive a mathematical relation between the system of interest and another system which can then be created in the laboratory. In the case considered in this project, the second system in the laboratory is a type of superfluid. Superfluids are famous for their longrange quantum correlations and their self-interaction can be controlled by laser pulses with well-established techniques. The study conducted in this project showed that the class of systems that can be simulated with superfluids is larger than previously known. It also resulted in various mathematically derived relations that identify observables of the one system with observables of the other system. These relations are important to quantify how well the identification between the two systems works. A surprise finding during the research on this project has been that (for reasons not yet entirely understood) the same type of superfluid that can simulate certain gravitational systems (such as black holes in spaces with a negative cosmological constant) might also constitute dark matter. The latter question will be studied in more detail in a follow-up project.

Publications

• “Analogue Gravity Models From Conformal Rescaling,” Class. Quant. Grav. 34, no. 16, 165004 (2017)
  S. Hossenfelder and T. Zingg
  
• “Analog Models for Holographic Transport,” Phys. Rev. D 100, no. 5, 056015 (2019)
  S. Hossenfelder and T. Zingg
  
• “Strong lensing with superfluid dark matter,” JCAP 1902, 001 (2019)
  S. Hossenfelder and T. Mistele