A global team of researchers has found a surprisingly easy relationship between the rates of energy and knowledge transmission across an interface connecting two quantum field theories. Their work was published in Physical Review Letters on August 30.
The interface between different quantum field theories is a vital concept that arises in quite a lot of problems in particle physics and condensed matter physics. Nonetheless, it has been difficult to calculate the transmission rates of energy and knowledge across interfaces.
Hirosi Ooguri, Professor on the Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU, WPI) on the University of Tokyo and Fred Kavli Professor on the California Institute of Technology, together along with his collaborators, Associate Professor Yuya Kusuki at Kyushu University, and Professor Andreas Karch and graduate students Hao-Yu Sun and Mianqi Wang on the University of Texas, Austin, showed that for theories in two dimensions with scale invariance there are easy and universal inequalities between three quantities: Energy transfer rate, Information transfer rate, and the scale of Hilbert space (measured by the speed of increase of the variety of states at high energy). Namely,
[ energy transmittance ] ≤ [ information transmittance] ≤ [ size of the Hilbert space ].
These inequalities imply that, in an effort to transmit energy, information must even be transmitted, and each require a sufficient variety of states. In addition they showed that no stronger inequality is feasible.
Each energy and knowledge transmissions are necessary quantities, but they’re difficult to calculate, and no relationship between them was known. By showing the inequality between these quantities, this paper sheds latest light on this necessary but difficult problem.
