Researchers have discovered a surprising link between energy transmission and information transfer across interfaces connecting different quantum field theories. Led by Hirosi Ooguri, Professor at the Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU) at the University of Tokyo, an international team found that in two-dimensional theories with scale invariance, there are simple and universal inequalities between energy transfer rate, information transfer rate, and the size of Hilbert space.
The study, published in Physical Review Letters, reveals that to transmit energy, information must also be transmitted, and both require a sufficient number of states. This breakthrough sheds new light on a previously difficult problem in particle physics and condensed matter physics. The team included Associate Professor Yuya Kusuki at Kyushu University, Professor Andreas Karch and graduate students Hao-Yu Sun and Mianqi Wang at the University of Texas, Austin.
Energy Transmission and Information in Quantum Field Theory
The transmission of energy across an interface connecting two quantum field theories is a fundamental concept that arises in various problems in particle physics and condensed matter physics. However, calculating the transmission rates of energy and information across interfaces has been a challenging task. Recently, an international team of researchers has made a significant breakthrough by discovering a surprisingly simple relationship between the rates of energy and information transmission.
The research, published in Physical Review Letters on August 30, 2024, was led by Hirosi Ooguri, Professor at the Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU, WPI) at the University of Tokyo, and Fred Kavli Professor at the California Institute of Technology. The team included Associate Professor Yuya Kusuki at Kyushu University, and Professor Andreas Karch and graduate students Hao-Yu Sun and Mianqi Wang at the University of Texas, Austin.
The researchers focused on theories in two dimensions with scale invariance, where they found simple and universal inequalities between three quantities: energy transfer rate, information transfer rate, and the size of Hilbert space (measured by the rate of increase of the number of states at high energy). Specifically, they showed that [energy transmittance] ≤ [information transmittance] ≤ [size of the Hilbert space]. These inequalities imply that, in order to transmit energy, information must also be transmitted, and both require a sufficient number of states.
The significance of this discovery lies in the fact that it sheds new light on an important but difficult problem. Energy and information transmissions are crucial quantities, but they are challenging to calculate, and no relationship between them was known until now. By establishing the inequality between these quantities, the researchers have provided valuable insights into the fundamental principles governing energy transmission in quantum field theory.
The Interface Between Quantum Field Theories
The interface between different quantum field theories is a critical concept that arises in various problems in particle physics and condensed matter physics. It represents a boundary surface where two distinct quantum systems interact with each other. However, calculating the transmission rates of energy and information across these interfaces has been a daunting task.
In this context, the recent research provides a significant breakthrough by establishing a simple relationship between the rates of energy and information transmission. The discovery is particularly important because it highlights the intricate connection between energy and information transmission in quantum field theory. By showing that energy transmission requires information transmission, the researchers have demonstrated that these two quantities are intimately linked.
The interface between quantum field theories is a complex system where various physical phenomena occur. The recent research has provided a deeper understanding of this system by revealing the fundamental principles governing energy transmission. This knowledge can be applied to various areas of physics, including particle physics and condensed matter physics, where the interface between different quantum systems plays a crucial role.
Scale Invariance and Hilbert Space
The researchers focused on theories in two dimensions with scale invariance, which is a fundamental concept in quantum field theory. Scale invariance implies that the physical laws governing a system remain unchanged under different scales or resolutions. This property is essential for understanding various phenomena in physics, including critical behavior and phase transitions.
In this context, the size of Hilbert space (measured by the rate of increase of the number of states at high energy) plays a crucial role. The researchers showed that the size of Hilbert space sets an upper bound on the information transfer rate, which in turn sets an upper bound on the energy transfer rate. This hierarchy is a fundamental aspect of quantum field theory and highlights the intricate connection between energy, information, and the underlying mathematical structure of the system.
The discovery has significant implications for our understanding of quantum systems and their behavior under different conditions. By establishing a relationship between energy transmission, information transmission, and the size of Hilbert space, the researchers have provided valuable insights into the fundamental principles governing quantum field theory.
Implications and Future Directions
The recent research has far-reaching implications for various areas of physics, including particle physics and condensed matter physics. The discovery provides a deeper understanding of the interface between different quantum systems and highlights the intricate connection between energy transmission, information transmission, and the underlying mathematical structure of the system.
In the future, researchers can apply this knowledge to various problems in physics, including the study of black holes, cosmology, and condensed matter physics. The discovery also opens up new avenues for exploring the fundamental principles governing quantum field theory and its applications to various areas of physics.
Furthermore, the research has significant implications for our understanding of information transmission in quantum systems. By establishing a relationship between energy transmission and information transmission, the researchers have demonstrated that these two quantities are intimately linked. This knowledge can be applied to various areas of physics, including quantum computing and quantum communication, where the efficient transmission of information is crucial.
In conclusion, the recent research has provided a significant breakthrough in our understanding of energy transmission in quantum field theory. By establishing a simple relationship between the rates of energy and information transmission, the researchers have highlighted the intricate connection between these two quantities and the underlying mathematical structure of the system. The discovery has far-reaching implications for various areas of physics and opens up new avenues for exploring the fundamental principles governing quantum field theory.
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