Title: Quantum Capacity and Thermodynamics of Spacetime

Speaker: Bei-Lok Hu 胡悲樂 (University of Maryland)

Bei Lok Hu received his B.A. in 1967 from the University of California - Berkeley and his Ph.D. in 1972 from Princeton University. He is a Fellow of the American Physical Society and a Senior Fellow of the Japan Society for the Promotion of Science.

Abstract:

An important yet perplexing result from work in the 1990s and 2000s is the near-unity value of the ratio of fluctuations in the vacuum energy density of quantum fields to the mean in a collection of generic spacetimes. This was carried out by way of calculating the noise kernels which are the correlators of the stress-energy tensor of quantum fields.

In this paper, we revisit this issue via a quantum thermodynamics approach, by calculating two quintessential thermodynamic quantities: the heat capacity and the quantum compressibility of some model geometries filled with a quantum field at high and low temperatures. This is because heat capacity at constant volume gives a measure of the fluctuations of the energy density to the mean. When this ratio approaches or exceeds unity, the validity of the canonical distribution is called into question. Likewise, a system’s compressibility at constant pressure is a criterion for the validity of grand canonical ensemble.

We derive the free energy density and, from it, obtain the expressions for these two thermodynamic quantities for thermal and quantum fields in 2d Casimir space, 2d Einstein cylinder and 4d (S1× S3 ) Einstein universe, as well as S1 × S2 and S1 × S4. With this array of spacetimes we can investigate the thermodynamic stability of quantum matter fields in them and make some qualitative observations on the compatibility condition for the coexistence between quantum fields and spacetimes, a fundamental issue in the quantum and gravitation conundrum.

2023-4-18,2:00PM，物理学院422