Density matrices in quantum systems at infinite temperature

I. O. Vakarchuk

Hendrickje Nadeau

S. Glocke, Andreas Klümper, Jesko Sirker

Jiushu Shao, Mo‐Lin Ge, Hu Cheng

The density matrices of a generic quantum-nondemolition system coupled to the reservoir of an infinite number of harmonic oscillators and to the reservoir of an infinite number of two-level systems are evaluated exactly. It is found that quantum decoherence is independent of temperature in the latter case. \textcopyright{} 1996 The American Physical Society.

Phillip C. Burke, Goran Nakerst, Masudul Haque

In the study of thermalization in finite isolated quantum systems, an inescapable issue is the definition of temperature. We examine and compare different possible ways of assigning temperatures to energies or equivalently to eigenstates in such systems. A commonly used assignment of temperature in the context of thermalization is based on the canonical energy-temperature relationship, which depends only on energy eigenvalues and not on the structure of eigenstates. For eigenstates, we consider defining temperature by minimizing the distance between (full or reduced) eigenstate density matrices and canonical density matrices. We show that for full eigenstates, the minimizing temperature depends on the distance measure chosen and matches the canonical temperature for the trace distance; however, the two matrices are not close. With reduced density matrices, the minimizing temperature has fluctuations that scale with subsystem and system size but appears to be independent of distance measure. In particular limits, the two matrices become equivalent while the temperature tends to the canonical temperature.

É. A. Arinshtein