Quantum Relaxation Theory based on Quantum Thermodynamics III

Tenpei Morishita, Akira Ishikawa, Kiyoshi Kobayashi

Tenpei Morishita, Akira Ishikawa, Kiyoshi Kobayashi

Ronnie Kosloff

Quantum thermodynamics addresses the emergence of thermodynamic laws from quantum mechanics. The viewpoint advocated is based on the intimate connection of quantum thermodynamics with the theory of open quantum systems. Quantum mechanics inserts dynamics into thermodynamics, giving a sound foundation to finite-time-thermodynamics. The emergence of the 0-law, I-law, II-law and III-law of thermodynamics from quantum considerations is presented. The emphasis is on consistency between the two theories, which address the same subject from different foundations. We claim that inconsistency is the result of faulty analysis, pointing to flaws in approximations.

Mudassir Moosa

The number of non-Clifford gates needed to perform a task, or simply \textit{magic}, is a resource for fault-tolerant quantum computation. Von Neumann algebras provide a formal mathematical structure to describe infinite-dimensional quantum systems, such as those in quantum field theory or quantum statistical mechanics. A particularly important class of von Neumann algebras is called Type III algebras, for which the standard notions of finite-dimensional systems such as density matrices and traces break down. In this work, we argue that Type III von Neumann algebras fundamentally require an infinite amount of magic. Specifically, we consider the thermodynamic limit of finite-dimensional quantum systems, such as lattice systems, and show that if the states in the thermodynamic limit possess only a bounded amount of magic, the resulting local von Neumann algebra cannot be of Type III. Our result has direct implications for the quantum simulations of quantum field theories, for which the algebra of a local subregion is known to be of Type III.

Charles E. Smith

Intrinsic Quantum Thermodynamics (IQT) is a theory that combines Thermodynamics and Quantum Mechanics into a single theory and asserts that irreversibility and the increase of entropy has its origin at the fundamental, atomistic level. The merits and details of IQT are discussed and compared with the well-known theory of Quantum Statistical Mechanics (QSM) and the more recent development of Quantum Thermodynamics (QT). IQT is then used to model in 3D the time evolution of the adsorption of hydrogen on a single-walled carbon nanotube. The initial state of the hydrogen molecules is far from stable equilibrium and over time the system relaxes to a state of stable equilibrium with the hydrogen near the walls of the carbon nanotube. The details of the model are presented, which include the construction of the energy eigenlevels for the system, the treatment of the interactions between the hydrogen and the nanotube along with the interactions of the hydrogen molecules with each other, and the solution of the IQT equation of motion as well as approximation methods that are developed to deal with extremely large numbers of energy eigenlevels. In addition, a new extension to the theory of IQT is proposed for modeling systems that undergo heat interactions with a heat reservoir. The formulation of a new heat interaction operator is discussed, implemented, tested, and compared with a previous version extant in the literature. IQT theory is then further extended to encompass simple mass interactions with a mass reservoir. The formulation, implementation, and testing of the mass interaction operator is also discussed in detail. Finally, IQT is used to model the results of two experiments found in the literature. The first experiment deals with the spin relaxation of rubidium atoms and the second tests the relaxation behavior of single trapped ion that is allowed to interact with an external heat reservoir. Good agreement between experiment and the model predictions is found.

Karl Blum