Temperature dependence of the Gibbs energy of vacancy formation of fcc Ni

Abstract

Quantum-mechanical calculations are used to determine the temperature dependence of the Gibbs energy of vacancy formation in nickel. Existing data reveal a discrepancy between the high-temperature estimates from experiments and low-temperature approximations from density functional theory. Our finite-temperature calculations-which include the effects of magnetism and fully interacting phonon vibrations-demonstrate that this discrepancy is mostly caused by the previously neglected explicit anharmonic contribution.

Piecewise adiabatic following: General analysis and exactly solvable models

“…Note that the two energy eigenstates have not swapped, which evidently means that no EP has been circled. This profound breakdown of the adiabatic theorem in non-Hermitian systems was first reported by us [15].…”

“…As seen below, even when the dynamics is not exactly solvable, there is still a powerful technique that allows us to carry out necessary asymptotic analysis in the slow-driving limit. The rather general treatment in these systems not only extend the models we studied before [8,15], but can also cover interesting models studied by others [20,22]. Our comprehensive results shall become a useful reference for any future theoretical and experimental study of adiabatic following dynamics in periodically driven and non-Hermitian systems.…”

“…The common wisdom would say Yes to the question here, but caution must be taken because even in the domain of conventional quantum mechanics, new understandings of the physics of adiabatic following are still emerging [9][10][11][12][13][14]. Indeed, as shown by a recent study by us [15], the concept of adiabatic following with the instantaneous eigenstates of the system Hamiltonian is actually not necessarily true. Instead, a non-Hermitian system can display unexpected behavior of sudden switching between different instantaneous eigenstates of the system Hamiltonian.…”

“…That is, contrary to our naïve expectations, the adiabatic following dynamics is piecewise. For several two-level non-Hermitian systems subject to a harmonic driving, the system's timeevolution was analyzed from a geometrical point of view, via the projected Hilbert space depicted by the Bloch sphere [15]. During the time evolution, the system's trajectory on the Bloch sphere may display drastic changes, a phenomenon unique in non-Hermitian systems.…”

“…It is also a distinctly different phenomenon from the unstable evolution when the initial state is chosen to be an energy eigenstate [20][21][22][23]. To demonstrate this, we actually went a long way by adopting a physical and highly useful geometrical phase concept [16][17][18] to characterize the exotic dynamical behavior [15]. This geometrical approach has recently led to a new scheme to characterize the so-called dynamical phase transitions in non-Hermitian systems [19].…”