Lifetimes of metal nanowires with broken axial symmetry

Abstract

We present a theoretical approach for understanding the stability of simple metal nanowires, in particular monovalent metals such as the alkalis and noble metals. Their cross sections are of order one nanometer so that small perturbations from external (usually thermal) noise can cause large geometrical deformations. The nanowire lifetime is defined as the time required for making a transition into a state with a different cross-sectional geometry. This can be a simple overall change in radius, or a change in the cross section shape, or both. We develop a stochastic field theoretical model to describe this noise-induced transition process, in which the initial and final states correspond to locally stable states on a potential surface derived by solving the Schrödinger equation for the electronic structure of the nanowire numerically. The numerical string method is implemented to determine the optimal transition path governing the lifetime. Using these results, we tabulate the lifetimes of sodium and gold nanowires for several different initial geometries.

Piecewise adiabatic following in non-Hermitian cycling

“…As previously shown by us [22], though H 2 (t) is non-Hermitian, its time evolution can be stable because its cyclic states may only acquire a real overall phase after one period. Our results discussed below are indeed in this stable region.…”

“…Below we work on periodically driven non-Hermitian systems, where non-unitary but stable time evolution is recently shown to be possible [21,22]. Thanks to this stable nature of a wide class of non-Hermitian systems, it is convenient to adopt conventional quantum mechanics concepts and tools to explore periodically driven non-Hermitian systems.…”

Piecewise adiabatic following: General analysis and exactly solvable models

“…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.…”

“…In this sense, the system possesses "extended unitarity" according to Ref. [8]. The special situation with degenerated eigenphases must be treated carefully.…”

“…These states are simply the eigenstates of the one-period time evolution operator and hence simply acquire an overall phase factor after one period, with the phase, called Floquet eigenphase, being complex in general. Interestingly, it was earlier shown that by tuning the system parameters, some peculiar dynamical regime can emerge, where periodic time modulation may help to stabilize non-Hermitian systems because all cyclic states can be made to possess real eigenphases [7,8]. Indeed, under such circumstances, the stroboscopic time evolution becomes unitary up to a similarity transformation [8] and hence resembles much to the familiar quantum evolution governed by Hermitian Hamiltonians.…”