Nonclassical properties of electronic states of aperiodic chains in a homogeneous electric field

Abstract

The electronic energy levels of one-dimensional aperiodic systems driven by a homogeneous electric field are studied by means of a phase-space description based on the Wigner distribution function. The formulation provides physical insight into the quantum nature of the electronic states for the aperiodic systems generated by the Fibonacci and Thue-Morse sequences. The nonclassical parameter for electronic states is studied as a function of the magnitude of homogeneous electric field to achieve the main result of this work, which is to prove that the nonclassical properties of the electronic states in the aperiodic systems determine the transition probability between electronic states in the region of anticrossings. The localization properties of electronic states and the uncertainty product of momentum and position variables are also calculated as functions of the electric field.

Dynamical localisation of conduction electrons in one-dimensional disordered systems

“…Fig. 1b,c,d], as a result of the quantum interference phenomena [15]. Figure 2 shows the marginal distributions of the WDF in coordinate and momentum spaces, corresponding to the snapshots presented in the previous figure.…”

“…In contrast to the classical distribution functions the WDF can take negative values in some regions of the phasespace [14]. The negativity of the WDF is the reason for the non-classical character of this distribution function [15]. This property of the WDF is a consequence of the Wigner-Weyl transform which "forces" the off-diagonal elements of the density matrix to the resulting distribution function.…”

Phase-Space Approach to the Position-Momentum Correlations of the Conduction Electron States in a Double-Barrier Resonant Nanosystem

“…On the other hand, this property of the WDF can be also explained in terms of the quantum interference between correlated pieces of the WDF which occupy different regions of the phase space [5]. Hence, we can conclude that the WDF comprises the mutually dependent quantum correlations between the momentum and position states of the electrons.…”

Phase-space description of the coherent state dynamics in a small one-dimensional system

“…During the time evolution of the WDF according to the Moyal equation the region of the phase space occupied by the WDF increases. Simultaneously, the negative values of the WDF emerge as a re-sult of the quantum correlations between different pieces of the state in the phase space [27]. It stems from the fact that the information from the off-diagonal terms in Eq.…”

“…This observation suggests that the autocorrelation function contains information on the properties of the dynamical localization of the WDF during its time evolution. Regardless of this observation, the degree of localization of the quantum state in the phase space can be investigated in terms of the Husimi function [27] which is defined as the convolution of the Wigner distribution function and a window function with the resolution corresponding to the minimum resulting from the uncertainty principle. …”