Non-commutativity as a measure of inequivalent quantization

Abstract

We show that the strength of non-commutativity could play a role in determining the boundary condition of a physical problem. As a toy model, we consider the inverse-square problem in non-commutative space. The scale invariance of the system is explicitly broken by the scale of non-commutativity Θ. The effective problem in non-commutative space is analyzed. It is shown that despite the presence of a higher singular potential coming from the leading term of the expansion of the potential to first order in Θ, it can have a self-adjoint extension. The boundary conditions are obtained, which belong to a 1-parameter family and are related to the strength of non-commutativity.

Electrical Properties of Zr-Doped La₂O₃ Nanocrystallites as a Good Gate Dielectric

“…The continuous downscaling of CMOS technology is leading to some fundamental physical limits in the new devices. The effective oxide thickness (EOT) of the traditional silicon dioxide dielectrics are required to be smaller than 1 nm, which is approximately 3 monolayers and close to the physical limit, that resulting in high gate leakage currents due to the quantum tunneling effect, tunneling and light atom penetration through the film that is caused performance degradation in electronic devices thus new materials and novel architectures are required at this scale [8][9][10][11]. Temperature is also a significant factor in determination of performance CMOS.…”