![]() ![]() Accordingly, simulating quantum systems relies on computational approaches of wave mechanics. ![]() They have been developed in the framework of operator mechanics, in terms of Hilbert spaces, eigenbasis sets, and tensor products. While the two concepts describe very different physical notions, the two theories have a common mathematical foundation. The quantification theory of coherence has recently been developed based on the quantification theory of entanglement. Similarly, one can use the deviation of \(tr(\rho ^2)\) from unity, which serves as a convenient heuristic measure of the purity of a state, based on the fact that for pure states \(\rho =\rho ^2\) holds.Ĭoherence is an underlying quantum concept. Entanglement is measured by different quantities, such as the von-Neumann entropy \(tr(\rho ln(\rho ))\) or the linear entropy \(tr(\rho (1-\rho ))\), where \(\rho \) represents the density matrix. However, the core effect of the electron–electron interaction, occurring during the common evolution in the adjacent wires, is the process of entanglement, to the degree that such structures are collectively known as so-called Coulomb entanglers. The initial state can be represented by two separate electrons, or can be correlated, if the electrons are indistinguishable. A classical and fundamental case for the development of quantum computing approaches is the evolution of two electrons in two adjacent quantum wires. However, recent efforts to develop novel devices by using alternative operating principles focus on coherence and entanglement. Usually, nonequilibrium electron dynamics is sufficient to describe the charge transport in general nanometer structures, governed by boundary conditions. Cutting-edge nanoelectronic devices are usually described in terms of single-electron quantum mechanics, or in terms of Schrödinger–Poisson models, up to the exhaustive many-body Schrödinger equation used in quantum chemistry and materials science. ![]() Sophisticated particle models have been developed, where the mesh-dependent Boltzmann–Poisson model is accomplished by short range interactions to correctly represent the Coulomb interaction without using computationally expensive methods such as molecular dynamics. Conventionally, this requires coupling the Boltzmann equation (or the macroscopic models derived from it, such as the drift-diffusion equations) with the Poisson equation. Purity, identified as the maximal coherence for a quantum state, is also analyzed and its corresponding analysis demonstrates that the entanglement due to the Coulomb interaction is well accounted for by the introduced local approximation.Ĭollective phenomena such as Coulomb interaction play a dominant role in determining the behaviour of classical microelectronic devices. It is demonstrated that for some particular configurations of an electron–electron system, the introduced approximations are feasible. ![]() In particular, we replace the Wigner potential of the electron–electron interaction by a local electrostatic field, which is introduced through the spectral decomposition of the potential. In this work, we reduce the computational complexity of the time evolution of two interacting electrons by resorting to reasonable approximations. Considering electrons, one approach to analyzing their entanglement is through modeling the Coulomb interaction via the Wigner formalism. However, fully-describing entanglement in traditional time-dependent quantum transport simulation approaches requires significant computational effort, bordering on being prohibitive. Entangled quantum particles, in which operating on one particle instantaneously influences the state of the entangled particle, are attractive options for carrying quantum information at the nanoscale. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |