The mixed-state inverse engineering scheme is a control scheme used for engineering the quantum state of a driven open quantum system from an initial steady state to a final steady state. In this paper, we present an analytical study of this scheme appli
This work discusses some rigorous analytical results for resonant states. It will be mainly concerned with full discrete resonant expansions, i.e., the second class of expansions mentioned above. We shall restrict the discussion to coherent (elastic) processes in one (1D) and three (3D) dimensio...
Here, we will work through the steps to explain why the eigenvector associated with the largest eigenvalue allows us to determine the stable distribution of individuals across stage classes. Suppose that A is a projection matrix that meets the assumptions of the Perron-Frobenius theorem and that ...
Instead, as explained in my Eighth Theorem of Government, they simply use poor people as props so they can expand the size and scope of the welfare state. Second, I sometimes speculate that our friends on the left are more motivated by a disdain for the rich than they are by any desire...
Furthermore, we show here that the eigenvalue estimate can be used to obtain the 2nd order term (which is of order $ln\\Gamma$) of the lower bound of the ground state energy as the coefficient $\\Gamma$ of the nonlinear term tends to infinity.Lin, Tai-Chia; Belic, Milivoj R; ...
(TRIM) points and reciprocal lattice vectors labeled. By virtue of inversion symmetry and TRS, all bands are doubly degenerate in the BZ due to Kramers theorem. The bands of interest arise by hybridization from Rhdand Biporbitals. From the small but finite density of states (DOS) atEFin ...
ALL, the trivial class that contains all languages. Yet the characterization MIP=NEXP of its classical counterpart by Babai et al. in the 1990s had led to one of the most productive lines of work in complexity of the past few decades, through the PCP theorem and its use from hardness ...
With the Lagrange multiplier Theorem, they concluded that ū(x) := ŵ(x/tŵ) with tw^=N−22N∥∇w^∥2 is a least energy solution of (1.3). By noting the one-to-one correspondence between 𝓢 and 𝓜∞, Jeanjean-Tanaka [6] proved that ū is also a ground state solution ...
The most widespread class of TD-DFT implementation is a linear-response approach [36]. It is noteworthy that the linear response approach directly provides the transition energy rather than the total energies of the ground and excited states. This implies that the excited states themselves are not...
work (UNDO and REDO) that must be done to recover the database to a known consistent state. The operating system, on the other hand, will do this based on its needs to reallocate storage for processes in execution. The operating system will not take into account that this least recently ...