Multi-State Density Functional Theory for Ground and Excited States

We report a rigorous formulation of multi-state density functional theory (MSDFT) that extends the Kohn-Sham (KS) energy functional for the ground state to a Hamiltonian matrix functional H[D] of the density matrix D in the space spanned by the lowest N adiabatic states. We establish a variational principle of MSDFT, which guarantees that the variational optimization results in a Hamiltonian matrix, whose eigenvalues are the lowest N eigen-energies of the system. We present an explicit expression of H[D] and introduce the correlation matrix functional. Akin to KS-DFT for the ground state, a universal multi-state correlation potential is derived for a two-state system as an illustrative example. This work shows that MSDFT is an exact density functional theory that treats the ground and excited states on an equal footing and provides a framework for practical applications and future developments of approximate functionals for excited states.

Exact density matrix elements for a driven dissipative system described by a quadratic Hamiltonian

For a prototype quadratic Hamiltonian describing a driven, dissipative system, exact matrix elements of the reduced density matrix are obtained from a generating function in terms of the normal characteristic functions. The approach is based on the Heisenberg equations of motion and operator calculus. The special and limiting cases are discussed.

Exact Density Matrix Elements for a Driven Dissipative Bosonic Mode in a Kerr-Like Medium

For a prototype Hamiltonian describing a driven, dissipative bosonic mode in a Kerr-like medium, the exact matrix elements of the reduced density matrix are obtained from a generating function in terms of the normal characteristic functions. The approach is based on the Heisenberg equations and operator calculus. The special and limiting cases are discussed.

Prices and sold amount dynamics, endogenous knowledge and distribution of Picralima nitida (Stapf) T. Durand and H. Durand across in the Dahomey Gap and Guinea-Congolese regions

Picralima nitida (Apocynaceae) represents is an important African medicinal plant species. It is frequently used in traditional medicine and pharmaceutical industries for drugs manufacturing against infectious diseases, malaria and diabetes and commercially traded as well. Despite its importance, the species is becoming rare, especially in the Dahomey Gap because of it is commercial importance. There is an issue about the controversy of the plant species on its distribution across both regions. Without further forest resources inventory, it is difficult to address efficiently the issue of the controversy of its distribution, the unsustainable use and the endogenous knowledge about of plant species usages. Ethnobotanical surveys were conducted in the Dahomey Gap with 120 informants randomly selected and interviewed. A literature review of scientific papers and books was also used to provide information on the sale prices dynamic, amount sold per units, uses, distribution area using the GBIF Platform, and threats of the species in both climatic regions. P. nitida products were more expensive (per sale unit) in the DG than the GC region. All parts of the species were collected and used to treat 34 diseases. The plant species appear to be poorly distributed in the DG than the GC region. The overuse, endogenous knowledge loss in DG and deforestation in GC region appeared the main driver of scarcity of the species. P. nitida has various medicinal uses across both regions. The sale price and amount sold per unit tend all to vary across both regions as well. However, the plant species is becoming scarcer in the DG than CG region. The issue of resource scarcity may drive loss of endogenous knowledge about the plant species uses. A forest inventory and documentation of uses are highly needed to assess the exact density and distribution area of P.nitida across both regions

The double scaled limit of super-symmetric SYK models

We compute the exact density of states and 2-point function of the $$ \mathcal{N} $$ N = 2 super-symmetric SYK model in the large N double-scaled limit, by using combinatorial tools that relate the moments of the distribution to sums over oriented chord diagrams. In particular we show how SUSY is realized on the (highly degenerate) Hilbert space of chords. We further calculate analytically the number of ground states of the model in each charge sector at finite N, and compare it to the results from the double-scaled limit. Our results reduce to the super-Schwarzian action in the low energy short interaction length limit. They imply that the conformal ansatz of the 2-point function is inconsistent due to the large number of ground states, and we show how to add this contribution. We also discuss the relation of the model to SLq(2|1). For completeness we present an overview of the $$ \mathcal{N} $$ N = 1 super-symmetric SYK model in the large N double-scaled limit.

Real-time ab initio simulation of inelastic electron scattering using the exact, density functional, and alternative approaches

Inelastic electron scattering phenomena in chemical/physical/materials interests: electron radiation damage in materials; DNA damaged by electron scattering; electron therapy; electron microscope; electron-beam-induced deposition for nanofabrication.

Piecewise linearity, freedom from self-interaction, and a Coulomb asymptotic potential: three related yet inequivalent properties of the exact density functional

Three properties of the exact energy functional of DFT are important in general and for spectroscopy in particular, but are not necessarily obeyed by approximate functionals. We explain what they are, why they are important, and how they are related yet inequivalent.

A paper-filter system to investigate the real micro-environment circuiting plant roots

The micro-environment circling the plant root is an interesting topic for many researchers. Until now there is not an approach to investigate the exact density of chemicals surrounding the plant roots. here we use a simple paper filter system and gas chromatography to quantify the exact density of chemicals surrounding the plant roots. this can help solve a long-existing doubt about the ‘real micro-environment’ surrounding the plant roots.