The purpose of this paper is to articulate a coherent and easy-to-understand way of doing quantum mechanics in any finite-dimensional Liouville space, based on the use of a Kronecker product and what we have termed the ‘bra-flipper’ operator. One of the greater strengths of the formalism expatiated on here is the striking similarities it bears with Dirac’s bra-ket notation. For the purpose of illustrating how the formalism can be effectively employed, we use it to solve a quantum optical master equation for a two-level quantum system and find its Kraus operator sum representation. The paper is addressed to students and researchers with some basic knowledge of linear algebra who want to acquire a deeper understanding of the Liouville space formalism. The concepts are conveyed so as to make the application of the formalism to more complex problems in quantum physics straightforward and unencumbered.
The whole enterprise of spin compositions can be recast as simple enumerative combinatoric problems. We show here that enumerative combinatorics (EC)[1] is a natural setting for spin composition, and easily leads to very general analytic formulae -many of which hitherto not present in the literature. Based on it, we propose three general methods for computing spin multiplicities; namely, 1) the multi-restricted composition, 2) the generalized binomial and 3) the generating function methods. Symmetric and anti-symmetric compositions of SU (2) spins are also discussed, using generating functions. Of particular importance is the observation that while the common Clebsch-Gordan decomposition (CGD) -which considers the spins as distinguishable -is related to integer compositions, the symmetric and anti-symmetric compositions (where one considers the spins as indistinguishable) are obtained considering integer partitions. The integers in question here are none other but the occupation numbers of the Holstein-Primakoff bosons.The pervasiveness of q−analogues in our approach is a testament to the fundamental role they play in spin compositions. In the appendix, some new results in the power series representation of Gaussian polynomials (or q−binomial coefficients) -relevant to symmetric and antisymmetric compositions -are presented. a
Dissociative electron attachment, that is, the cleavage of chemical bonds induced by lowenergy electrons, is difficult to model with standard quantum-chemical methods because the involved anions are not bound but subject to autodetachment. We present here a new computational development for simulating the dynamics of temporary anions on complexvalued potential energy surfaces. The imaginary part of these surfaces describes electron loss, whereas the gradient of the real part represents the force on the nuclei. In our method, the forces are computed analytically based on Hartree-Fock theory with a complex absorbing potential. Ab initio molecular dynamics simulations for the temporary anions of dinitrogen, ethylene, chloroethane, and the five monoto tetrachlorinated ethylenes show qualitative agreement with experiments and offer mechanistic insights into dissociative electron attachments. The results also demonstrate how our method evenhandedly deals with molecules that may undergo dissociation upon electron attachment and those which only undergo autodetachment.
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