Solutions of the Two-State Potential-Curve-Crossing Problem

A general theory of the two-state curve-crossing problem has been developed, with a complete solution of an accurate model for close crossings (including numerical computations for strong coupling). Results clarify the position of the Landau-Zener approximation and its improvements by Nikitin and others, provide a general way of extending these approximations into regions often treated incorrectly (including the high-energy limit), and can be readily adapted to simple, rapid calculations

Diabatic and Adiabatic Representations for Atomic Collision Processes

ABSTRACT A consistent general definition of diabatic representations has not previously been given, even though many practical examples of such representations have been constructed for specific problems. Such a definition is provided in this paper. Beginning with a classical trajectory formulation, we describe the form and behavior of velocity‐dependent couplings in slow collisions, including the effects of electron‐translation factors (ETF’s). We compare the couplings arising from atomic representations and atomic ETF’s with those arising from molecular representations and ’’switching function’’ ETF’s. We show that a unique set of switching functions makes the two descriptions identical in their effects. We then show that an acceptable general definition of a diabatic representation is provided by the condition P+A=0, where P is the usual nonadiabatic coupling matrix and A represents corrections to it arising from electron translation factors (ETF’s). Two distinct types of diabatic representation result, depending on the definition taken for A. States that undergo no deformation are called F diabatic; those that have no velocity‐dependent couplings are called M diabatic. Finally, we discuss the properties of representations that are partially diabatic and partially adiabatic, and we give some rules for the construction of representations that should be nearly optimal for describing many types of collision processes

Theory of Near-Adiabatic Collisions. II. Scattering Coordinate Method

A rigorously correct and fully quantum-mechanical theory of slow atomic collisions is presented, which removes the formal defects and spurious nonadiabatic couplings of perturbed-stationary-states theory, and arrives at coupled equations for the heavy-particle motion which are the same as those obtained in the preceding paper by the electron translation factor formulation. Here, however, the theory is formulated in terms of suitably defined scattering coordinates, and electron translation factors do not appear. A unified physical interpretation of both approaches can thereby be made, and smaller terms in the coupled equations, describing corrections of order mμ to electronic binding energies and to the collision kinetic energy, are placed on a firmer footing. Particular attention is paid to the critical test case of isotopic systems such as HD+ and it is shown how a correct theory of isotopic charge exchange can be formulated

Studies of the Potential Curve Crossing Problem II. General Theory and a Model for Close Crossings

A unified formal treatment of the two-state potential-curve-crossing problem in atomic collision theory is presented, and the case of close crossings analyzed in detail. A complete solution for this case, including necessary computations, is given using a suitable generalization of the linear model originally suggested by Landau, Zener, and Stueckelberg. Our solution is based upon a hierarchy of approximations concerned with (i) choice of a discrete basis set for electronic coordinates, (ii) semiclassical treatment of the nuclear motion, (iii) an appropriate model for the two-state electronic Hamiltonian, and (iv) a complete solution to that model

Theory of Near-Adiabatic Collisions. I. Electron-Translation-Factor Method

The theory of near-adiabatic collisions is formulated in a fully quantum-mechanical form, correctly taking into account the role of electron translation factors (ETF\u27s). A general form for the ETF, using switching functions, is given for systems which are electrically either asymmetric or symmetric (with or without mass asymmetry). The main result is that the close-coupled scattering equations obtained in the perturbed-stationary-states theory must be replaced by equations of identical form, but having modified nonadiabatic coupling matrices. In general, the corrections involved are substantial; their nature, and effect on coupling matrices, is discussed, and conditions when they are likely to be important are described. The remaining problem of determining the switching function is discussed briefly. The correct form for ETF\u27s, their quantum-mechanical formulation, and the resulting correct form for the coupled equations, have not been given previously

Semiclassical Theory of Inelastic Collisions I. Classical Picture and Semiclassical

This series of papers is concerned with the derivation of the equations of the classical picture of atomic collisions, iℏddtdi(t)=Σjhij(t)dj(t), which describe the time dependence of electronic-quantum-state amplitudes as the nuclei move along a classical trajectory. These equations are derived in two ways. In the first formulation, which coincides with the intuitive classical picture of the collision, the nuclear part of the wave function is treated as a superposition of narrow wave packets, each traveling along a classical trajectory. In the second formulation, a semiclassical approach is used. The validity and meaning of the two formulations are discussed and compared

Studies of the Potential Curve Crossing Problem I. Analysis of Stueckelberg\u27s Method

A detailed critical analysis is made of Stueckelberg\u27s treatment of inelastic transitions at a crossing of two potential curves. Using an asymptotic method analogous to the WKB approximation, Stueckelberg obtained the well-known Landau-Zener-Stueckelberg (LZS) formula for the inelastic transition probability. His method involved the determination of connection formulas linking amplitudes associated with his asymptotic approximants on either side of the crossing-point region. Here we show that (a) Stueckelberg\u27s asymptotic approximants are just the WKB approximants for elastic scattering on the adiabatic (noncrossing) potential curves; (b) Stueckelberg\u27s method for obtaining the connection formulas can be put on a rigorous footing, including sufficient conditions for its validity, using the classical trajectory equations derivable from a general semiclassical theory of inelastic atomic collisions; (c) there is an undetermined phase in the S matrix, which Stueckelberg incorrectly assumed to be zero, and which has the value 14π in the distorted-wave approximation; (d) Stueckelberg\u27s derivation is not valid whenever the inelastic transition probability is small, either in the rapid-passage (diabatic) case or the near-adiabatic limit; (e) for realistic model parameters, the conditions needed for Stueckelberg\u27s derivation to be valid are almost never satisfied. Since the LZS formula is known from numerical computations to be valid under some conditions when the Stueckelberg derivation is not valid, we conclude that analysis via connection-formula methods is not a useful technique for treating the crossing problem. In an appendix we derive an analytical result for the Stokes\u27s constants determining the Stueckelberg connection formulas. The result is an absolutely convergent, infinite series whose numerical evaluation would yield exactly the unknown phase associated with the LZS formula

Who acquires infection from whom and how? Disentangling multi-host and multi-mode transmission dynamics in the 'elimination' era

Multi-host infectious agents challenge our abilities to understand, predict and manage disease dynamics. Within this, many infectious agents are also able to use, simultaneously or sequentially, multiple modes of transmission. Furthermore, the relative importance of different host species and modes can itself be dynamic, with potential for switches and shifts in host range and/ or transmission mode in response to changing selective pressures, such as those imposed by disease control interventions. The epidemiology of such multi-host, multi-mode infectious agents thereby can involve a multi-faceted community of definitive and intermediate/secondary hosts or vectors, often together with infectious stages in the environment, all of which may represent potential targets, as well as specific challenges, particularly where disease elimination is proposed. Here, we explore, focusing on examples fromboth human and animal pathogen systems, why and how we should aim to disentangle and quantify the relative importance of multi-host multi-mode infectious agent transmission dynamics under contrasting conditions, and ultimately, how this can be used to help achieve efficient and effective disease control. This article is part of the themed issue 'Opening the black box: re-examining the ecology and evolution of parasite transmission'

Temporal Interferometry: A Mechanism for Controlling Qubit Transitions During Twisted Rapid Passage with Possible Application to Quantum Computing

In an adiabatic rapid passage experiment, the Bloch vector of a two-level system (qubit) is inverted by slowly inverting an external field to which it is coupled, and along which it is initially aligned. In twisted rapid passage, the external field is allowed to twist around its initial direction with azimuthal angle $\phi (t)$ at the same time that it is inverted. For polynomial twist: $\phi (t) \sim Bt^{n}$. We show that for $n \geq 3$, multiple avoided crossings can occur during the inversion of the external field, and that these crossings give rise to strong interference effects in the qubit transition probability. The transition probability is found to be a function of the twist strength $B$, which can be used to control the time-separation of the avoided crossings, and hence the character of the interference. Constructive and destructive interference are possible. The interference effects are a consequence of the temporal phase coherence of the wavefunction. The ability to vary this coherence by varying the temporal separation of the avoided crossings renders twisted rapid passage with adjustable twist strength into a temporal interferometer through which qubit transitions can be greatly enhanced or suppressed. Possible application of this interference mechanism to construction of fast fault-tolerant quantum CNOT and NOT gates is discussed.Comment: 29 pages, 16 figures, submitted to Phys. Rev.

Antibacterial Activity of Endophytic Actinomycetes Isolated from the Medicinal Plant \u3cem\u3eVochysia divergens\u3c/em\u3e (Pantanal, Brazil)

Endophytic actinomycetes from medicinal plants produce a wide diversity of secondary metabolites (SM). However, to date, the knowledge about endophytes from Brazil remains scarce. Thus, we analyzed the antimicrobial potential of 10 actinomycetes isolated from the medicinal plant Vochysia divergens located in the Pantanal sul-mato-grossense, an unexplored wetland in Brazil. Strains were classified as belonging to the Aeromicrobium, Actinomadura, Microbacterium, Microbispora, Micrococcus, Sphaerisporangium, Streptomyces, and Williamsia genera, through morphological and 16S rRNA phylogenetic analyzes. A susceptibility analysis demonstrated that the strains were largely resistant to the antibiotics oxacillin and nalidixic acid. Additionally, different culture media (SG and R5A), and temperatures (28 and 36°C) were evaluated to select the best culture conditions to produce the active SM. All conditions were analyzed for active metabolites, and the best antibacterial activity was observed from metabolites produced with SG medium at 36°C. The LGMB491 (close related to Aeromicrobium ponti) extract showed the highest activity against methicillin-resistant Staphylococcus aureus (MRSA), with a MIC of 0.04 mg/mL, and it was selected for SM identification. Strain LGMB491 produced 1-acetyl-β-carboline (1), indole-3-carbaldehyde (2), 3-(hydroxyacetyl)-indole (4), brevianamide F (5), and cyclo-(L-Pro-L-Phe) (6) as major compounds with antibacterial activity. In this study, we add to the knowledge about the endophytic community from the medicinal plant V. divergens and report the isolation of rare actinomycetes that produce highly active metabolites