Density functional theory study of (OCS)2^-

The structural and electronic properties of the carbonyl sulfide dimer anion are calculated using density functional theory within a pseudopotential method. Three geometries are optimized and investigated: C2v and C2 symmetric, as well as one asymmetric structure. A distribution of an excess charge in three isomers are studied by the Hirshfeld method. In an asymmetric (OCS)2^- isomer the charge is not equally divided between the two moieties, but it is distributed as OCS^{-0.6} OCS^{-0.4}. Low-lying excitation levels of three isomers are compared using the time-dependent density functional theory in the Casida approach.Comment: pdf (included all figures): http://www.phy.hr/~goranka/Research/ocs.pd

Polynomial maps over finite fields and residual finiteness of mapping tori of group endomorphisms

We prove that every mapping torus of any free group endomorphism is residually finite. We show how to use a not yet published result of E. Hrushovski to extend our result to arbitrary linear groups. The proof uses algebraic self-maps of affine spaces over finite fields. In particular, we prove that when such a map is dominant, the set of its fixed closed scheme points is Zariski dense in the affine space.Comment: 18 page

A quantum version of Sanov's theorem

We present a quantum extension of a version of Sanov's theorem focussing on a hypothesis testing aspect of the theorem: There exists a sequence of typical subspaces for a given set $\Psi$ of stationary quantum product states asymptotically separating them from another fixed stationary product state. Analogously to the classical case, the exponential separating rate is equal to the infimum of the quantum relative entropy with respect to the quantum reference state over the set $\Psi$. However, while in the classical case the separating subsets can be chosen universal, in the sense that they depend only on the chosen set of i.i.d. processes, in the quantum case the choice of the separating subspaces depends additionally on the reference state.Comment: 15 page

Vibronic coupling in the superoxide anion: The vibrational dependence of the photoelectron angular distribution

We present a comprehensive photoelectron imaging study of the O₂(X³Σg⁻,v′=0–6)←O₂⁻(X²Πg,v′′=0) and O₂(a¹Δg,v′=0–4)←O₂⁻(X²Πg,v′′=0)photodetachment bands at wavelengths between 900 and 455 nm, examining the effect of vibronic coupling on the photoelectron angular distribution (PAD). This work extends the v′=1–4 data for detachment into the ground electronic state, presented in a recent communication [R. Mabbs, F. Mbaiwa, J. Wei, M. Van Duzor, S. T. Gibson, S. J. Cavanagh, and B. R. Lewis, Phys. Rev. A82, 011401–R (2010)]. Measured vibronic intensities are compared to Franck–Condon predictions and used as supporting evidence of vibronic coupling. The results are analyzed within the context of the one-electron, zero core contribution (ZCC) model [R. M. Stehman and S. B. Woo, Phys. Rev. A23, 2866 (1981)]. For both bands, the photoelectron anisotropy parameter variation with electron kinetic energy,β(E), displays the characteristics of photodetachment from a d-like orbital, consistent with the π∗g 2p highest occupied molecular orbital of O₂⁻. However, differences exist between the β(E) trends for detachment into different vibrational levels of the X³Σg⁻ and a ¹Δg electronic states of O₂. The ZCC model invokes vibrational channel specific “detachment orbitals” and attributes this behavior to coupling of the electronic and nuclear motion in the parent anion. The spatial extent of the model detachment orbital is dependent on the final state of O₂: the higher the neutral vibrational excitation, the larger the electron binding energy. Although vibronic coupling is ignored in most theoretical treatments of PADs in the direct photodetachment of molecular anions, the present findings clearly show that it can be important. These results represent a benchmark data set for a relatively simple system, upon which to base rigorous tests of more sophisticated models.The authors gratefully acknowledge support by the National Science Foundation Grant No. CHE-0748738 and ANU ARC Discovery Projects under Grant Nos. DP0666267 and DP0880850

Positive contraction mappings for classical and quantum Schrodinger systems

The classical Schrodinger bridge seeks the most likely probability law for a diffusion process, in path space, that matches marginals at two end points in time; the likelihood is quantified by the relative entropy between the sought law and a prior, and the law dictates a controlled path that abides by the specified marginals. Schrodinger proved that the optimal steering of the density between the two end points is effected by a multiplicative functional transformation of the prior; this transformation represents an automorphism on the space of probability measures and has since been studied by Fortet, Beurling and others. A similar question can be raised for processes evolving in a discrete time and space as well as for processes defined over non-commutative probability spaces. The present paper builds on earlier work by Pavon and Ticozzi and begins with the problem of steering a Markov chain between given marginals. Our approach is based on the Hilbert metric and leads to an alternative proof which, however, is constructive. More specifically, we show that the solution to the Schrodinger bridge is provided by the fixed point of a contractive map. We approach in a similar manner the steering of a quantum system across a quantum channel. We are able to establish existence of quantum transitions that are multiplicative functional transformations of a given Kraus map, but only for the case of uniform marginals. As in the Markov chain case, and for uniform density matrices, the solution of the quantum bridge can be constructed from the fixed point of a certain contractive map. For arbitrary marginal densities, extensive numerical simulations indicate that iteration of a similar map leads to fixed points from which we can construct a quantum bridge. For this general case, however, a proof of convergence remains elusive.Comment: 27 page

Sanov and central limit theorems for output statistics of quantum Markov chains

In this paper, we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov’s theorem for the multi-site empirical measure associated to finite sequences of consecutive outcomes of a classical stochastic process. Our result relies on the construction of an extended quantum transition operator (which keeps track of previous outcomes) in terms of which we compute moment generating functions, and whose spectral radius is related to the large deviations rate function. As a corollary to this, we obtain a central limit theorem for the empirical measure. Such higher level statistics may be used to uncover critical behaviour such as dynamical phase transitions, which are not captured by lower level statistics such as the sample mean. As a step in this direction, we give an example of a finite system whose level-1 (empirical mean) rate function is independent of a model parameter while the level-2 (empirical measure) rate is not

Vibronic coupling in the superoxide anion: the vibrational dependence of the photoelectron angular distribution

We present a comprehensive photoelectron imaging study of the O2(X 3Σg−,v′ = 0–6)←O2−(X 2Πg,v″ = 0) and O2(a 1Δg,v′ = 0–4)←O2−(X 2Πg,v″ = 0) photodetachment bands at wavelengths between 900 and 455 nm, examining the effect of vibronic coupling on the photoelectron angular distribution (PAD). This work extends the v′ = 1–4 data for detachment into the ground electronic state, presented in a recent communication. Measured vibronic intensities are compared to Franck–Condon predictions and used as supporting evidence of vibronic coupling. The results are analyzed within the context of the one-electron, zero core contribution (ZCC) model. For both bands, the photoelectron anisotropy parameter variation with electron kinetic energy, β(E), displays the characteristics of photodetachment from a d-like orbital, consistent with the πg∗ 2p highest occupied molecular orbital of O2−. However, differences exist between the β(E) trends for detachment into different vibrational levels of the X 3Σg− and a 1Δg electronic states of O2. The ZCC model invokes vibrational channel specific “detachment orbitals” and attributes this behavior to coupling of the electronic and nuclear motion in the parent anion. The spatial extent of the model detachment orbital is dependent on the final state of O2: the higher the neutral vibrational excitation, the larger the electron binding energy. Although vibronic coupling is ignored in most theoretical treatments of PADs in the direct photodetachment of molecular anions, the present findings clearly show that it can be important. These results represent a benchmark data set for a relatively simple system, upon which to base rigorous tests of more sophisticated models

Typical support and Sanov large deviations of correlated states

Discrete stationary classical processes as well as quantum lattice states are asymptotically confined to their respective typical support, the exponential growth rate of which is given by the (maximal ergodic) entropy. In the iid case the distinguishability of typical supports can be asymptotically specified by means of the relative entropy, according to Sanov's theorem. We give an extension to the correlated case, referring to the newly introduced class of HP-states.Comment: 29 pages, no figures, references adde

Extremal flows in Wasserstein space

We develop an intrinsic geometric approach to the calculus of variations in theWasserstein space. We show that the flows associated with the Schr\ua8odinger bridge with general prior, with optimal mass transport, and with the Madelung fluid can all be characterized as annihilating the first variation of a suitable action. We then discuss the implications of this unified framework for stochastic mechanics: It entails, in particular, a sort of fluid-dynamic reconciliation between Bohm\u2019s and Nelson\u2019s stochastic mechanics