PAHs molecules and heating of the interstellar gas

Until now it has remained difficult to account for the rather high temperatures seen in many diffuse interstellar clouds. Various heating mechanisms have been considered: photoionization of minor species, ionization of H by cosmic rays, and photoelectric effect on small grains. Yet all these processes are either too weak or efficient under too restricting conditions to balance the observed cooling rates. A major heat source is thus still missing in the thermal balance of the diffuse gas. Using photoionization cross sections measured in the lab, it was shown that in order to balance the observed cooling rates in cold diffuse clouds (T approx. 80 K) the PAHs would have to contain 15 percent of the cosmic abundance of carbon. This value does not contradict the former estimation of 6 percent deduced from the IR emission bands since this latter is to be taken as a lower limit. Further, it was estimated that the contribution to the heating rate due to PAH's in a warm HI cloud, assuming the same PAH abundance as for a cold HI cloud, would represent a significant fraction of the value required to keep the medium in thermal balance. Thus, photoionization of PAHs might well be a major heat source for the cold and warm HI media

Binegativity and geometry of entangled states in two qubits

We prove that the binegativity is always positive for any two-qubit state. As a result, as suggested by the previous works, the asymptotic relative entropy of entanglement in two qubits does not exceed the Rains bound, and the PPT-entanglement cost for any two-qubit state is determined to be the logarithmic negativity of the state. Further, the proof reveals some geometrical characteristics of the entangled states, and shows that the partial transposition can give another separable approximation of the entangled state in two qubits.Comment: 5 pages, 3 figures. I made the proof more transparen

Discrete adjoint for coupled conjugate heat transfer

The typical method to solve multi-physics problems such as Conjugate Heat Transfer (CHT) is the partitioned approach which couples separate solvers through boundary conditions. Effective gradient-based optimisation of partitioned CHT problems requires the adjoint of the coupling to maintain the efficiency of the original multi-physics coupling, which is a significant challenge. The use of automatic differentiation (AD) has the potential to ease this burden and leads to generic gradient computation methods. In this paper, we present how to automate the generation of adjoint fluid and solid solvers for a CHT adjoint using Automatic Differentiation (AD). The derivation of the adjoint of the loose coupling algorithms is shown for three fixed-point coupling algorithms. Application of the coupled adjoint algorithm is shown to two CHT optimisation benchmark cases for inverse design and shape optimisation. The results demonstrate that Robin-based coupling algorithms have faster runtimes and are an attractive option for CHT optimisation problems

Low energy phases of bilayer Bi predicted by structure search in two dimensions

We employ an ab-initio structure search algorithm to explore the configurational space of Bi in quasi two dimensions. A confinement potential restricts the movement of atoms within a pre-defined thickness during structure search calculations within the minima hopping method to find the stable and metastable forms of bilayer Bi. In addition to recovering the two known low-energy structures (puckered monoclinic and buckled hexagonal), our calculations predict three new structures of bilayer Bi. We call these structures the $\alpha$, $\beta$, and $\gamma$ phases of bilayer Bi, which are, respectively, 63, 72, and 83 meV/atom higher in energy than that of the monoclinic ground state, and thus potentially synthesizable using appropriate substrates. We also compare the structural, electronic, and vibrational properties of the different phases. The puckered monoclinic, buckled hexagonal, and $\beta$ phases exhibit a semiconducting energy gap, whereas $\alpha$ and $\gamma$ phases are metallic. We notice an unusual Mexican-hat type band dispersion leading to a van Hove singularity in the buckled hexagonal bilayer Bi. Notably, we find symmetry-protected topological Dirac points in the electronic spectrum of the $\gamma$ phase. The new structures suggest that bilayer Bi provides a novel playground to study distortion-mediated metal-insulator phase transitions

Asymptotic Entanglement Dynamics and Geometry of Quantum States

A given dynamics for a composite quantum system can exhibit several distinct properties for the asymptotic entanglement behavior, like entanglement sudden death, asymptotic death of entanglement, sudden birth of entanglement, etc. A classification of the possible situations was given in [M. O. Terra Cunha, {\emph{New J. Phys}} {\bf{9}}, 237 (2007)] but for some classes there were no known examples. In this work we give a better classification for the possibile relaxing dynamics at the light of the geometry of their set of asymptotic states and give explicit examples for all the classes. Although the classification is completely general, in the search of examples it is sufficient to use two qubits with dynamics given by differential equations in Lindblad form (some of them non-autonomous). We also investigate, in each case, the probabilities to find each possible behavior for random initial states.Comment: 9 pages, 2 figures; revised version accepted for publication in J. Phys. A: Math. Theo

Method of convex rigid frames and applications in studies of multipartite quNit pure-states

In this Letter we suggest a method of convex rigid frames in the studies of the multipartite quNit pure-states. We illustrate what are the convex rigid frames and what is the method of convex rigid frames. As the applications we use this method to solve some basic problems and give some new results (three theorems): The problem of the partial separability of the multipartite quNit pure-states and its geometric explanation; The problem of the classification of the multipartite quNit pure-states, and give a perfect explanation of the local unitary transformations; Thirdly, we discuss the invariants of classes and give a possible physical explanation.Comment: 6 pages, no figur

Fermionic concurrence in the extended Hubbard dimer

In this paper, we introduce and study the fermionic concurrence in a two-site extended Hubbard model. Its behaviors both at the ground state and finite temperatures as function of Coulomb interaction $U$ (on-site) and $V$ (nearest-neighbor) are obtained analytically and numerically. We also investigate the change of the concurrence under a nonuniform field, including local potential and magnetic field, and find that the concurrence can be modulated by these fields.Comment: 5 pages, 7 figure

Rescaling multipartite entanglement measures for mixed states

A relevant problem regarding entanglement measures is the following: Given an arbitrary mixed state, how does a measure for multipartite entanglement change if general local operations are applied to the state? This question is nontrivial as the normalization of the states has to be taken into account. Here we answer it for pure-state entanglement measures which are invariant under determinant 1 local operations and homogeneous in the state coefficients, and their convex-roof extension which quantifies mixed-state entanglement. Our analysis allows to enlarge the set of mixed states for which these important measures can be calculated exactly. In particular, our results hint at a distinguished role of entanglement measures which have homogeneous degree 2 in the state coefficients.Comment: Published version plus one important reference (Ref. [39]

Temperature dependence of the electronic structure of semiconductors and insulators

The renormalization of electronic eigenenergies due to electron-phonon coupling is sizable in many materials with light atoms. This effect, often neglected in ab-initio calculations, can be computed using the perturbation-based Allen-Heine-Cardona theory in the adiabatic or non-adiabatic harmonic approximation. After a short description of the numerous recent progresses in this field, and a brief overview of the theory, we focus on the issue of phonon wavevector sampling convergence, until now poorly understood. Indeed, the renormalization is obtained numerically through a q-point sampling inside the BZ. For q-points close to G, we show that a divergence due to non-zero Born effective charge appears in the electron-phonon matrix elements, leading to a divergence of the integral over the BZ for band extrema. Although it should vanish for non-polar materials, unphysical residual Born effective charges are usually present in ab-initio calculations. Here, we propose a solution that improves the coupled q-point convergence dramatically. For polar materials, the problem is more severe: the divergence of the integral does not disappear in the adiabatic harmonic approximation, but only in the non-adiabatic harmonic approximation. In all cases, we study in detail the convergence behavior of the renormalization as the q-point sampling goes to infinity and the imaginary broadening parameter goes to zero. This allows extrapolation, thus enabling a systematic way to converge the renormalization for both polar and non-polar materials. Finally, the adiabatic and non-adiabatic theory, with corrections for the divergence problem, are applied to the study of five semiconductors and insulators: a-AlN, b-AlN, BN, diamond and silicon. For these five materials, we present the zero-point renormalization, temperature dependence, phonon-induced lifetime broadening and the renormalized electronic bandstructure.Comment: 27 pages and 26 figure