The minimum Rényi entropy output of a quantum channel is locally additive

We show that the minimum Rényi entropy output of a quantum channel is locally additive for Rényi parameter \(\alpha >1\). While our work extends the results of Gour and Friedland (IEEE Trans. Inf. Theory 59(1):603, 2012) (in which local additivity was proven for \(\alpha =1\)), it is based on several new techniques that incorporate the multiplicative nature of \(\ell _p\)-norms, in contrast to the additivity property of the von-Neumann entropy. Our results demonstrate that the counterexamples to the Rényi additivity conjectures exhibit purely global effects of quantum channels. Interestingly, the approach presented here cannot be extended to Rényi entropies with parameter \(\alpha <1\).     

TiS2 Monolayer as an Emerging Ultrathin Bifunctional Catalyst: Influence of Defects and Functionalization

We have envisaged the hydrogen evolution and oxygen evolution reactions (HER and OER) on a two-dimensional (2D) noble-metal-free titanium disulfide (TiS₂) monolayer, which belongs to the exciting family of transition metal dichalcogenides (TMDCs). Our theoretical investigation to probe the HER and OER on both the H and T phases of 2D TiS₂ is based on electronic-structure calculations witihin the framework of density functional theory (DFT). Since TiS₂ is the lightest compound among the group-IV TMDCs, it is worth exploring the catalytic activity of a TiS₂ monolayer through the functionalization at the anion (S) site, substituting with P, N, and C dopants as well as by incorporating single sulfur vacancy defects. We have investigated the effect of functionalization and vacancy defects on the structural, electronic, and optical response of a TiS₂ monolayer by determining the density of states, work-function, and optical absorption spectra. We have determined the HER and OER activities for the functionalized and defective TiS₂ monolayers based on the reaction coordinate, which can be constructed from the adsorption free energies of the intermediates (H*, O*, OH* and OOH*, where * denotes the adosrbed state) in the HER and OER mechanisms. Finally, we have shown that TiS₂ monolayers are emerging as a promising material for the HER and OER mechanisms under the influence of functionalization and defects.     

Study of high-pressure phase transition of CeTe and EuTe through three-body interaction potential approach

The high pressure phase transition of lanthanum monotellurides having NaCl-type (B₁) structure have been studied using three-body interaction potential (TBIP) approach. The potential model consists of long-range Coulombic, three-body interaction forces, short-range overlap repulsive forces operative up to next nearest neighbor ions, van der Walls interactions and zero point energy effects. To understand the effect of pressure on elastic constant and their combinations, they have also been studied. The Born stability criterion was also found to be fulfiled in the present study. Our calculated results of phase transitions, volume collapses and elastic behavior of these monotellurides are found to be close to the experimental results. This shows that the inclusion of three-body interaction effects makes the present model suitable for high-pressure studies.     

The Quantum Phase Problem: Steps Toward a Resolution

Defining the observable canonically conjugate to the number observable N has long been an open problem in quantum theory. The problem stems from the fact that N is bounded from below. In a previous work we have shown how to define the absolute phase observable || by suitably restricting the Hilbert space of x and p like variables. Here we show that also from the classical point of view, there is no rigorous definition for the phase even though it's absolute value is well defined.     

Extension of the renormalized coupled-cluster methods exploiting left eigenstates of the similarity-transformed hamiltonian to open-shell systems: a benchmark study

The recently formulated completely renormalized coupled-cluster method with singles, doubles, and noniterative triples, exploiting the biorthogonal form of the method of moments of coupled-cluster equations (Piecuch, P.; W?och, M. J. Chem. Phys. 2005, 123, 224105; Piecuch, P.; W?och, M.; Gour, J. R.; Kinal, A. Chem. Phys. Lett. 2006, 418, 467), termed CR-CC(2,3), is extended to open-shell systems. Test calculations for bond breaking in the OH radical and the F2+ ion and singlet-triplet gaps in the CH2, HHeH, and (HFH)- biradical systems indicate that the CR-CC(2,3) approach employing the restricted open-shell Hartree--Fock (ROHF) reference is significantly more accurate than the widely used CCSD(T) method and other noniterative triples coupled-cluster approximations without making the calculations substantially more expensive. A few molecular examples, including the activation energies of the C2H4 + H --> C2H5 forward and reverse reactions and the triplet states of the CH2 and H2Si2O2 biradicals, are used to show that the dependence of the ROHF-based CR-CC(2,3) energies on the method of canonicalization of the ROHF orbitals is, for all practical purposes, negligible.     

Will Small Particles Exhibit Brownian Motion in the Quantum Vacuum?

The Brownian motion of small particles interacting with a field at a finite temperature is a well-known and well-understood phenomenon. At zero temperature, even though the thermal fluctuations are absent, quantum fields still possess vacuum fluctuations. It is then interesting to ask whether a small particle that is interacting with a quantum field will exhibit Brownian motion when the quantum field is assumed to be in the vacuum state. In this paper, we study the cases of a small charge and an imperfect mirror interacting with a quantum scalar field in (1 + 1) dimensions. Treating the quantum field as a classical stochastic variable, we write down a Langevin equation for the particles. We show that the results we obtain from such an approach agree with the results obtained from the fluctuation-dissipation theorem. Unlike the finite temperature case, there exists no special frame of reference at zero temperature and hence it is essential that the particles do not break Lorentz invariance. We find that that the scalar charge breaks Lorentz invariance, whereas the imperfect mirror does not. We conclude that small particles such as the imperfect mirror will exhibit Brownian motion even in the quantum vacuum, but this effect can be so small that it may prove to be difficult to observe it experimentally.     

The impact of early reflections on binaural cues

Animals live in cluttered auditory environments, where sounds arrive at the two ears through several paths. Reflections make sound localization difficult, and it is thought that the auditory system deals with this issue by isolating the first wavefront and suppressing later signals. However, in many situations, reflections arrive too early to be suppressed, for example, reflections from the ground in small animals. This paper examines the implications of these early reflections on binaural cues to sound localization, using realistic models of reflecting surfaces and a spherical model of diffraction by the head. The fusion of direct and reflected signals at each ear results in interference patterns in binaural cues as a function of frequency. These cues are maximally modified at frequencies related to the delay between direct and reflected signals, and therefore to the spatial location of the sound source. Thus, natural binaural cues differ from anechoic cues. In particular, the range of interaural time differences is substantially larger than in anechoic environments. Reflections may potentially contribute binaural cues to distance and polar angle when the properties of the reflecting surface are known and stable, for example, for reflections on the ground.     

Atmospheric chemistry of HFE-7000 (i-C3F7OCH3) and isofluoro-propyl formate (i-C3F7OC(O)H): reactions with OH radicals,atmospheric lifetime and fate of alkoxy radical (i-C3F7OCH2O•) – a DFT study

ABSTRACT

The mechanism of hydrogen abstraction reaction between HFE-7000 (i-C₃F₇OCH₃) and OH radicals using M06-2X functional in conjunction with 6-31+G(d,p) basis set is investigated. The pre-reactive and post-reactive complexes from intrinsic reaction coordinate calculations are validated at entrance and exit channels, respectively. The standard enthalpies of formation for the species and bond dissociation energy for C–H bond are also estimated. The rate constants of the titled reactions over the temperature range of 250–450 K are reported. The OH-driven atmospheric life time of i-HFE-7000 is computed to be 3.19 years. The atmospheric fate of the alkoxy radical (i-C₃F₇OCH₂O^?) is also explored here for the first time. Three prominent plausible decomposition channels including oxidation are considered in detail. The thermochemical data reveal that reaction with O₂ is the dominant path for the decomposition of i-C₃F₇OCH₂O^? radical. Moreover, rate constant for the OH-initiated hydrogen abstraction of isofluoro-propyl formate (i-C₃F₇OC(O)H) is also reported.     

Phase matching,X-Ray topography,optical and thermal analysis of L-alanine cadmium chloride monohydrate: a nonlinear optical material

A potential semiorganic nonlinear optical material, L-alanine cadmium chloride monohydrate has been successfully synthesised and single crystals have been grown by slow evaporation solution growth technique at room temperature by using double distilled water as the solvent. The lattice dimensions of the grown crystal have been analysed by adopting powder X-ray diffraction technique and found that it crystallised in monoclinic system with space group C2. The crystalline perfection of the as-grown crystal has been assessed by high resolution X-ray diffraction and X-ray topography techniques and observed that the quality of the grown specimen is reasonably good. Its optical properties were examined by UV–Vis and photoluminescence techniques and found that there is no absorption in the entire visible range. Its functional groups were identified from FT-Raman and observed that there is no incorporation of other impurities during crystallisation. Its relative second harmonic generation efficiency has been tested with different particle size by Kurtz powder technique and found that within the coherence length the title compound is phase matchable. Its various thermal properties like thermal conductivity, specific heat, thermal effusivity, etc. have been evaluated by photopyroelectric technique and compared with other organic and inorganic materials. To confirm its piezoelectric response, its piezoelectric charge coefficient was measured using piezometer and found low. Its optical homogeneity as well as birefringence measurement of the grown specimen has been carried out by interferometric technique. The surface defects of the grown LACCM single crystal were analysed with etching at room temperature using water as an etchant.     

Novel localized waves and interaction solutions for a dimensionally reduced (2 + 1)-dimensional Boussinesq equation from N-soliton solutions

Nonlinear Dynamics - The Boussinesq equation has been of considerable interest in coastal and ocean engineering models for simulating surface water waves in shallow seas and harbors, tsunami wave...