The problem of a particle moving freely inside a box with rigid, perfectly reflecting walls is a standard exercise in basic quantum mechanics (QM), the box being taken to be a line interval, a ...square, and a cube, respectively, in the 1, 2, and 3 dimensional cases. The problem illustrates several aspects of QM, such as stationary states, uncertainty relations, eigenvalues, eigenfunctions, orthonormality, completeness, and so on. The purpose of this two-part article is to provide some insights into how the particle-in-a-box problem acts as a paradigm for the understanding of these and other aspects, such as the roles played by dimensionality, discrete and continuous symmetry, degeneracy, etc. Further, we shall also see (in Part 2) how the same problem leads directly to some non-trivial matters such as quantum chaos and deep results in mathematical physics. Finally, it must be emphasized that the particle-in-a-box problem is no longer just a theoretical exercise. With modern technology, it is physically realized in different kinds of nanostructures such as nanowires, atomic corrals, quantum dots, conjugated polymers, among others. This makes it all the more important to analyze various problems of this class and their solutions.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
The problem of a particle moving freely inside a region with rigid, perfectly reflecting walls serves as a paradigm to illustrate numerous aspects of quantum mechanics (QM). In Part 1
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of this ...two-part article, we discussed several of these aspects using, respectively, a line segment, a ring, and a square as the region concerned. In the present part, we shall consider the cases of a circular region and a surface of constant positive curvature (a sphere). We shall then comment on the general case of a dynamical billiard. Finally, we turn to the inverse problem: given the energy spectrum of a particle moving freely inside a region, what can be deduced about the geometrical properties of the region? Some important results in this regard will be described in brief.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Blowflies and houseflies are mechanical vectors inhabiting synanthropic environments around the world. They feed and breed in fecal and decaying organic matter, but the microbiome they harbour and ...transport is largely uncharacterized. We sampled 116 individual houseflies and blowflies from varying habitats on three continents and subjected them to high-coverage, whole-genome shotgun sequencing. This allowed for genomic and metagenomic analyses of the host-associated microbiome at the species level. Both fly host species segregate based on principal coordinate analysis of their microbial communities, but they also show an overlapping core microbiome. Legs and wings displayed the largest microbial diversity and were shown to be an important route for microbial dispersion. The environmental sequencing approach presented here detected a stochastic distribution of human pathogens, such as Helicobacter pylori, thereby demonstrating the potential of flies as proxies for environmental and public health surveillance.
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IZUM, KILJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
The analysis of phyllosphere microbiomes traditionally relied on DNA extracted from whole leaves. To investigate the microbial communities on the adaxial (upper) and abaxial (lower) leaf surfaces, ...swabs were collected from both surfaces of two garden plants, Rhapis excelsa and Cordyline fruticosa. Samples were collected at noon and midnight and at five different locations to investigate if the phyllosphere microbial communities change with time and location. The abaxial surface of Rhapis excelsa and Cordyline fruticosa had fewer bacteria in contrast to its adaxial counterpart. This observation was consistent between noon and midnight and across five different locations. Our co-occurrence network analysis further showed that bacteria were found almost exclusively on the adaxial surface while only a small group of leaf blotch fungi thrived on the abaxial surface. There are higher densities of stomata on the abaxial surface and these openings are vulnerable ports of entry into the plant host. While one might argue about the settling of dust particles and microorganisms on the adaxial surface, we detected differences in reactive chemical activities and microstructures between the adaxial and abaxial surfaces. Our results further suggest that both plant species deploy different defence strategies to deter invading pathogens on the abaxial surface. We hypothesize that chemical and mechanical defence strategies evolved independently for harnessing and controlling phyllosphere microbiomes. Our findings have also advanced our understanding that the abaxial leaf surface is distinct from the adaxial surface and that the reduced microbial diversity is likely a consequence of plant-microbe interactions.
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DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
The atmosphere is vastly underexplored as a habitable ecosystem for microbial organisms. In this study, we investigated 795 timeresolved metagenomes from tropical air, generating 2.27 terabases of ...data. Despite only 9 to 17% of the generated sequence data currently being assignable to taxa, the air harbored a microbial diversity that rivals the complexity of other planetary ecosystems. The airborne microbial organisms followed a clear diel cycle, possibly driven by environmental factors. Interday taxonomic diversity exceeded day-to-day and month-to-month variation. Environmental time series revealed the existence of a large core of microbial taxa that remained invariable over 13 mo, thereby underlining the longterm robustness of the airborne community structure. Unlike terrestrial or aquatic environments, where prokaryotes are prevalent, the tropical airborne biomass was dominated by DNA from eukaryotic phyla. Specific fungal and bacterial species were strongly correlated with temperature, humidity, and CO₂ concentration, making them suitable biomarkers for studying the bioaerosol dynamics of the atmosphere.
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BFBNIB, NMLJ, NUK, PNG, SAZU, UL, UM, UPUK
We have examined both single and entangled two-mode multiphoton coherent states and shown how the 'Janus-faced' properties between two partner states are mirrored in appropriate tomograms. Entropic ...squeezing, quadrature squeezing and higher-order squeezing properties for a wide range of nonclassical states are estimated directly from tomograms. We have demonstrated how squeezing properties of two-mode entangled states produced at the output port of a quantum beamsplitter are sensitive to the relative phase between the reflected and transmitted fields. This feature allows for the possibility of tuning the relative phase to enhance squeezing properties of the state. Finally, we have examined the manner in which decoherence affects squeezing and the changes in the optical tomogram of the state due to interaction with the environment.
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BFBNIB, GIS, IJS, KISLJ, NUK, PNG, UL, UM, UPUK
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