Quantum phase analysis with quantum trajectories: A step towards the creation of a Bohmian thinking

We introduce a pedagogical discussion on Bohmian mechanics and its physical implications in connection with the important role played by the quantum phase in the dynamics of quantum processes. In particular, we focus on phenomena such as quantum coherence, diffraction, and interference, due to their historical relevance in the development of the quantum theory and their key role in a myriad of fundamental and applied problems of current interest.Comment: 10 pages, 5 figure

Interplay of causticity and vorticality within the complex quantum Hamilton-Jacobi formalism

Interference dynamics is analyzed in the light of the complex quantum Hamilton-Jacobi formalism, using as a working model the collision of two Gaussian wave packets. Though simple, this model nicely shows that interference in quantum scattering processes gives rise to rich dynamics and trajectory topologies in the complex plane, both ruled by two types of singularities: caustics and vortices, where the former are associated with the regime of free wave-packet propagation, and the latter with the collision (interference) process. Furthermore, an unambiguous picture connecting the complex and real frameworks is also provided and discussed.Comment: 12 pages, 3 figure

A trajectory-based understanding of quantum interference

Interference is one of the most fundamental features which characterizes quantum systems. Here we provide an exhaustive analysis of the interfere dynamics associated with wave-packet superpositions from both the standard quantum-mechanical perspective and the Bohmian one. From this analysis, clear and insightful pictures of the physics involved in this kind of processes are obtained, which are of general validity (i.e., regardless of the type of wave packets considered) in the understanding of more complex cases where interference is crucial (e.g., scattering problems, slit diffraction, quantum control scenarios or, even, multipartite interactions). In particular, we show how problems involving wave-packet interference can be mapped onto problems of wave packets scattered off potential barriers.Comment: 27 pages, 12 figures (shortened version

Adsorbate surface diffusion: The role of incoherent tunneling in light particle motion

The role of incoherent tunneling in the diffusion of light atoms on surfaces is investigated. With this purpose, a Chudley-Elliot master equation constrained to nearest neighbors is considered within the Grabert-Weiss approach to quantum diffusion in periodic lattices. This model is applied to recent measurements of atomic H and D on Pt(111), rendering friction coefficients that are in the range of those available in the literature for other species of adsorbates. A simple extension of the model has also been considered to evaluate the relationship between coverage and tunneling, and therefore the feasibility of the approach. An increase of the tunneling rate has been observed as the surface coverage decreases.Comment: 7 pages, 2 figures; important reorganization of the work (including title changes

Phonon lineshapes in atom-surface scattering

Phonon lineshapes in atom-surface scattering are obtained from a simple stochastic model based on the so-called Caldeira-Leggett Hamiltonian. In this single-bath model, the excited phonon resulting from a creation or annihilation event is coupled to a thermal bath consisting of an infinite number of harmonic oscillators, namely the bath phonons. The diagonalization of the corresponding Hamiltonian leads to a renormalization of the phonon frequencies in terms of the phonon friction or damping coefficient. Moreover, when there are adsorbates on the surface, this single-bath model can be extended to a two-bath model accounting for the effect induced by the adsorbates on the phonon lineshapes as well as their corresponding lineshapes.Comment: 14 pages, 2 figure

Understanding interference experiments with polarized light through photon trajectories

Bohmian mechanics allows to visualize and understand the quantum-mechanical behavior of massive particles in terms of trajectories. As shown by Bialynicki-Birula, Electromagnetism also admits a hydrodynamical formulation when the existence of a wave function for photons (properly defined) is assumed. This formulation thus provides an alternative interpretation of optical phenomena in terms of photon trajectories, whose flow yields a pictorial view of the evolution of the electromagnetic energy density in configuration space. This trajectory-based theoretical framework is considered here to study and analyze the outcome from Young-type diffraction experiments within the context of the Arago-Fresnel laws. More specifically, photon trajectories in the region behind the two slits are obtained in the case where the slits are illuminated by a polarized monochromatic plane wave. Expressions to determine electromagnetic energy flow lines and photon trajectories within this scenario are provided, as well as a procedure to compute them in the particular case of gratings totally transparent inside the slits and completely absorbing outside them. As is shown, the electromagnetic energy flow lines obtained allow to monitor at each point of space the behavior of the electromagnetic energy flow and, therefore, to evaluate the effects caused on it by the presence (right behind each slit) of polarizers with the same or different polarization axes. This leads to a trajectory-based picture of the Arago-Fresnel laws for the interference of polarized light.Comment: 36 pages, 6 figure

Long non-coding RNAs and GATA4-FOG2 interaction cardiomyocyte hypertrophy

Sydämen vasemman kammion hypertrofia (engl. left ventricular hypertrophy, LVH) on seurausta sydänlihassolujen, eli kardiomyosyyttien koon kasvamisesta vastineena kohonneeseen työtaakkaan. Kardiomyosyyteillä on häviävän pieni jakautumiskyky, ja siksi hypertrofinen kasvu on käytännössä niiden ainoa tapa vastata suuremman työtaakan vaatimuksiin. Pitkällä tähtäimellä LVH kuitenkin aiheuttaa suurempia ongelmia, kuten sydämen vajaatoimintaa ja kohonnutta sydäninfarktin riskiä. Kohonnut verenpaine on yleisin LVH:n aiheuttaja, minkä vuoksi lääkehoito nojautuukin pitkälti verenpainelääkkeisiin. Niillä voidaan vähentää sydämen työtaakkaa ja siten lievittää oireita, mutta ne eivät korjaa syntyneitä vaurioita. Solutason signalointijärjestelmien ymmärtäminen on olennaista tulevaisuuden lääkekehityksessä LVH:ta vastaan. Geenien ilmentymisen säätely on monimutkainen prosessi, johon kuuluu muutakin kuin pelkästään DNA:n translaatio proteiiniksi. Tässä erikoistyössä keskityttiin kahteen tähän ilmiöön vaikuttavaan tekijään: pitkät ei-koodaavat RNAt (engl. long non-coding RNA, lncRNA) sekä transkriptiotekijät GATA4 ja FOG2. LncRNA:t ovat yli 200 nukleotidiä pitkiä RNA-sekvenssejä, jotka eivät itsessään koodaa mitään tiettyä proteiinia, vaan hienosäätävät muiden geenien ilmentymistä ja toimintaa. Tiettyä lncRNA:ta esiintyy pääasiassa vain tietyssä elimessä tai kudoksessa, minkä vuoksi ne ovat kiinnostavia lääkekehityksen kannalta. Tutkimusryhmämme on aiemmin tunnistanut joukon kardiomyosyyttispesifisiä lncRNA:ita, joiden ilmentyminen vastasyntyneillä hiirillä noudattaa samanlaista kaavaa syntymää seuraavina päivinä ja viikkoina. Tässä erikoistyössä niistä valikoitiin kolme, joiden ilmentymistä hiljennettiin vastasyntyneiden hiirten kardiomyosyyteissä samanaikaisesti altistamalla niitä hypertrofiselle stimulaatiolle. Tavoitteena oli tutkia, onko näillä lncRNA:illa vaikutusta apoptoosiin ja hypertrofiseen vasteeseen kardiomyosyyteissä. Transkriptiotekijät ovat proteiineja, joiden toiminnot ovat osin samanlaisia kuin lncRNA:iden: ne säätelevät kohde-elimensä geenien ilmentymistä eri olosuhteissa. GATA4 on tärkeä transkriptiotekijä sydämessä, sillä sen kohteisiin lukeutuu monia kardiomyosyyttien kehitykseen ja toiminnan ylläpitämiseen liittyviä geenejä. FOG2 on GATA4:n kofaktori; niiden yhteisvaikutus säätelee GATA4:n aktiivisuutta. Tutkimusryhmämme on aiemmin kehittänyt kymmeniä GATA4:n ja NKX2-5:n, toisen sydämessä keskeisen transkriptiotekijän, väliseen interaktioon vaikuttavia yhdisteitä. Erikoistyön toisessa osassa pyrittiin asettamaan ja optimoimaan koeasetelma yhdisteiden vaikutuksien GATA4:n ja FOG2:n vuorovaikutukseen seulomiseksi. Tuloksien perusteella hypertrofinen vaste ei muuttunut lncRNAita hiljennettäessä. On kuitenkin mahdollista, että kaikkia vaikutuksia ei voinut havaita käytetyillä menetelmillä, minkä vuoksi muiden koeasetelmien kokeileminen voisi tuottaa lisätietoa aiheesta. Tutkittavilla lncRNA:illa ei ollut vaikutusta apoptoosiin. GATA4-FOG2-interaktiokokeiden perusteella transfektoimalla COS-1 soluja suhteessa 10:1 GATA4- ja FOG2-plasmideilla saadaan yhdisteiden testaamiseen sopiva signaali. Alustavien tulosten perusteella yhdisteillä saattaa olla vaikutusta GATA4-FOG2-interaktioon, mutta ennen johtopäätösten tekemistä on tehtävä lisää tutkimuksia.Left ventricular hypertrophy (LVH) takes place when cardiomyocytes respond to excessive stress by growing in size. Cardiomyocytes have a very marginal capability to proliferate, which is why hypertrophic growth is almost their only option to meet the requirements of increased workload. In the long run, however, LVH leads to further problems, such as cardiac failure and an increased risk of myocardial infarction. Hypertension is the most prevalent cause of LVH, and its current treatment relies on antihypertensive drugs. They decrease the workload of the heart and therefore alleviate symptoms but have very little effect on the built damage and remodeling. Understanding the details of cellular level signaling pathways and genetic expression in LVH is crucial for future drug development. Regulation of gene expression is a very complex process, which involves more than just DNA being translated into a protein. In this project, two types of factors participating in this regulation were in focus: long non-coding RNAs (lncRNA) and transcription factors GATA4 and FOG2. LncRNAs are RNA sequences of more than 200 nucleotides that do not code for any protein final products themselves but are involved in chromatin remodeling as well as transcriptional and post-transcriptional gene regulation. They are highly organ-selective, which makes them potential targets for drug development. Our group has previously found a selection of cardiomyocyte-selective lncRNAs, which share a similar expression pattern in neonatal mouse hearts. In this project, three of them were silenced in a primary cardiomyocyte culture while simultaneously hormonally inducing hypertrophy. The goal was to see whether these lncRNAs have an effect on the hypertrophic response and apoptosis in the cardiomyocytes. Transcription factors are proteins with partially similar activities to lncRNAs; they regulate, which genes are expressed under certain circumstances. GATA4 is an important transcription factor in the heart as it targets various developmental and functional genes in cardiomyocytes. FOG2 is a cofactor of GATA4; interaction between them regulates the activity of GATA4. Our group has recently developed a selection of compounds that affect protein-protein interaction between GATA4 and NKX2-5, another important transcription factor. The second part of the project was to set up and optimize a compound screening assay for GATA4-FOG2 interaction. The results showed no change in hypertrophic response when the lncRNAs were silenced. Other experimental designs could still reveal if they have effects that could not be seen with these protocols. The silencing had no effect on apoptosis. As for the GATA4-FOG2 interaction experiments, transfecting COS-1 with GATA4 and FOG2 plasmids in a ratio of 10:1 resulted in a signal suitable for compound screening. Initial compound screening results indicated the compounds may have an effect on GATA4-FOG2 interaction, but further studies are needed before drawing conclusions