We have seen that we can understand matter with increasing complexity from the simple two-level system up to molecules. We further studied, how they can be control by classical electromagnetic fields to a very high accuracy. In the last lecture we also studied how we can understand the electromagnetic field as an ensemble of quantum mechanical photon modes. So in today’s lecture we will focus on the interaction between atoms and light, which is in a particularly clean set-up, namely cavity quantum electrodynamics. The fundamental ingredients are sketched in Fig. [305911].

We will study the existance of vibrational and rotational levels in molecules. It allows us investigate the transitions of molecules and introduce the Franck-Condon principle. Finally, we will study how such intruiging molecules are used for the study of the permanent electric dipole moment of the electron.

In this lecture we will discuss a systematic approach to build up molecules from more complex atoms.

In the last lecture we have seen that we can typically treat complex atomic systems within the central field approximation. &&=& {2} ^2_{_i} + V_ (r_i) \right)}_{_0} + \left( {r_{ij}} - S(r_i) \right)}_{_1} So we we can can treat atoms through the shell structure known from the atom, but the screening lifts the l degeneracy. For a single outer electron, we have even seen how this screening can be described by the quantum defect. We would now like to go beyond this simple picture and discuss the following questions: - How should the residual term $_1$ be taken into account? - How do we properly take into account the Pauli principle ? - How can we treat the fine-splitting ? ON THE RESIDUAL COUPLING If we ignore the residual coupling, we obtain a spherically symmetric problem, which implies that the angular momentum $_i$ of each electron is conserved. This conservation will be broken by $_{1}$. However, these forces are internal, which implies that the total angular momentum $ = \sum_i _i$ is conserved. So we should label the states in the complex Hamiltonian by $$. The total angular momentum will then set the symmetry of the spatial wavefunction. As already discussed in some detail for the He atom, this has wide-reaching consquence on the spin degree of freedom through exchange interaction. THE PAULI PRINCIPLE AND SPIN - According to the Pauli principle, each single-particle state can be occupied only by one electron. After distributing all electrons over different single-particle eigenstates (“orbitals”), the resulting state needs to be fully antisymmetrized (Slater determinant). - There is a simplification for atoms with many electrons: The angular momenta and spins of a complete subshell with n,  l,  {m−l, ⋯, ml} add to zero and can be ignored in the further considerations (“shell structure”). Note that this is often broken in molecular binding! - Alkali atoms are the simplest atoms with shell structure: All but one _valence_ electron add to L = 0, S = 0. The ground state thus has L = 0, S = 1/2. - For more complex atoms, the valence electrons couple to a total orbital angular momentum L with a given symmetry according to particle exchange. Let us have a look at two examples for light atoms, starting with : - 1s² → L = 0, S = 0. The corresponding term is ¹S - 1s2s → L = 0, {S = 0, S = 1}. The corresponding terms are ¹S and ³S. . The electronic configuration of is: _{L=0,\,S=0} 3p^2 Per valence electron we have l = 1 and s = 1/2. So we get L = 0, 1, 2 and S = 0, 1. Here S = 1 means symmetry and S = 0 antisymmetry with respect to particle exchange. In principle we can form the following terms: ^1S,\,^3S,\,^1P,\,^3P,\,^1D,\,^3D Which of these terms can be fully antisymmetrized? Here, only the terms ¹S, ³P and ¹D fulfill Pauli’s principle. In general the exchange interaction (seen in the discussion of He), will then lower the energy of the states with high spins. Optional: Symmetry of the L states We can construct the following L-states for them: &= ^{l_1},^{m_{l_1}};^{l_2},^{m_{l_2}}} &= {} ( ^{m_{l_1}},^{m_{l_2}}} - ) &= {}(^{m_{l_1}},^{m_{l_2}}} - + ) The states and are symmetric and the state is antisymmetric with respect to particle exchange.

After our discussion of extremely simple atoms like hydrogen and helium, we will now discuss the most important properties of more complex atoms. We will see, how we can categorize them and discuss some of the general properties

We will finish our discussion of the Helium atom. Most importantly, we will dive into the strong separation between singlet and triplet states.

We will discuss the creation of entangled photons and how they can be used for the test of Bell's inequalities.

In this lecture we will use the hydrogen atom to study static perturbations in form of external magnetic fields and relativistic effects, leading to the fine structure splitting.

We will continue with some properties of the hydrogen atom. First compare it to the harmonic oscillator, then look into dipole transitions and end with the coupling to static magnetic fields.

In this lecture we will first discuss the diagonalization of the harmonic oscillator and then discuss the main properties of the hydrogen atom.

In the lecture, we will see how a time dependent coupling allows us to engineer a new Hamiltonian. Most importantly, we will discuss the resonant coupling of two levels and the decay of a single level to a continuum.

We are going to discuss the two-level system, it's static properties like level splitting at avoided crossings and dynamical properties like Rabi oscillations.

In this second lecture we will finish the discussion of the basic cooking recipes and discuss a few of the consequences like the uncertainty relation, the existance of wave packages and the Ehrenfest theorem.

In this first lecture we will review the foundations of quantum mechanics at the level of a cooking recipe. This will enable us to use them later for the discussion of the atomic structure and interaction between atoms and light.

IntroductionThermometer calibrationFollowing the method outlined in Ref. \cite{Fortune_2000}, we approximate the magnetic field and temperature dependence \(R\left(T,\ B\right)\) of a resistive thermometer using a linear combination of Chebyshev polynomials \(t_n\left(x\right)\) 

This is a preprint Journal Club review of Memory sequencing reveals heritable single cell gene expression programs associated with distinct cellular behaviors by Sydney M Shaffer, Benjamin L Emert, Ann E. Sizemore, Rohit Gupte, Eduardo Torre, Danielle S Bassett, and Arjun Raj. The preprint was originally posted on July 27, 2018 (DOI: https://doi.org/10.1101/379016).  Dear authors,Thank you for posting your work as a preprint on BioRxiv. We discussed your work at our latest quantitative and systems biology journal club at UCLA. Below is a summary of our feedback containing our main remarks, points of discussion, and suggestions.This study aimed to identify genes and groups of genes that exhibit memory persisting over multiple cell divisions. The authors hypothesized that any such genes would manifest phenotypically as rare cell subsets within a seemingly homogeneous population. To test their hypothesis, they developed a clever new method, termed MemorySeq, which adapts the classic Luria-Delbrück fluctuation experiment to examine gene expression at the genome scale. In this experiment, a clonal population of cells was passed through a bottleneck and gene expression was quantified by RNA sequencing. Genes that exhibited high inter-clonal expression variability were identified as exhibiting multi-generational memory. MemorySeq also allowed them to identify genes that conferred drug resistance, confirming that heritable expression can create specialized cell subsets. In general, the methods were innovative and well-suited to analyze gene expression heritability at the systems scale. The paper was very clearly written and the figures were, for the most part, well-presented. Our comments are outlined below. 

It is our great pleasure to welcome you to NRM18 - ‘Mapping Neuroreceptors at Work’. The meeting, established by Prof Albert Gjedde in 1997, represents a vibrant community of in vivo brain researchers deciphering the mysteries of the living human brain: exploring how CNS molecule - protein recognition makes us human – for better or for worse – in sickness and in health. This year’s meeting is no exception and brings together delegates from around the globe to discuss the latest advances and controversies in this constantly evolving field. A record-breaking number of attendees (ca. 300) will be joining the 2018 meeting at KCL Waterloo Campus in central London.In addition to keynote talks on ‘The Neurobiology of Beauty’ (Prof. Semir Zeki) and ‘Of Psychotic Mice and Men’ (Prof. Oliver Howes), the programme includes an impressive collection of the latest scientific research in the field, scheduled as oral and poster presentations. In order to maximise exposure of the submitted abstracts, we have also implemented two ‘rapid-fire’ sessions during the meeting. Other programme additions include the NRM18 ‘Grand Challenge’, a session on ‘Opportunities and Challenges for Total Body Imaging’ and a status update on the ‘Data Sharing Initiative’.In addition to enjoying an excellent scientific program, the conference dinner and entertainment on Wednesday will be held aboard the ‘Dixie Bell’ for a cruise along the river Thames, details of which will be provided during the meeting.The organization of NRM18 would not have been possible without the dedicated efforts of many individuals, including the local organising committee and administration, scientific advisory board, reviewers, session chairs, presenters, sponsors, exhibitors and supporters for their invaluable contribution to the conference. Most importantly we would like to thank YOU, the delegates, who never fail to provide lively scientific (and non-scientific) debate during the meeting. We hope you have a stimulating and enjoyable NRM18. Book of abstracts: https://authorea.com/users/242183/articles/323425/master/file/Book_of_abstracts_NRM.pdf

Abstract.Relatively unstructured expression of some preliminary thoughts about how a priori explanatory models of dynamic complex systems might be constructed outside of a canonical approach.Body.A canonical approach consists of inference that strictly follows from precisely defined concepts, or spatio-temporal maps, the variation from which is some kind of confounding error to form a new hypothesis. If precision, whether of a concept, or a mathematical relation, is not retained from one state of a system to another, then the canonical approach does not capture what is relevant (if there is a sense in which a system incorporates a model of itself, so there is some kind of repetition or homeostasis that can't be explained through a continuous model).What might questions associated with a non-canonical approach be?Defining where an analogue representation of a system within itself is possible (different dependencies of variables tending to be separable).If there is no possibility that these are separable, and an analogue representation of a system within itself cannot occur, then a system of coded representation would be necessary for a system to maintain these characteristics of homeostasis or repetition.As such, if a coded representation of a system are necessary within the system this may be explained by a mathematical model which answers the question of when differing dependencies of variables are separable.The inferential relation between parameters affecting the model may provide a guide for which principal components to look for in the data from such a system (this guide being a mathematical rather than a conceptual heuristic)

It is our great pleasure to welcome you to NRM18 - ‘Mapping Neuroreceptors at Work’. The meeting, established by Prof Albert Gjedde in 1997, represents a vibrant community of in vivo brain researchers deciphering the mysteries of the living human brain: exploring how CNS molecule - protein recognition makes us human – for better or for worse – in sickness and in health. This year’s meeting is no exception and brings together delegates from around the globe to discuss the latest advances and controversies in this constantly evolving field. A record-breaking number of attendees (ca. 300) will be joining the 2018 meeting at KCL Waterloo Campus in central London.In addition to keynote talks on ‘The Neurobiology of Beauty’ (Prof. Semir Zeki) and ‘Of Psychotic Mice and Men’ (Prof. Oliver Howes), the programme includes an impressive collection of the latest scientific research in the field, scheduled as oral and poster presentations. In order to maximise exposure of the submitted abstracts, we have also implemented two ‘rapid-fire’ sessions during the meeting. Other programme additions include the NRM18 ‘Grand Challenge’, a session on ‘Opportunities and Challenges for Total Body Imaging’ and a status update on the ‘Data Sharing Initiative’.In addition to enjoying an excellent scientific program, the conference dinner and entertainment on Wednesday will be held aboard the ‘Dixie Bell’ for a cruise along the river Thames, details of which will be provided during the meeting.The organization of NRM18 would not have been possible without the dedicated efforts of many individuals, including the local organising committee and administration, scientific advisory board, reviewers, session chairs, presenters, sponsors, exhibitors and supporters for their invaluable contribution to the conference. Most importantly we would like to thank YOU, the delegates, who never fail to provide lively scientific (and non-scientific) debate during the meeting. We hope you have a stimulating and enjoyable NRM18. Book of abstracts: https://authorea.com/users/242183/articles/323425/master/file/Book_of_abstracts_NRM.pdf

In this experiment we will find that the wavelength of light from a laser can be measured fairly well with the clever use of a ruler. This is a fine way to introduce more advanced forms of error propagation, as well as some introductory statistical analysis tools, to students in an upper division physics lab who are looking to understand the appropriate ways to interpret and report data. The evaluation methods used come directly from John R. Taylor's "An Introduction to Error Analysis" 

ABSTRACT Preferential trade agreements are meant to promote trade within the targeted region. Once such agreements are put into effect, it is interesting to investigate the impact and effectiveness in the targeted region. This paper analyzes world trade network as a graph and introduces the measure to evaluate a change in strength or degree of regional integration. The measure or index introduced also captures the contribution of member countries in the regional integration. INTRODUCTION The Number of preferential trade agreements has been increasing since the 1990s and has increased more than four-fold . Do preferential trade agreements foster trade between the member countries? This question has been as important today as it was when such agreements were formed. This paper analyzes world trade network data to answer this question. The main aim of such agreements is to foster mutual trade in the region and they are considered helpful for promoting the regional economic competitiveness as well. Whereas the impact of such agreements is not homogeneous across countries, the impact is large for industrialized nations and small for developing nations. Several measures of regional integration are devised and found in the literature . Intra-regional trade share ( Si ) measures the ratio of regions i intra-regional trade to total trade . Intraregional Trade Share, Intraregional Trade Intensity Index, and Regional Trade Introversion Index measure the degree of trade interdependence in a certain region . This paper analyze Regional Trade Integration Index and introduce an index, which measures the individual contribution of member countries in the given region. METHODOLOGY This paper introduces an index to study regional trade integration and examines trade data before and after the formation of such agreements. Collection of countries around the world and their trade relationship is represented by graph G(W, E) . W represents a set of all countries and E represents a set of all directed edges or all possible exports. Let eij represents the amount of export from country i to j country. REGIONAL TRADE INTEGRATION INDEX (RTII): This index is the ratio of the sum of exports of all member nations within the region to the sum of export of member nations outside the region. The index range from 0 to 1. Index 0 indicates the member countries do not export within region index 1 indicates the members in a group export everything to other group members. Let g(W′, E′) be a subgraph of G(W, E) and W′ ⊆ W and E′ ⊆ E. In real world, graph G(W, E) all countries in the world and their export relationship. And, subgraph g(W′, E′) represent some preferential trade agreements e.g. NAFTA. Regional Trade Integration Index (RTII) for subgraph g is calculated as Ig. $$I_g=}}e_{ij}}} {}e_{ij}}$$ Individual contribution to the regional integration is computed as Individual Contribution Index (ICI) $$ICI_g^{i}=}e_{ij}}} {}e_{ij}}$$ Where, ICIgi is the ICI for a country i in subgraph g. The weighted sum of Individual Contribution Index is equal to Regional Trade Integration Index . $$I_g = \sum}ICI_g^{i}$$ INDIVIDUAL TRADE INTEGRATION INDEX (ITII): The index indicates how integrated a country is in a certain or group. The index compares the country’s export within the region to export outside the region. Or, the index calculates the ratio of the sum of the export of a country to all another member country in a region to the sum of export of the country to all nations around the globe. This index range from 0 to 1. Integration index 0 indicates the country export within the region is 0 or the country doesn’t export at all to the member countries in the region. Integration index 1 indicates the country’s whole export is within the region and exports nothing outside the region. This paper introduces an integration index Igi, which represents the integration of a country i in some region g or trade agreement or subgraph is given by $$I^{i}_{g} = }{e_{ij}}}{\sum{e_{ij}}}$$ DISCUSSION This paper analyzes and investigates the trend of regional integration for regional trade agreements NAFTA. The ITII of a country with respect to a particular region indicates the country’s contribution to regional integration and RTII represents a ratio of the region’s export within the same region to export to all other countries. Figure [109874] shows RTII for the NAFTA region and the ITII for all countries in the that region. The figure shows RTII for the NAFTA region is almost at the same level in 1990 and 2016 with some fluctuations in between. RTII shown by the red solid line in the figure indicates, the percentage of trade export that NAFTA does within the region compared to all around the world. The RTII trend indicates gradual increment from the inception of NAFTA to downward trend particularly during the global financial slowdowns around the year 2008. The RTII was 0.430114 when the group was formed and reached up to 0.576939 in 2002, then decreased to 0.487429 in 2009, eventually follows an increasing trend after the financial crisis of 2008. Downward trend before 2008 and the upward trend after 1999 is noticeable. If we look at the individual countries ITII, Mexico’s the ITII index is highest among the three countries followed by Canada and the USA. Notably, the ITII is moving parallel for three nations.

En esta tarea se abordan problemas relacionados con los temas: vectores, momento de una fuerza y teorema de Varignon.

Popular culture has traditionally tended to paint a skewed image of the average marijuana user. The typical cannabis consumer – we've been led to believe by media imagery – is invariably a lazy, unmotivated millennial, often black, and typically living paycheck-to-paycheck. As cannabis becomes legalized and regulated across the nation, along with the implementation of seed-to-sale systems that track some consumer behavior at the point-of–sale, more information has become available to shed light on cannabis consumer behavior to help lawmakers and businesses make better informed decisions. What is so far resulting is a portrait of the cannabis industry retail landscape looking an awful lot like the same as the landscape for other retail generally.

This is a review of Carter, Helm et al. bioRxiv 374264; doi: https://doi.org/10.1101/374264 posted on July 23, 2018. In this paper, the authors showed that diverse barley cultivars are able to respond to the Pseudomonas syringae effector AvrPphB and they characterized  both the effector target (PBS1) and the receptor (PBR1) responsible for this recognition. Furthermore, their phylogenetic analyses revealed that the immune receptor involved in this response is not orthologous to a previously characterized receptor (RPS5) from Arabidopsis thaliana that has a functionally analogous AvrPphB recognition mechanism. This leads the authors to conclude that recognition of the AvrPphB protease has evolved independently in Arabidopsis and barley.