1.
Switzerland
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Switzerland, officially the Swiss Confederation, is a federal republic in Europe. It consists of 26 cantons, and the city of Bern is the seat of the federal authorities. The country is situated in western-Central Europe, and is bordered by Italy to the south, France to the west, Germany to the north, and Austria and Liechtenstein to the east. Switzerland is a country geographically divided between the Alps, the Swiss Plateau and the Jura, spanning an area of 41,285 km2. The establishment of the Old Swiss Confederacy dates to the medieval period, resulting from a series of military successes against Austria. Swiss independence from the Holy Roman Empire was formally recognized in the Peace of Westphalia in 1648. The country has a history of armed neutrality going back to the Reformation, it has not been in a state of war internationally since 1815, nevertheless, it pursues an active foreign policy and is frequently involved in peace-building processes around the world. In addition to being the birthplace of the Red Cross, Switzerland is home to international organisations. On the European level, it is a member of the European Free Trade Association. However, it participates in the Schengen Area and the European Single Market through bilateral treaties, spanning the intersection of Germanic and Romance Europe, Switzerland comprises four main linguistic and cultural regions, German, French, Italian and Romansh. Due to its diversity, Switzerland is known by a variety of native names, Schweiz, Suisse, Svizzera. On coins and stamps, Latin is used instead of the four living languages, Switzerland is one of the most developed countries in the world, with the highest nominal wealth per adult and the eighth-highest per capita gross domestic product according to the IMF. Zürich and Geneva have each been ranked among the top cities in the world in terms of quality of life, with the former ranked second globally, according to Mercer. The English name Switzerland is a compound containing Switzer, a term for the Swiss. The English adjective Swiss is a loan from French Suisse, also in use since the 16th century. The name Switzer is from the Alemannic Schwiizer, in origin an inhabitant of Schwyz and its associated territory, the Swiss began to adopt the name for themselves after the Swabian War of 1499, used alongside the term for Confederates, Eidgenossen, used since the 14th century. The data code for Switzerland, CH, is derived from Latin Confoederatio Helvetica. The toponym Schwyz itself was first attested in 972, as Old High German Suittes, ultimately related to swedan ‘to burn’
2.
ETH Zurich
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ETH Zurich is a science, technology, engineering and mathematics university in the city of Zürich, Switzerland. ETH Zurich is consistently ranked among the top universities in the world, twenty-one Nobel Prizes have been awarded to students or professors of the Institute in the past, the most famous of whom was Albert Einstein. It is a member of the IDEA League and the International Alliance of Research Universities. ETH was founded in 1854 by the Swiss Confederation and began giving its first lectures in 1855 as a polytechnic institute and it is locally still known as Poly, derived from the original name Eidgenössische polytechnische Schule, which translates to Federal Polytechnic School. ETH is an institute, whereas the University of Zürich is a cantonal institution. In the beginning, both universities were co-located in the buildings of the University of Zürich, from 1905 to 1908, under the presidency of Jérôme Franel, the course program of ETH was restructured to that of a real university and ETH was granted the right to award doctorates. In 1909 the first doctorates were awarded, in 1911, it was given its current name, Eidgenössische Technische Hochschule. In 1924, another reorganization structured the university in 12 departments, however, it now has 16 departments. ETH Zurich, the EPFL, and four associated research institutes form the ETH Domain with the aim of collaborating on scientific projects, ETH Zurich is ranked among the top universities in the world. Historically, ETH Zurich has achieved its reputation particularly in the fields of chemistry, there are 21 Nobel Laureates who are associated with ETH. The most recent Nobel Laureate is Richard F, heck who was awarded the Nobel Prize in chemistry in 2010. Albert Einstein is perhaps its most famous alumnus, in 2016, the QS World University Rankings placed ETH Zurich at 8th overall in the world. In 2015, ETH also ranked 6th in the world in Natural Sciences, ETH Zurich had an budget of 1.712 billion CHF in the year 2015 to support its cutting-edge research. For Swiss students, ETH is not selective in its admission procedures. Like every public university in Switzerland, ETH is obliged to grant admission to every Swiss resident who took the Matura, an applicant can be admitted to ETH even without any verifiable educational records by passing the comprehensive entrance exam. As at all universities in Switzerland, the year is divided into two semesters. Examinations are often held during examination sessions which are immediately before the beginning of the next semester, after the first year of study, bachelor students must pass a block examination of all courses taken in the first year, called the Basisprüfung. If the weighted average score is not sufficient, a student is required to retake the entire Basisprüfung which usually means having to re-sit the whole first year
3.
Leipzig University
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Leipzig University, in Leipzig in the Free State of Saxony, Germany, is one of the worlds oldest universities and the second-oldest university in Germany. Famous alumni include Leibniz, Goethe, Ranke, Nietzsche, Wagner, Angela Merkel, Raila Odinga, Tycho Brahe, and nine Nobel laureates are associated with the university. The university was founded on December 2,1409 by Frederick I, Elector of Saxony and his brother William II, Margrave of Meissen, since its inception, the university has engaged in teaching and research for over 600 years without interruption. The university was modelled on the University of Prague, from which the German-speaking faculty members withdrew to Leipzig after the Jan Hus crisis, the Alma mater Lipsiensis opened in 1409, after it had been officially endorsed by Pope Alexander V in his Bull of Acknowledgment on. Its first rector was Johann von Münsterberg, from its foundation, the Paulinerkirche served as the university church. After the Reformation, the church and the buildings were donated to the university in 1544. As many European universities, the university of Leipzig was structured into colleges responsible for organising accommodation, among the colleges of Leipzig were the Small College, the Large College, the Red College, the College of our Lady and the Pauliner-College. There were also private residential halls, the colleges had jurisdiction over their members. The college structure was abandoned later and today only the names survive, during the first centuries, the university grew slowly and was a rather regional institution. This changed, however, during the 19th century when the university became an institution of higher education. At the end of the 19th century, important scholars such as Bernhard Windscheid, Leipzig University was one of the first German universities to allow women to register as guest students. At its general assembly in 1873, the Allgemeiner Deutscher Frauenverein thanked the University of Leipzig and this was the year that the first woman in Germany obtained her JD, Johanna von Evreinov. Many of the alumni became important scientists. Under Nazi rule many Jews degrees were cancelled, some were reinstated as Karl-Marx University degrees by the GDR. The university was open throughout World War II, even after the destruction of its buildings. After the destruction of most of the buildings and the majority of its libraries and this is what must be preserved as the great repository of value in the university. By the end of the war 60 per cent of the buildings and 70 per cent of its books had been destroyed. The university reopened after the war on February 5,1946, in 1948 the freely elected student council was disbanded and replaced by Free German Youth members
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Nuclear magnetic resonance
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Nuclear magnetic resonance is a physical phenomenon in which nuclei in a magnetic field absorb and re-emit electromagnetic radiation. NMR allows the observation of quantum mechanical magnetic properties of the atomic nucleus. Many scientific techniques exploit NMR phenomena to study physics, crystals. NMR is also used in advanced medical imaging techniques, such as in magnetic resonance imaging. The most commonly studied nuclei are 1H and 13C, although nuclei from isotopes of other elements have been studied by high-field NMR spectroscopy as well. A key feature of NMR is that the frequency of a particular substance is directly proportional to the strength of the applied magnetic field. Since the resolution of the technique depends on the magnitude of magnetic field gradient, many efforts are made to develop increased field strength. The effectiveness of NMR can also be improved using hyperpolarization, and/or using two-dimensional, three-dimensional and higher-dimensional multi-frequency techniques, the principle of NMR usually involves two sequential steps, The alignment of the magnetic nuclear spins in an applied, constant magnetic field B0. The perturbation of this alignment of the nuclear spins by employing an electro-magnetic, the required perturbing frequency is dependent upon the static magnetic field and the nuclei of observation. The two fields are chosen to be perpendicular to each other as this maximizes the NMR signal strength. The resulting response by the magnetization of the nuclear spins is the phenomenon that is exploited in NMR spectroscopy. NMR phenomena are also utilized in low-field NMR, NMR spectroscopy and MRI in the Earths magnetic field, in 1946, Felix Bloch and Edward Mills Purcell expanded the technique for use on liquids and solids, for which they shared the Nobel Prize in Physics in 1952. Yevgeny Zavoisky likely observed nuclear magnetic resonance in 1941, well before Felix Bloch and Edward Mills Purcell, russell H. Varian filed the Method and means for correlating nuclear properties of atoms and magnetic fields, U. S. Patent 2,561,490 on July 24,1951, Varian Associates developed the first NMR unit called NMR HR-30 in 1952. Purcell had worked on the development of radar during World War II at the Massachusetts Institute of Technologys Radiation Laboratory. His work during that project on the production and detection of radio frequency power, when this absorption occurs, the nucleus is described as being in resonance. Different atomic nuclei within a molecule resonate at different frequencies for the magnetic field strength. The observation of magnetic resonance frequencies of the nuclei present in a molecule allows any trained user to discover essential chemical and structural information about the molecule
5.
Magnon
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A magnon is a quasiparticle, a collective excitation of the electrons spin structure in a crystal lattice. In the equivalent wave picture of quantum mechanics, a magnon can be viewed as a spin wave. Magnons carry a fixed amount of energy and lattice momentum, and are spin-1, the concept of a magnon was introduced in 1930 by Felix Bloch in order to explain the reduction of the spontaneous magnetization in a ferromagnet. At absolute zero temperature, a Heisenberg ferromagnet reaches the state of lowest energy, as the temperature increases, more and more spins deviate randomly from the alignment, increasing the internal energy and reducing the net magnetization. Each magnon reduces the total spin along the direction of magnetization by one unit of ℏ and the magnetization by γ ℏ, where γ is the gyromagnetic ratio. This leads to Blochs law for the dependence of spontaneous magnetization, M = M0 where T c is the critical temperature. The quantitative theory of magnons, quantized spin waves, was developed further by Theodore Holstein, Henry Primakoff, using the second quantization formalism they showed that magnons behave as weakly interacting quasiparticles obeying Bose–Einstein statistics. A comprehensive treatment can be found in the state textbook by Charles Kittel or the early review article by Van Kranendonk. Direct experimental detection of magnons by inelastic neutron scattering in ferrite was achieved in 1957 by Bertram Brockhouse, since then magnons have been detected in ferromagnets, ferrimagnets, and antiferromagnets. The fact that magnons obey the Bose–Einstein statistics was confirmed by the scattering experiments done during the 1960s through the 1980s. Classical theory predicts equal intensity of Stokes and anti-Stokes lines, Bose–Einstein condensation of magnons was proven in an antiferromagnet at low temperatures by Nikuni et al. and in a ferrimagnet by Demokritov et al. at room temperature. Recently Uchida et al. reported the generation of spin currents by surface plasmon resonance, paramagnons are magnons in magnetic materials which are in their high temperature, disordered phase. For low enough temperatures, the local magnetic moments in ferromagnetic or anti-ferromagnetic compounds will become ordered. Small oscillations of the moments around their natural direction will propagate as waves, at temperatures higher than the critical temperature, long range order is lost, but spins will still align locally in patches, allowing for spin waves to propagate for short distances. These waves are known as a paramagnon, and undergo diffusive transport, magnon behavior can be studied with a variety of scattering techniques. Magnons behave as a Bose gas with no chemical potential, microwave pumping can be used to excite spin waves and create additional non-equilibrium magnons which thermalize into phonons. At a critical density, a condensate is formed, which appears as the emission of monochromatic microwaves and this microwave source can be tuned with an applied magnetic field. Kittel, Introduction to Solid State Physics, 7th edition, Bloch, F. Zur Theorie des Ferromagnetismus
6.
Domain wall (magnetism)
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A domain wall is a term used in physics which can have similar meanings in magnetism, optics, or string theory. These phenomena can all be described as topological solitons which occur whenever a discrete symmetry is spontaneously broken. In magnetism, a wall is an interface separating magnetic domains. It is a transition between different magnetic moments and usually undergoes a displacement of 90° or 180°. A domain wall is a gradual reorientation of individual moments across a finite distance, the domain wall thickness depends on the anisotropy of the material, but on average spans across around 100–150 atoms. The energy of a wall is simply the difference between the magnetic moments before and after the domain wall was created. This value is expressed as energy per unit wall area. The anisotropy energy is lowest when the magnetic moments are aligned with the crystal lattice axes thus reducing the width of the domain wall. Conversely, the energy is reduced when the magnetic moments are aligned parallel to each other and thus makes the wall thicker. In the end an equilibrium is reached between the two and the walls width is set as such. An ideal domain wall would be independent of position, but the structures are not ideal and so get stuck on inclusion sites within the medium. These include missing or different atoms, oxides, insulators and even stresses within the crystal and this prevents the formation of domain walls and also inhibits their propagation through the medium. Thus a greater applied magnetic field is required to overcome these sites, note that the magnetic domain walls are exact solutions to classical nonlinear equations of magnets. Since domain walls can be considered as thin layers, their symmetry is described by one of the 528 magnetic layer groups, to determine the layers physical properties, a continuum approximation is used which leads to point-like layer groups. If continuous translation operation is considering as identity, these groups transform to magnetic point groups and it was shown that there are 125 such groups. It was found if a magnetic point group is pyroelectric and/or pyromagnetic then the domain wall carries polarization and/or magnetization respectively. These criteria were derived from the conditions of the appearance of the uniform polarization and/or magnetization, after their application to any inhomogeneous region, they predict the existence of even parts in functions of the distribution of order parameters. Identification of the odd parts of these functions was formulated based on symmetry transformations that interrelate domains
7.
Bloch wave
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A Bloch wave, named after Swiss physicist Felix Bloch, is a type of wavefunction for a particle in a periodically-repeating environment, most commonly an electron in a crystal. In other words, if you multiply a plane wave by a periodic function, Bloch waves are important because of Blochs theorem, which states that the energy eigenstates for an electron in a crystal can be written as Bloch waves. This fact underlies the concept of electronic band structures, within a band, ψn k varies continuously with k, as does its energy. Also, for any lattice vector K, ψn k = ψn. Therefore, all distinct Bloch waves occur for k-values within the first Brillouin zone of the reciprocal lattice, the most common example of Blochs theorem is describing electrons in a crystal. However, a Bloch-wave description applies more generally to any wave-like phenomenon in a periodic medium, for example, a periodic dielectric in electromagnetism leads to photonic crystals, and a periodic acoustic medium leads to phononic crystals. It is generally treated in the forms of the dynamical theory of diffraction. Suppose an electron is in a Bloch state ψ = e i k ⋅ r u, the actual quantum state of the electron is entirely determined by ψ, not k or u directly. This is important because k and u are not unique, specifically, if ψ can be written as above using k, it can also be written using, where K is any reciprocal lattice vector. Therefore, wave vectors that differ by a lattice vector are equivalent. The first Brillouin zone is a set of k-vectors with the property that no two of them are equivalent, yet every possible k is equivalent to one vector in the first Brillouin zone. Therefore, if we restrict k to the first Brillouin zone, therefore, the first Brillouin zone is often used to depict all of the Bloch states without redundancy, for example in a band structure, and it is used for the same reason in many calculations. When k is multiplied by the reduced Plancks constant, it equals the electrons crystal momentum, related to this, the group velocity of an electron can be calculated based on how the energy of a Bloch state varies with k, for more details see crystal momentum. For a detailed example in which the consequences of Blochs theorem are worked out in a specific situation, see the article, Particle in a one-dimensional lattice. The defining property of a crystal is translational symmetry, which means if the crystal is shifted an appropriate amount. A three-dimensional crystal has three primitive lattice vectors a1, a2, a3, another helpful ingredient in the proof is the reciprocal lattice vectors. These are three vectors b1, b2, b3, with the property that ai · bi = 2π, let T ^ n 1, n 2, n 3 denote a translation operator that shifts every wave function by the amount n1a1 + n2a2 + n3a3. The following fact is helpful for the proof of Blochs theorem, Lemma, If a wavefunction ψ is an eigenstate of all of the translation operators, proof, Assume that we have a wavefunction ψ which is an eigenstate of all the translation operators
8.
Bloch sphere
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In quantum mechanics, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system, named after the physicist Felix Bloch. Quantum mechanics is formulated in Hilbert space or projective Hilbert space. The space of states of a quantum system is given by the one-dimensional subspaces of the corresponding Hilbert space. For a two-dimensional Hilbert space, this is simply the complex projective line ℂℙ1, the Bloch sphere is a unit 2-sphere, with each pair of antipodal points corresponding to mutually orthogonal state vectors. The points on the surface of the sphere correspond to the states of the system. The Bloch sphere may be generalized to a quantum system. In optics, the Bloch sphere is known as the Poincaré sphere. 6 common polarization types exist and are called Jones Vectors, the natural metric on the Bloch sphere is the Fubini–Study metric. The mapping from the unit 3-sphere in the state space ℂ2 to the Bloch sphere is the Hopf fibration. Since only the phase between the coefficients of the two basis vectors has any physical meaning, we can take the coefficient of |0 ⟩ to be real. We also know from quantum mechanics that the probability of the system has to be one, ⟨ ψ | ψ ⟩ =1. Except in the case where | ψ ⟩ is one of the ket vectors |0 ⟩ or |1 ⟩, for mixed states, one considers the density operator. Any two-dimensional density operator ρ can be expanded using the identity I and the Hermitian, traceless Pauli matrices σ →, ρ =12 =12 and it is this vector that indicates the point within the sphere that corresponds to a given mixed state. Specifically, as a feature of the Pauli vector, the eigenvalues of ρ are 12. Density operators must be positive-semidefinite, so we conclude that | a → | ≤1, for pure states, we must then have t r =12 =1 ⇔ | a → | =1, in accordance with the above. As a consequence, the surface of the Bloch sphere represents all the states of a two-dimensional quantum system. This basis is used in laser theory, where w is known as the population inversion. Consider an n-level quantum mechanical system and this system is described by an n-dimensional Hilbert space Hn
