... the HLH family of proteins and binds to DNA as a heterodimer usually composed of USF1 and USF2 USF has been implicated in the regulation of many genes and normally acts as a transcriptional activator ... the deacetylation and inactivation ofthe embryonic domain This idea is supported by the data of Forsberg et al [89] showing that the pattern of histone acetylation across the globin locus varies ... regulation ofthe human b-globin locus focuses on the ability ofthe LCR to act as acenterof attraction for various regulatory activities found in the cellular milieu The LCR nucleates and perpetuates...
... and 16,000 lemmas from both European and American variants of Portuguese They are aligned with the translationally equivalent concepts ofthe English Princeton WordNet and, transitively, ofthe ... with the corresponding values for its inflectional features of Gender and Number, that resulted from its morphological analysis; lemmata — the lemmata (singular and masculine forms when available) ... upon HMMs with the help of TnT (Brants, 2000) It was trained over a manually annotated corpus of approximately 208,000 words, and evaluated against an unseen portion with approximately 52,000 words...
... mechanicsofa particle in a central potential Quantummechanicsofa particle in a central potential QuantumMechanicsofthe Hydrogen Atom Energy levels and eigenfunctions Sizes and Shapes Radiative ... Classical magnets Quantum magnets Magnetic energies and the Stern±Gerlach experiment Orbital Angular Momentum Classical orbital angular momentum Quantum orbital angular momentum Angular shape of ... togetherness of distant objects are that: (1) the initial state ofthe gloves is a superposition of right and left-handedness, in much the same way as the state ofaquantum particle can be a linear...
... potential U0 sin2 (k0 x) a wave packet in the n = band with a sharp distribution in q, and that we apply to the atom a constant extra force F = ma We recall the adiabatic theorem: suppose that a system ... on linearly the potential U0 until it reaches the value ER What is the condition on the time τ ofthe operation in order for the process to remain adiabatic? Calculate the minimal value of τ for ... = − The diagonalization ofthe matrix U0 −1 −1 gives the two eigenvalues 3U0 /4 and U0 /4, which means that the two bands n = and n = not touch each other anymore, but that they are separated...
... Delande for Quantum reflection of atoms on a surface” and Quantum motion in a periodic potential” Palaiseau, April 2005 Jean-Louis Basdevant Jean Dalibard Contents Summary ofQuantumMechanics ... given to the physical aspects ofthe phenomena rather than to analytical or computational considerations Many fundamental questions raised since the very beginnings ofquantum theory have received ... ofquantummechanics and its philosophical implications Teaching quantummechanics relies mostly on theoretical courses, which are illustrated by simple exercises often ofa mathematical character...
... Summary ofQuantumMechanics Measurement To a given physical quantity A one associates a self-adjoint (or Hermitian) ˆ operator A acting in the Hilbert space In a measurement ofthe quantity A, ... identical and independent, and are all prepared in the same state |ψ (we assume N 1) For N of them, we measure a physical quantity A, and for the N others , we measure a physical quantity B The ... Summary ofQuantumMechanics In the following pages we remind the basic definitions, notations and results ofquantummechanics Principles Hilbert Space The first step in treating aquantum physical...
... general case We will analyze the data obtained with nuclear reactors The average energy ofthe (anti-)neutrinos produced in reactors is E = MeV, with a dispersion ofthe same order In all what ... plane wave eik·r and a scattered wave Such a state is called a stationary scattering state The scattering amplitude f depends on the energy, on the incident direction u = k/k, and on the final ... the normalization factors ofthe states |i and |f ) Consider an atomic transition treated as a two-level system, an excited state |e and a ground state |g , separated by an energy hω and ¯ coupled...
... cavity Cold atoms Fig 2.1 Sketch ofthe principle of an atomic clock with an atomic fountain, using laser-cooled atoms 2.2 The Atomic Fountain 31 2.2 The Atomic Fountain The atoms are initially ... that H splits the ground state in two substates of energies E1 = E0 + Asn /2 and E2 = E0 − A( 1 + sn )/2 Recover the particular case ofthe hydrogen atom 2.1.4 What are the degeneracies ofthe ... modifies this ratio Naturally, this effect is taken into account in an accurate treatment ofthe data 1.2.5 For an energy of GeV, we have found that the minimum distance to observe the oscillation resulting...
... beam is along the y axis, the z axis is in the ABCD plane, and the x axis is perpendicular to this plane We assume that the spin variables and the space variables are uncorrelated, i.e at any ... gravitational effects 3.2.2 For an angle φ, we define the gravitational potential V to be V = along AC and V = V0 along BD (a) Calculate the difference ∆p ofthe neutron momenta in the beams AC and ... atom), these two eigenvalues are A/ 4 and − 3A/ 4 2.1.4 There are 2sn × matrices to be diagonalized, each of which gives a vector associated to Asn /2 and a vector associated to A( 1 + sn )/2 In addition...
... v and a? The existence of this width puts a limit on the accuracy ofthe measurement of ω0 , and therefore of γ Is there an explanation of this on general grounds? 4.1.3 On the path ofthe beam, ... important to locate the exact position ofthe maximum ofthe peak Multiplying the width ofthe peak by a factor a/ b ( since a b) results in a major improvement ofthe measurement accuracy Of course ... probability has a resonant behavior as a function ofthe applied angular frequency ω Plot P−+ as a function ofthe distance from the resonance ω − ω0 How does the width ofthe resonance curve vary...
... before the slit, and that the vertical extension δ ofthe beam on the detector is the sum ofthe width aofthe slit and the width ofthe diffraction peak Show that one can choose a in an optimal way ... space and in time The Stern–Gerlach experiment is actually a very good example ofa measuring apparatus in quantummechanics since it transfers quantum information – here the spin state ofthe ... ofthe field gradient, or the length ofthe apparatus, etc., but the particular combination ofthe product ofthe energy transferred to the system and the interaction time ofthe system with the...
... 7.1.3 Calculate the expectation value E ofthe energy ofthe electron after the decay One can for instance make use ofthe fact that: ψ0 | 1 |ψ0 = r a1 e2 ˆ ˆ H2 = H − r and Give the value of E ... Write the Hamiltonian ofthe relative motion ofthe two particles in terms of their separation r and their relative momentum p 8.1.3 What are the energy levels ofthe system, and their degeneracies? ... this calculated value of A? 8.2.5 Actually, the possibility that the electron and the positron can annihiˆ late, leads to an additional contribution HA in the hyperfine Hamiltonian One ˆ A does...
... 3.2, as a function ofthe field B ¿From now on, we assume that the field is weak, i.e |x| = |8¯ ω/( 7A) | h 1, and we shall make the corresponding approximations (a) What are, as a function of x, the ... ofthe static fields E0 and B0 Knowing that ωe is a function ofthe principal quantum number n ofthe form: ωe = (3/2)f (n)Ωe , and that ω0 and Ωe are the constants introduced above, answer the ... due to the value ofthe wave function at the origin Altogether, this results in a factor of ∼ 22/2000 ∼ 1% for the ratio of hyperfine splittings H/(e+ e− ) (b) The numerical value ofA is A= 12π...
... enormous advantage, from the medical point of view, of heavy ion beams These permit to attack and destroy tumors in a very accurate and localized manner, as opposed to γ rays which produce damages all ... the crucial parameter is the effective interaction time, and give a simple explanation of this effect 10.2 Energy Loss in Matter We assume in the following that the Hamiltonian ofthe atom is of ... comparatively recent years, it has allowed a major improvement in the medical treatment of tumors in the eyes (proton therapy) and in the brain (ion therapy) Owing to the factor 1/β , or equivalently...
... is basically the same as here As an example, Fig 11.1 presents experimental results obtained by A Aspect and his collaborators in 1982 It gives the variation of E(α, β) as a function ofthe difference ... for a series of experiments, the results ofthe measurements on the electron and the proton are later compared, that one can find this non-local character ofquantummechanics 11.3.4 Individually, ... this value, what is the state ofthe system after the measurement? Is the proton spin state a ected by the measurement ofthe electron spin? ˆ ˆ 11.2.2 Calculate the expectation values Seα and...
... in the state (12.3), but that Alice is actually dealing with a nonparadoxical “statistical mixture”, that is to say that half ofthe N systems are in the state |α and the other half in the state ... eigenstate ofa with eigenvalue α: a| α = α|α ˆ ˆ 12.1.3 Calculate the expectation value ofthe energy in a quasi-classical state |α Calculate also the expectation values x and p and the root mean ... (12.3) and measures the momentum of each of these systems The measuring apparatus has a resolution δp such that: √ m¯ ω h δp p0 For N ments 1, draw qualitatively the histogram ofthe results of the...