Mathematisches Forschungsinstitut Oberwolfach Subfactors and
... is the first one to take a concrete, though by no means big enough, step in that direction. Planar algebra is an abstraction of the notion of (planar) manipulations of the tensor powers of a given finite dimensional Hilbert space (thus in some sense a planar version of [24]), and our constructions b ...
... is the first one to take a concrete, though by no means big enough, step in that direction. Planar algebra is an abstraction of the notion of (planar) manipulations of the tensor powers of a given finite dimensional Hilbert space (thus in some sense a planar version of [24]), and our constructions b ...
Thèse de doctorat - IMJ-PRG
... Around quantum shuffle algebras: defining ideals, specializations and cohomology Abstract The main part of this thesis is devoted to study some constructions and structures around quantum shuffle algebras: differential algebras and Kashiwara operators; defining ideals and specialization problem; coH ...
... Around quantum shuffle algebras: defining ideals, specializations and cohomology Abstract The main part of this thesis is devoted to study some constructions and structures around quantum shuffle algebras: differential algebras and Kashiwara operators; defining ideals and specialization problem; coH ...
Algebraic aspects of topological quantum field theories
... In this thesis it is examined how certain algebraic structures arise in the study of topological quantum field theory. The notion of a topological quantum field theory (TQFT) was coined by Witten [Wit88] in 1988. The physically motivated idea is to provide a mathematical framework for studying quant ...
... In this thesis it is examined how certain algebraic structures arise in the study of topological quantum field theory. The notion of a topological quantum field theory (TQFT) was coined by Witten [Wit88] in 1988. The physically motivated idea is to provide a mathematical framework for studying quant ...
Classical and quantum mechanics via Lie algebras
... mechanics are discussed independently of computational techniques for obtaining quantitatively correct numbers from the assumptions made. This allows us to focus attention on the simplicity and beauty of theoretical physics, which is often hidden in a jungle of techniques for estimating or calculati ...
... mechanics are discussed independently of computational techniques for obtaining quantitatively correct numbers from the assumptions made. This allows us to focus attention on the simplicity and beauty of theoretical physics, which is often hidden in a jungle of techniques for estimating or calculati ...
Chapter 3 Vectors
... In this example, we show two ways to analyze the problem of finding the resultant of two vectors. The first way is to solve the problem geometrically, using graph paper and a protractor to measure the magnitude of R and its direction in Figure 3.12a. (In fact, even when you know you are going to be ...
... In this example, we show two ways to analyze the problem of finding the resultant of two vectors. The first way is to solve the problem geometrically, using graph paper and a protractor to measure the magnitude of R and its direction in Figure 3.12a. (In fact, even when you know you are going to be ...
Ferrier_kinematics5
... • Composition of elementary motion of each link • Use linear algebra + systematic approach • Obtain an expression for the pose of the end-effector as a function of joint variables qi (angles/displacements) and link geometry (link lengths and relative orientations) Pe = f(q1,q2,,qn ;l1,ln,1,n) M ...
... • Composition of elementary motion of each link • Use linear algebra + systematic approach • Obtain an expression for the pose of the end-effector as a function of joint variables qi (angles/displacements) and link geometry (link lengths and relative orientations) Pe = f(q1,q2,,qn ;l1,ln,1,n) M ...
pdf
... The standard definition of a von Neumann algebra involves reference to a topology, and it is then shown (by von Neumann’s double commutant theorem) that this topological condition coincides with an algebraic condition (condition 2 in the Definition 1.2). But for present purposes, it will suffice to ...
... The standard definition of a von Neumann algebra involves reference to a topology, and it is then shown (by von Neumann’s double commutant theorem) that this topological condition coincides with an algebraic condition (condition 2 in the Definition 1.2). But for present purposes, it will suffice to ...
Phys. Rev. Lett. 110, 156402 - Institute for Quantum Optics and
... NV-based quantum information and sensing applications. Recent experiments have demonstrated coupling of NV electronic spins to nuclear spins [1,2], entanglement with photons [3], as well as single spin [4,5] and ensemble [6,7] magnetometry. An outstanding challenge is the realization of controlled i ...
... NV-based quantum information and sensing applications. Recent experiments have demonstrated coupling of NV electronic spins to nuclear spins [1,2], entanglement with photons [3], as well as single spin [4,5] and ensemble [6,7] magnetometry. An outstanding challenge is the realization of controlled i ...
Optical probing of spin fluctuations of a single paramagnetic Mn
... excitons.12,13 Direct recombination of the dark exciton can be observed in some Mn-doped QDs because of a slight admixture of the bright states with the dark ones induced by a valence-band mixing. However, the dark excitons mainly contribute to the signal by undergoing a spin flip to become bright e ...
... excitons.12,13 Direct recombination of the dark exciton can be observed in some Mn-doped QDs because of a slight admixture of the bright states with the dark ones induced by a valence-band mixing. However, the dark excitons mainly contribute to the signal by undergoing a spin flip to become bright e ...
6 Product Operators
... understand the spectrum, therefore, it is necessary to have a knowledge of the energy levels and this in turn requires a knowledge of the Hamiltonian operator. In NMR, the Hamiltonian is seen as having a more subtle effect than simply determining the energy levels. This comes about because the Hamil ...
... understand the spectrum, therefore, it is necessary to have a knowledge of the energy levels and this in turn requires a knowledge of the Hamiltonian operator. In NMR, the Hamiltonian is seen as having a more subtle effect than simply determining the energy levels. This comes about because the Hamil ...
6 Product Operators
... interest in coupled spin systems, so we really must have some way of describing the behaviour of such systems under multiple-pulse experiments. The tools we need are provided by quantum mechanics, specifically in the form of density matrix theory which is the best way to formulate quantum mechanics ...
... interest in coupled spin systems, so we really must have some way of describing the behaviour of such systems under multiple-pulse experiments. The tools we need are provided by quantum mechanics, specifically in the form of density matrix theory which is the best way to formulate quantum mechanics ...
Spin current source based on a quantum point contact with local
... maps of Figs. 8(b,f) show that the modes where the electron spin is oriented parallel to the x-direction [Fig. 8(a,e)] are mainly backscattered at the constriction and the corresponding transfer probabilities are T+ = 0.16 and T+ = 0.04. On the other hand the spin negative modes are conducting with ...
... maps of Figs. 8(b,f) show that the modes where the electron spin is oriented parallel to the x-direction [Fig. 8(a,e)] are mainly backscattered at the constriction and the corresponding transfer probabilities are T+ = 0.16 and T+ = 0.04. On the other hand the spin negative modes are conducting with ...
Quantum Groups: A Path to Current Algebra
... The standard argument shows that identity morphisms are unique. The notation A(A, B) (or HomA (A, B)) is used for the set of all morphisms in A from A to B . There is a category Set whose objects are sets, morphisms are functions, and composition is the usual composition of functions. There is a cat ...
... The standard argument shows that identity morphisms are unique. The notation A(A, B) (or HomA (A, B)) is used for the set of all morphisms in A from A to B . There is a category Set whose objects are sets, morphisms are functions, and composition is the usual composition of functions. There is a cat ...
pdf book - Lowndes County Historical Society Museum
... eternity), permanently fixed in potentiality, and God brings them out to actuality incessantly and perpetually ... He goes on transforming the possibilities (isti dadat, lit. 'preparednesses') that have been there from the beginningless past and that are (tehrefore) essentially uncreated, into infin ...
... eternity), permanently fixed in potentiality, and God brings them out to actuality incessantly and perpetually ... He goes on transforming the possibilities (isti dadat, lit. 'preparednesses') that have been there from the beginningless past and that are (tehrefore) essentially uncreated, into infin ...
Vectors - Light and Matter
... has moved clockwise past the nine-o’clock position by some imperceptibly small angle φ. Let positive x be to the right and positive y up. If the hand, with length `, is represented by a ∆r vector going from the dial’s center to the tip of the hand, find this vector’s ∆x. . The following shortcut is ...
... has moved clockwise past the nine-o’clock position by some imperceptibly small angle φ. Let positive x be to the right and positive y up. If the hand, with length `, is represented by a ∆r vector going from the dial’s center to the tip of the hand, find this vector’s ∆x. . The following shortcut is ...
Spin Algebra, Spin Eigenvalues, Pauli Matrices Lecture 10
... But bbot (a) must be smaller than btop (a), so only the second solution works. Therefore bbot (a) = −btop (a). Hence b, which is the eigenvalue of Sz , ranges from −btop (a) to btop (a). Furthermore, since S− lowers this value by ~ each time it is applied, these two values must differ by an integer ...
... But bbot (a) must be smaller than btop (a), so only the second solution works. Therefore bbot (a) = −btop (a). Hence b, which is the eigenvalue of Sz , ranges from −btop (a) to btop (a). Furthermore, since S− lowers this value by ~ each time it is applied, these two values must differ by an integer ...
Introduction to Integrable Models
... • different choice of symmetry algebra. The spin 1/2 spin chain corresponds to su(2), but any Lie algebra or even super-algebra can be chosen instead. • for the rank of the symmetry algebra r > 1, there are more particle species on the chain, e.g. ↑, ↓, ◦ (hole) of the tJ–model, where ↑, ↓ are fermi ...
... • different choice of symmetry algebra. The spin 1/2 spin chain corresponds to su(2), but any Lie algebra or even super-algebra can be chosen instead. • for the rank of the symmetry algebra r > 1, there are more particle species on the chain, e.g. ↑, ↓, ◦ (hole) of the tJ–model, where ↑, ↓ are fermi ...
Algebra in Braided Tensor Categories and Conformal Field Theory
... the methods necessary to gain complete control over a large class of examples for CFTs, the so-called rational conformal field theories. This research effort can be broadly divided in two parts, a “bottom up”, or complex-analytic part, and a “top down”, or algebraic part. In the complex-analytic par ...
... the methods necessary to gain complete control over a large class of examples for CFTs, the so-called rational conformal field theories. This research effort can be broadly divided in two parts, a “bottom up”, or complex-analytic part, and a “top down”, or algebraic part. In the complex-analytic par ...
3. Angular Momentum States.
... r, from the axis of rotation, and in the other case the center of mass is at a distance, r, from the axis of rotation. Quantum Electron Spin Angular Momentum The results of classical angular momentum provide a clear physical model for representation of orbital and spin angular momentum in terms of ...
... r, from the axis of rotation, and in the other case the center of mass is at a distance, r, from the axis of rotation. Quantum Electron Spin Angular Momentum The results of classical angular momentum provide a clear physical model for representation of orbital and spin angular momentum in terms of ...
Functorial Field Theories and Factorization Algebras
... from the tangent space Tx X to the cotangent space Tx∗ X is injective. This of course implies that this map is an isomorphism since the finite dimensional vector space Tx M and its dual space Tx∗ M have the same dimension. Later, we’ll be talking about scalar The informal statement that h−, −ix depe ...
... from the tangent space Tx X to the cotangent space Tx∗ X is injective. This of course implies that this map is an isomorphism since the finite dimensional vector space Tx M and its dual space Tx∗ M have the same dimension. Later, we’ll be talking about scalar The informal statement that h−, −ix depe ...