Light-Front Holographic QCD and Emerging
... Thus, in principle, one can compute physical observables in a strongly coupled gauge theory in terms of a weakly coupled classical gravity theory, which encodes information of the boundary theory. In the prototypical example [22] of this duality, the gauge theory is N = 4 supersymmetric SU(NC ) Yang ...
... Thus, in principle, one can compute physical observables in a strongly coupled gauge theory in terms of a weakly coupled classical gravity theory, which encodes information of the boundary theory. In the prototypical example [22] of this duality, the gauge theory is N = 4 supersymmetric SU(NC ) Yang ...
NUCLEAR MAGNETIC RESONANCE QUANTUM COMPUTATION
... NMR signal detection is best described using a classical view [8]. The ensemble average of the spins behaves like a classical magnetisation rotating at the Larmor frequency, and the NMR detector is a coil of wire wrapped around the sample. As the magnetisation cuts across the wires it induces an EMF ...
... NMR signal detection is best described using a classical view [8]. The ensemble average of the spins behaves like a classical magnetisation rotating at the Larmor frequency, and the NMR detector is a coil of wire wrapped around the sample. As the magnetisation cuts across the wires it induces an EMF ...
Quantum Transport in Finite Disordered Electron Systems
... The thesis has three parts. In the first Chapter of Part I the quantum transport methods have been used to extract the bulk resistivity of a three-dimensional conductor, modeled by an Anderson model on an nanoscale lattice (composed of several thousands of atoms), from the linear scaling of disorder- ...
... The thesis has three parts. In the first Chapter of Part I the quantum transport methods have been used to extract the bulk resistivity of a three-dimensional conductor, modeled by an Anderson model on an nanoscale lattice (composed of several thousands of atoms), from the linear scaling of disorder- ...
Contributions to the Quantum Optics of Multi
... a “temporary member” of their research groups, and for treating me like a fellow researcher, giving me all the tools needed to become productive under their watch. As a PhD student it is easier to hear the not–so–nice stories about ...
... a “temporary member” of their research groups, and for treating me like a fellow researcher, giving me all the tools needed to become productive under their watch. As a PhD student it is easier to hear the not–so–nice stories about ...
Quantum Field Theory in Condensed Matter Physics 2nd Ed.
... dimensions and in Fermi liquids, where scattering of quasi-particles on the Fermi surface changes only their phase (forward scattering). Another possibility is that the interactions, being weak at the bare level, grow stronger for small energies, introducing profound changes in the low energy sector ...
... dimensions and in Fermi liquids, where scattering of quasi-particles on the Fermi surface changes only their phase (forward scattering). Another possibility is that the interactions, being weak at the bare level, grow stronger for small energies, introducing profound changes in the low energy sector ...
Lecture 20 Scattering theory
... Consider a collision experiment in which a detector measures the number of particles per unit time, N dΩ, scattered into an element of solid angle dΩ in direction (θ, φ). This number is proportional to the incident flux of particles, jI defined as the number of particles per unit time crossing a uni ...
... Consider a collision experiment in which a detector measures the number of particles per unit time, N dΩ, scattered into an element of solid angle dΩ in direction (θ, φ). This number is proportional to the incident flux of particles, jI defined as the number of particles per unit time crossing a uni ...
Entanglement Spectrum in the Fractional Quantum Hall Effect
... In particular the FQHE exhibits a new type of order different from the classical or quantum orders that can be described by the paradigm of Landau’s symmetry breaking theory. This new type of order is robust upon local perturbations and cannot be described by a symmetry or a broken symmetry. In part ...
... In particular the FQHE exhibits a new type of order different from the classical or quantum orders that can be described by the paradigm of Landau’s symmetry breaking theory. This new type of order is robust upon local perturbations and cannot be described by a symmetry or a broken symmetry. In part ...
11 Harmonic oscillator and angular momentum — via operator algebra
... In the preceeding section we saw that the quantization of the number operator N = a† a could be based exclusively on the algebra [a, a† ] = 1 for the operators a and a† . We shall now use a similar algebraic method to find eigenstates and eigenvalues for a generalized angular momentum denoted by J. ...
... In the preceeding section we saw that the quantization of the number operator N = a† a could be based exclusively on the algebra [a, a† ] = 1 for the operators a and a† . We shall now use a similar algebraic method to find eigenstates and eigenvalues for a generalized angular momentum denoted by J. ...
Applications of Resolutions of the Coulomb Operator in Quantum
... The birth of quantum mechanics dates back to early 19th century. Classical or Newtonian mechanics failed to explain a number of experiments, for example, blackbody radiation, gas discharge tube and cathode ray. Attempts to explain these experiments led to the discovery of a new concept of physics wh ...
... The birth of quantum mechanics dates back to early 19th century. Classical or Newtonian mechanics failed to explain a number of experiments, for example, blackbody radiation, gas discharge tube and cathode ray. Attempts to explain these experiments led to the discovery of a new concept of physics wh ...
Test of the consistency of various linearized semiclassical initial
... challenging application and test of the LSC-IVR approximation to quantum mechanical time correlation functions, namely the incoherent dynamic structure factor for inelastic neutron scattering from liquid para-hydrogen,100,101 with special emphasis on how consistent the results are when obtaining thi ...
... challenging application and test of the LSC-IVR approximation to quantum mechanical time correlation functions, namely the incoherent dynamic structure factor for inelastic neutron scattering from liquid para-hydrogen,100,101 with special emphasis on how consistent the results are when obtaining thi ...
Electron-electron scattering in linear transport in two
... a given temperature T and density n, a symmetric matrix needs to be evaluated only once, and henceforth it can be used to describe electron-electron scattering in any Boltzmann equation linear-response calculation for that particular T and n. Using this method, we calculate the distribution function ...
... a given temperature T and density n, a symmetric matrix needs to be evaluated only once, and henceforth it can be used to describe electron-electron scattering in any Boltzmann equation linear-response calculation for that particular T and n. Using this method, we calculate the distribution function ...
- Philsci-Archive
... radiation and matter in an approximate way with just a few terms of a series expansion and not give an exact solution corresponding to treating radiation and matter as one closed system.2 Here I am not simply accepting pragmatically a fact. The use of only a few terms of an infinite series expansion ...
... radiation and matter in an approximate way with just a few terms of a series expansion and not give an exact solution corresponding to treating radiation and matter as one closed system.2 Here I am not simply accepting pragmatically a fact. The use of only a few terms of an infinite series expansion ...
Wave function
A wave function in quantum mechanics describes the quantum state of an isolated system of one or more particles. There is one wave function containing all the information about the entire system, not a separate wave function for each particle in the system. Its interpretation is that of a probability amplitude. Quantities associated with measurements, such as the average momentum of a particle, can be derived from the wave function. It is a central entity in quantum mechanics and is important in all modern theories, like quantum field theory incorporating quantum mechanics, while its interpretation may differ. The most common symbols for a wave function are the Greek letters ψ or Ψ (lower-case and capital psi).For a given system, once a representation corresponding to a maximal set of commuting observables and a suitable coordinate system is chosen, the wave function is a complex-valued function of the system's degrees of freedom corresponding to the chosen representation and coordinate system, continuous as well as discrete. Such a set of observables, by a postulate of quantum mechanics, are Hermitian linear operators on the space of states representing a set of physical observables, like position, momentum and spin that can, in principle, be simultaneously measured with arbitrary precision. Wave functions can be added together and multiplied by complex numbers to form new wave functions, and hence are elements of a vector space. This is the superposition principle of quantum mechanics. This vector space is endowed with an inner product such that it is a complete metric topological space with respect to the metric induced by the inner product. In this way the set of wave functions for a system form a function space that is a Hilbert space. The inner product is a measure of the overlap between physical states and is used in the foundational probabilistic interpretation of quantum mechanics, the Born rule, relating transition probabilities to inner products. The actual space depends on the system's degrees of freedom (hence on the chosen representation and coordinate system) and the exact form of the Hamiltonian entering the equation governing the dynamical behavior. In the non-relativistic case, disregarding spin, this is the Schrödinger equation.The Schrödinger equation determines the allowed wave functions for the system and how they evolve over time. A wave function behaves qualitatively like other waves, such as water waves or waves on a string, because the Schrödinger equation is mathematically a type of wave equation. This explains the name ""wave function"", and gives rise to wave–particle duality. The wave of the wave function, however, is not a wave in physical space; it is a wave in an abstract mathematical ""space"", and in this respect it differs fundamentally from water waves or waves on a string.For a given system, the choice of which relevant degrees of freedom to use are not unique, and correspondingly the domain of the wave function is not unique. It may be taken to be a function of all the position coordinates of the particles over position space, or the momenta of all the particles over momentum space, the two are related by a Fourier transform. These descriptions are the most important, but they are not the only possibilities. Just like in classical mechanics, canonical transformations may be used in the description of a quantum system. Some particles, like electrons and photons, have nonzero spin, and the wave function must include this fundamental property as an intrinsic discrete degree of freedom. In general, for a particle with half-integer spin the wave function is a spinor, for a particle with integer spin the wave function is a tensor. Particles with spin zero are called scalar particles, those with spin 1 vector particles, and more generally for higher integer spin, tensor particles. The terminology derives from how the wave functions transform under a rotation of the coordinate system. No elementary particle with spin 3⁄2 or higher is known, except for the hypothesized spin 2 graviton. Other discrete variables can be included, such as isospin. When a system has internal degrees of freedom, the wave function at each point in the continuous degrees of freedom (e.g. a point in space) assigns a complex number for each possible value of the discrete degrees of freedom (e.g. z-component of spin). These values are often displayed in a column matrix (e.g. a 2 × 1 column vector for a non-relativistic electron with spin 1⁄2).In the Copenhagen interpretation, an interpretation of quantum mechanics, the squared modulus of the wave function, |ψ|2, is a real number interpreted as the probability density of measuring a particle as being at a given place at a given time or having a definite momentum, and possibly having definite values for discrete degrees of freedom. The integral of this quantity, over all the system's degrees of freedom, must be 1 in accordance with the probability interpretation, this general requirement a wave function must satisfy is called the normalization condition. Since the wave function is complex valued, only its relative phase and relative magnitude can be measured. Its value does not in isolation tell anything about the magnitudes or directions of measurable observables; one has to apply quantum operators, whose eigenvalues correspond to sets of possible results of measurements, to the wave function ψ and calculate the statistical distributions for measurable quantities.The unit of measurement for ψ depends on the system, and can be found by dimensional analysis of the normalization condition for the system. For one particle in three dimensions, its units are [length]−3/2, because an integral of |ψ|2 over a region of three-dimensional space is a dimensionless probability.