QUANTUM COMPUTING

... Quantum computing is a potential. There are already results convincingly demonstrating that for some important practical problems quantum computers are theoretically exponentially more powerful than classical computers. Such results, as Shor's factorization algorithm, can be seen as apt killers for ...

... Quantum computing is a potential. There are already results convincingly demonstrating that for some important practical problems quantum computers are theoretically exponentially more powerful than classical computers. Such results, as Shor's factorization algorithm, can be seen as apt killers for ...

Ultracold Fermions in Two-Dimensional Planes with Dipolar

... in the rovibrational ground state. The strategy which lead to success was to first cool down atoms and then coherently convert them to ground state molecules at low temperatures without heating the sample. Mainly this is done by the use of Feshbach resonance to switch the interaction after the cooli ...

... in the rovibrational ground state. The strategy which lead to success was to first cool down atoms and then coherently convert them to ground state molecules at low temperatures without heating the sample. Mainly this is done by the use of Feshbach resonance to switch the interaction after the cooli ...

Lecture Notes for Physics 229: Quantum Information and Computation

... The moral we draw is that \information is physical." and it is instructive to consider what physics has to tell us about information. But fundamentally, the universe is quantum mechanical. How does quantum theory shed light on the nature of information? It must have been clear already in the early d ...

... The moral we draw is that \information is physical." and it is instructive to consider what physics has to tell us about information. But fundamentally, the universe is quantum mechanical. How does quantum theory shed light on the nature of information? It must have been clear already in the early d ...

Quantum Information Meets Quantum Matter

... matter being fromed by particles to the discovery of wave-like matter (electromanetics waves and gravitational waves), and to the unification of particle-like matter and wave-like matter by quantum theory. We feel that we are in the process of a new revolution where quantum information, matter, inte ...

... matter being fromed by particles to the discovery of wave-like matter (electromanetics waves and gravitational waves), and to the unification of particle-like matter and wave-like matter by quantum theory. We feel that we are in the process of a new revolution where quantum information, matter, inte ...

Define resistance V splitting between components V

... draw circuit diagram of circuit to take a VI plot explanation of internal resistance (must recognise this first) application of physic skills EMF calc Internal resistance calc define intensity (of a wave) efficiency calc ...

... draw circuit diagram of circuit to take a VI plot explanation of internal resistance (must recognise this first) application of physic skills EMF calc Internal resistance calc define intensity (of a wave) efficiency calc ...

Quantum Mediated Effective Interactions for Spatially Complex

... The origin of this complexity can be attributed to the nature of the discrete lattice on which the spins live, the nature of the mediating quantum particle - fermion versus a boson, and to the nature of the spins themselves - classical versus quantum. In this thesis, we present examples of how non-t ...

... The origin of this complexity can be attributed to the nature of the discrete lattice on which the spins live, the nature of the mediating quantum particle - fermion versus a boson, and to the nature of the spins themselves - classical versus quantum. In this thesis, we present examples of how non-t ...

Hyperspherical Approach to Quantal Three-body Theory

... (a) Full energy landscape for the three-body potentials at a = ∞ for our vλa model potential. (b) Effective diabatic potentials Wν relevant for Efimov physics for vλa with an increasingly large number of bound states (λ∗n is the value of λ that produces a = ∞ and n s-wave bound states). The Wν conve ...

... (a) Full energy landscape for the three-body potentials at a = ∞ for our vλa model potential. (b) Effective diabatic potentials Wν relevant for Efimov physics for vλa with an increasingly large number of bound states (λ∗n is the value of λ that produces a = ∞ and n s-wave bound states). The Wν conve ...

Ph125: Quantum Mechanics

... now that a vector in a Hilbert space is a far more complicated thing than the two numbers x and p that would define the classical state of a particle; the vector is an infinite set of numbers. The only useful immediate inference we can draw from this statement on its own, based on the definition of ...

... now that a vector in a Hilbert space is a far more complicated thing than the two numbers x and p that would define the classical state of a particle; the vector is an infinite set of numbers. The only useful immediate inference we can draw from this statement on its own, based on the definition of ...

Measuring a single spin in an arbitrary direction A spin 1/2

... Note that the sum of all probabilities is unity and that the probability of having "two spins the same" and "two spins opposite" is 1/2, i.e. there is spin - inversion symmetry. Also note that the probability for a given outcome depends only on the (cosine of the) angle between the two detectors and ...

... Note that the sum of all probabilities is unity and that the probability of having "two spins the same" and "two spins opposite" is 1/2, i.e. there is spin - inversion symmetry. Also note that the probability for a given outcome depends only on the (cosine of the) angle between the two detectors and ...

Quantum Orders and Symmetric Spin Liquids

... In a sense, the classical world described by positive probabilities is a world with only “black and white”. The Landau’s theory and the symmetry principle for classical orders are color blind which can only describe different “shades of grey” in the classical world. The quantum world described by co ...

... In a sense, the classical world described by positive probabilities is a world with only “black and white”. The Landau’s theory and the symmetry principle for classical orders are color blind which can only describe different “shades of grey” in the classical world. The quantum world described by co ...

Relativistic effects in atomic and molecular properties

... Nobel Prize Winner for Physics, 1979, ”Modern elementary–particle physics is founded upon the two pillars of quantum mechanics and relativity. I have made little mention of relativity so far because, while the atom is very much a quantum system, it is not very relativistic at all. Relativity becomes ...

... Nobel Prize Winner for Physics, 1979, ”Modern elementary–particle physics is founded upon the two pillars of quantum mechanics and relativity. I have made little mention of relativity so far because, while the atom is very much a quantum system, it is not very relativistic at all. Relativity becomes ...

Electron Fluxes During Chemical Processes - diss.fu

... The monograph at hand addresses the concept of the mechanism of a chemical reaction. This concept is one of the pillars on which the field of chemistry rests, and it is used with self-evidence to predict or rationalize the outcome of reactions. Yet, from the quantum dynamicist’s point of view the th ...

... The monograph at hand addresses the concept of the mechanism of a chemical reaction. This concept is one of the pillars on which the field of chemistry rests, and it is used with self-evidence to predict or rationalize the outcome of reactions. Yet, from the quantum dynamicist’s point of view the th ...

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.