The Unruh effect in quantum information beyond the single
... working with Unruh modes, there is no particular reason why to choose a specific qR . In fact, and as as we will see later, feasible elections of Minkowski states are in general, linear superpositions of different Unruh modes with different values of qR . The Minkowski-Unruh state under consideratio ...
... working with Unruh modes, there is no particular reason why to choose a specific qR . In fact, and as as we will see later, feasible elections of Minkowski states are in general, linear superpositions of different Unruh modes with different values of qR . The Minkowski-Unruh state under consideratio ...
Lectures on the Geometry of Quantization
... some sense macroscopic, the classical motions described by solutions of Hamilton’s equations lead to approximate solutions of Schrödinger’s equation. Establishing this relation between classical and quantum mechanics is important, not only in verifying that the theories are consistent with the fact ...
... some sense macroscopic, the classical motions described by solutions of Hamilton’s equations lead to approximate solutions of Schrödinger’s equation. Establishing this relation between classical and quantum mechanics is important, not only in verifying that the theories are consistent with the fact ...
Spin Physics in Two-dimensional Systems Daniel Gosálbez Martínez
... is reduced to two inequivalent points situated at the corners of the first Brillouin zone. At this point, the valence band and the conduction band touch each other with a lineal dispersion relation. The physics in the low energy spectrum is described by the π orbitals of the graphene, while the high ...
... is reduced to two inequivalent points situated at the corners of the first Brillouin zone. At this point, the valence band and the conduction band touch each other with a lineal dispersion relation. The physics in the low energy spectrum is described by the π orbitals of the graphene, while the high ...
Genuine Fortuitousness
... In the late 1920’s, due to the experimental success of quantum theory, many physicists who were now used to the accuracy of what was a phenomenologically descriptive theory of the quantum scale began to question how QM fit in with the rest of physics as whole. In short, physicists asked the question ...
... In the late 1920’s, due to the experimental success of quantum theory, many physicists who were now used to the accuracy of what was a phenomenologically descriptive theory of the quantum scale began to question how QM fit in with the rest of physics as whole. In short, physicists asked the question ...
Embedding Quantum Simulators Roberto Di Candia
... Pedernales, with whom I have achieved and understood the main results of this Thesis; and, last but not least, Dr. Mikel Sanz, which has guided me in a more abstract side of quantum physics. I thank all the members of the CCQED European Project, where I have been involved for the first three years o ...
... Pedernales, with whom I have achieved and understood the main results of this Thesis; and, last but not least, Dr. Mikel Sanz, which has guided me in a more abstract side of quantum physics. I thank all the members of the CCQED European Project, where I have been involved for the first three years o ...
Düren (ppt 10,1MB)
... When integrated over x, one gets the momentum density. When integrated over p, one gets the probability density. ...
... When integrated over x, one gets the momentum density. When integrated over p, one gets the probability density. ...
How long does it take until a quantum system
... principles of quantum mechanics and came up with various ideas to explain the apparent paradox or to modify Hawking’s calculations, e.g. [BSP84, tH90, CGHS92, Gid92]. But all of these approaches are either highly improbable or suffer from conceptual defects. There is an abundance of reviews on the c ...
... principles of quantum mechanics and came up with various ideas to explain the apparent paradox or to modify Hawking’s calculations, e.g. [BSP84, tH90, CGHS92, Gid92]. But all of these approaches are either highly improbable or suffer from conceptual defects. There is an abundance of reviews on the c ...
Aspects of quantum information theory
... this end the text is divided into two parts. The first (Part I. “Fundamentals”) is of introductory nature. It takes into account that most of the fundamental concepts and basic ideas of quantum information are developed during the last decade, and are therefore unfamiliar to most physicists. To make ...
... this end the text is divided into two parts. The first (Part I. “Fundamentals”) is of introductory nature. It takes into account that most of the fundamental concepts and basic ideas of quantum information are developed during the last decade, and are therefore unfamiliar to most physicists. To make ...
arXiv:quant-ph/0202122 v1 21 Feb 2002
... from a sender to a receiver with “letters” from a “classical alphabet” e.g. the two digits “0” and “1” or any other finite set of symbols. In the context of classical information theory, it is completely irrelevant which type of physical system is used to perform the transmission. This abstract appro ...
... from a sender to a receiver with “letters” from a “classical alphabet” e.g. the two digits “0” and “1” or any other finite set of symbols. In the context of classical information theory, it is completely irrelevant which type of physical system is used to perform the transmission. This abstract appro ...
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.