gaussian wavepackets
... turn now, therefore, to a simpler line of argument—a selected detail from that more comprehensive work—which captures the essence of the point at issue. ...
... turn now, therefore, to a simpler line of argument—a selected detail from that more comprehensive work—which captures the essence of the point at issue. ...
A Quantum Version of The Spectral Decomposition Theorem of
... is illustrated in the “chaos pyramid” of Fig. 1. According to this structure, Ergodic Hierarchy is one of features of classical chaos. Ergodic Hierarchy ranks the chaotic level of a dynamical system according to the way in which correlations between two arbitrary distributions cancel for large times ...
... is illustrated in the “chaos pyramid” of Fig. 1. According to this structure, Ergodic Hierarchy is one of features of classical chaos. Ergodic Hierarchy ranks the chaotic level of a dynamical system according to the way in which correlations between two arbitrary distributions cancel for large times ...
Duality Theory of Weak Interaction
... Note that the term ∇µ Φν does not correspond to any Lagrangian action density, and is the direct consequence of energy-momentum conservation constraint of the variation element X in (2.10). Also this new term, derived using energy-momentum conservation constraint variation (2.10), plays a similar ro ...
... Note that the term ∇µ Φν does not correspond to any Lagrangian action density, and is the direct consequence of energy-momentum conservation constraint of the variation element X in (2.10). Also this new term, derived using energy-momentum conservation constraint variation (2.10), plays a similar ro ...
- Free Documents
... A fundamental problem with quantum theories of gravity, as opposed to the other forces of nature, is that in Einsteins theory of gravity, general relativity, there is no background geometry to work with the geometry of spacetime itself becomes a dynamical variable. This is loosely sum marized by say ...
... A fundamental problem with quantum theories of gravity, as opposed to the other forces of nature, is that in Einsteins theory of gravity, general relativity, there is no background geometry to work with the geometry of spacetime itself becomes a dynamical variable. This is loosely sum marized by say ...
Decoherence and the Transition from Quantum to Classical–Revisited
... between the physical Universe and consciousness. Needless to say, this is a very uncomfortable place to do physics. In spite of the profound nature of the difficulties, recent years have seen a growing consensus that progress is being made in dealing with the measurement problem, which is the usual ...
... between the physical Universe and consciousness. Needless to say, this is a very uncomfortable place to do physics. In spite of the profound nature of the difficulties, recent years have seen a growing consensus that progress is being made in dealing with the measurement problem, which is the usual ...
Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation Dorit Aharonov
... due to several breakthrough discoveries. Shor’s quantum algorithm for factorization [1], followed by several other algorithms to solve algebraic and combinatorial problems (see, e.g., [2–5]) have demonstrated the possible exponential advantage of quantum computing systems over classical ones. These ...
... due to several breakthrough discoveries. Shor’s quantum algorithm for factorization [1], followed by several other algorithms to solve algebraic and combinatorial problems (see, e.g., [2–5]) have demonstrated the possible exponential advantage of quantum computing systems over classical ones. These ...
Dark Energy and Modified Gravity
... These are degrees of freedom that have a negative mass squared, m2 < 0. Using again the simple scalar field example, this means that the second derivative of the potential about the ‘vacuum value’ (φ = 0 with ∂φ V (0) = 0) is negative, ∂φ2 V (0) < 0. In general, this need not mean that the theory ma ...
... These are degrees of freedom that have a negative mass squared, m2 < 0. Using again the simple scalar field example, this means that the second derivative of the potential about the ‘vacuum value’ (φ = 0 with ∂φ V (0) = 0) is negative, ∂φ2 V (0) < 0. In general, this need not mean that the theory ma ...
Braid Topologies for Quantum Computation
... (TQC) [1, 2] offers a particularly elegant way to achieve this using quasiparticles which obey nonabelian statistics [3, 4]. These quasiparticles, which are expected to arise in a variety of two-dimensional quantum many-body systems [1, 4, 5, 6, 7, 8, 9, 10, 11], have the property that the usual pha ...
... (TQC) [1, 2] offers a particularly elegant way to achieve this using quasiparticles which obey nonabelian statistics [3, 4]. These quasiparticles, which are expected to arise in a variety of two-dimensional quantum many-body systems [1, 4, 5, 6, 7, 8, 9, 10, 11], have the property that the usual pha ...
Spin-Orbit Interactions in Topological Insulators
... To get the hopping amplitudes for the tight binding model, the overlap integrals between neighboring orbitals has to be evaluated. These will not be evaluated here, but will be left as arbitrary parameters. It is however assumed that the overlap between orbitals with opposite spins are zero1 . The r ...
... To get the hopping amplitudes for the tight binding model, the overlap integrals between neighboring orbitals has to be evaluated. These will not be evaluated here, but will be left as arbitrary parameters. It is however assumed that the overlap between orbitals with opposite spins are zero1 . The r ...
While the ramifications of quantum computers
... Gil Kalai writes, “The main concern regarding the feasibility of quantum computers has always been that quantum systems are inherently noisy: we cannot accurately control them, and we cannot accurately describe them…What is noise?... Noise refers to the general effect of neglecting degrees of freedo ...
... Gil Kalai writes, “The main concern regarding the feasibility of quantum computers has always been that quantum systems are inherently noisy: we cannot accurately control them, and we cannot accurately describe them…What is noise?... Noise refers to the general effect of neglecting degrees of freedo ...
Nonlocality and entanglement in Generalized
... physical theory of today. Although quantum theory is conceptually difficult to understand, its mathematical structure is quite simple. What determines this particularly simple and elegant mathematical structure? In short: Why is quantum theory as it is? Addressing such questions is the aim of invest ...
... physical theory of today. Although quantum theory is conceptually difficult to understand, its mathematical structure is quite simple. What determines this particularly simple and elegant mathematical structure? In short: Why is quantum theory as it is? Addressing such questions is the aim of invest ...
The Compton-Schwarzschild correspondence from extended de
... Other, more subtle, approaches such as the Schrödinger-Newton equation (see [8] and references therein) suffer from similar complications and require the inclusion of at least a semiclassical potential. The approach presented here has no such drawback and correctly predicts the emergence of black h ...
... Other, more subtle, approaches such as the Schrödinger-Newton equation (see [8] and references therein) suffer from similar complications and require the inclusion of at least a semiclassical potential. The approach presented here has no such drawback and correctly predicts the emergence of black h ...
Pion as a Nambu-Goldstone boson
... A symmetry is said to be spontaneously broken, if the Lagrangian exhibits a symmetry but the ground state/vacuum does not have this symmetry. Goldstone-theorem If the Lagrangian is invariant under a continuous global symmetry operation g∈G and the vacuum is invariant under a subgroup H⊂G, then there ...
... A symmetry is said to be spontaneously broken, if the Lagrangian exhibits a symmetry but the ground state/vacuum does not have this symmetry. Goldstone-theorem If the Lagrangian is invariant under a continuous global symmetry operation g∈G and the vacuum is invariant under a subgroup H⊂G, then there ...
Black Hole Formation and Classicalization in
... graviton scattering amplitudes, with number of soft gravitons in the final state being given by the number of black hole constituents, as suggested by classicalization. • Next, by using powerful field and string-theoretic techniques, in particular scattering equations [9] and Kawai-Lewellen-Tye (KLT ...
... graviton scattering amplitudes, with number of soft gravitons in the final state being given by the number of black hole constituents, as suggested by classicalization. • Next, by using powerful field and string-theoretic techniques, in particular scattering equations [9] and Kawai-Lewellen-Tye (KLT ...
Heisenberg`s original derivation of the uncertainty principle and its
... This article aims to resolve this longstanding confusion. It will be shown that in 1927 Heisenberg1 actually ‘proved’ not only eq. (2) but also eq. (1) from basic postulates for quantum mechanics. In showing that, it is pointed out that as one of the basic postulates Heisenberg supposed an assumptio ...
... This article aims to resolve this longstanding confusion. It will be shown that in 1927 Heisenberg1 actually ‘proved’ not only eq. (2) but also eq. (1) from basic postulates for quantum mechanics. In showing that, it is pointed out that as one of the basic postulates Heisenberg supposed an assumptio ...
Symplectic structures -- a new approach to geometry.
... this isomorphism is a rotation through a quarter turn. Every a symplectic structure ω determines a volume form ω n /n!, that is, a nonvanishing top-dimensional form that integrates to give a volume. In two dimensions of course, ω is simply an area form. In higher dimensions it was suspected long ago ...
... this isomorphism is a rotation through a quarter turn. Every a symplectic structure ω determines a volume form ω n /n!, that is, a nonvanishing top-dimensional form that integrates to give a volume. In two dimensions of course, ω is simply an area form. In higher dimensions it was suspected long ago ...
What classicality? Decoherence and Bohr`s classical concepts
... What we now find is that typically this density matrix will be approximately diagonal in an eigenbasis of some classical observable, such as position, and that the density matrix will remain approximately diagonal over time. (The specific basis is determined by the structure of the interaction Hamil ...
... What we now find is that typically this density matrix will be approximately diagonal in an eigenbasis of some classical observable, such as position, and that the density matrix will remain approximately diagonal over time. (The specific basis is determined by the structure of the interaction Hamil ...
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... We will often use a less cumbersome informal notation when defining functions. For example, the apply function above satisfies the following property apply f x −→ (f x) under beta reduction. Given this specification, the translation into a lambda term is straightforward. How do we represent data in ...
... We will often use a less cumbersome informal notation when defining functions. For example, the apply function above satisfies the following property apply f x −→ (f x) under beta reduction. Given this specification, the translation into a lambda term is straightforward. How do we represent data in ...