Poincaré group
... The origin of this behavior is that the Lorentz group, and in particular its subgroup SO(3), is not simply connected. The projective representations of a group correspond to the representations of its universal covering group: it has the same Lie algebra, which reflects the property of the group clo ...
... The origin of this behavior is that the Lorentz group, and in particular its subgroup SO(3), is not simply connected. The projective representations of a group correspond to the representations of its universal covering group: it has the same Lie algebra, which reflects the property of the group clo ...
Shankar`s Principles of Quantum Mechanics
... decide how much of this to cover; the more students know of these matters, the better they will understand the connection between classical and quantum mechanics. Chapter 3 is devoted to a brief study of idealized experiments that betray the inadequacy of classical mechanics and give a glimpse of qu ...
... decide how much of this to cover; the more students know of these matters, the better they will understand the connection between classical and quantum mechanics. Chapter 3 is devoted to a brief study of idealized experiments that betray the inadequacy of classical mechanics and give a glimpse of qu ...
New efficient integral algorithms for quantum chemistry
... to concerns about performance loss, which prompted IBM to develop the first optimizing compilers for FORTRAN. The generally good performance of the compiled programs popularized FORTRAN amongst scientists, until the language was finally standardized in 1966. During decades, supercomputer manufacture ...
... to concerns about performance loss, which prompted IBM to develop the first optimizing compilers for FORTRAN. The generally good performance of the compiled programs popularized FORTRAN amongst scientists, until the language was finally standardized in 1966. During decades, supercomputer manufacture ...
Machine invention of quantum computing circuits by means
... spins, trapped atoms, or other two-state physical systems, and the quantum gates would be implemented as processes or configurations that transform those systems. Such hardware is currently exotic and expensive, so the work described here uses a simulator that runs on ordinary classical digital hard ...
... spins, trapped atoms, or other two-state physical systems, and the quantum gates would be implemented as processes or configurations that transform those systems. Such hardware is currently exotic and expensive, so the work described here uses a simulator that runs on ordinary classical digital hard ...
Approximate local magnetic-to-electric surface
... that are then discretized to get a matrix representation. One crucial point in these approaches is to build approximate and accurate representations of the operators linking the magnetic (M) and the electric (J) surface currents through the so-called Magnetic-to-Electric (MtE) map [51]: MtE(M, J) = ...
... that are then discretized to get a matrix representation. One crucial point in these approaches is to build approximate and accurate representations of the operators linking the magnetic (M) and the electric (J) surface currents through the so-called Magnetic-to-Electric (MtE) map [51]: MtE(M, J) = ...
Quantum Computation: a Tutorial
... length and a notion of orthogonality, both defined by a scalar product. In this section, we develop the required notions for the 2-dimensional context. Complex numbers. A complex number is of the form a + b · i, where a and b are usual real numbers, and where i is a special symbol. Complex numbers c ...
... length and a notion of orthogonality, both defined by a scalar product. In this section, we develop the required notions for the 2-dimensional context. Complex numbers. A complex number is of the form a + b · i, where a and b are usual real numbers, and where i is a special symbol. Complex numbers c ...
Computational complexity in electronic structure PERSPECTIVE
... stated that Hartree–Fock has a runtime which scales as the third power of the number of basis functions. This scaling disregards difficult instances of the calculation where Hartree–Fock does not converge. Such instances require manual intervention to tweak the algorithm used or adjust the convergence ...
... stated that Hartree–Fock has a runtime which scales as the third power of the number of basis functions. This scaling disregards difficult instances of the calculation where Hartree–Fock does not converge. Such instances require manual intervention to tweak the algorithm used or adjust the convergence ...
q -entropies and the entanglement dynamics of two-qubits interacting with an... 408 A. Hamadou-Ibrahim et al.
... applications, such as quantum computation [2, 3] and quantum metrology [6]. The phenomenon of decoherence comprises, basically, a family of effects arising from the interaction (and the accompanying entanglement-development) between quantum systems and their environments [3, 4]. Physical systems in ...
... applications, such as quantum computation [2, 3] and quantum metrology [6]. The phenomenon of decoherence comprises, basically, a family of effects arising from the interaction (and the accompanying entanglement-development) between quantum systems and their environments [3, 4]. Physical systems in ...
Stability of Matter
... When we compare the length scales above, we notice that for atomic physics the nuclei are essentially point particles and thus atoms are essentially empty. This was initially shown experimentally by E. Rutherford in 1911 [25]. From a classical point of view, it is utterly unclear why the electrons a ...
... When we compare the length scales above, we notice that for atomic physics the nuclei are essentially point particles and thus atoms are essentially empty. This was initially shown experimentally by E. Rutherford in 1911 [25]. From a classical point of view, it is utterly unclear why the electrons a ...
Conservative, unconditionally stable
... and reindexing of variables gives the familiar real canonical Hamiltonian form with J = JN +M ; then the above condition on G is simply that it is real-valued for real Qn and Pn . However, the partially complex form is more convenient here. The time discretization procedure introduced here works bes ...
... and reindexing of variables gives the familiar real canonical Hamiltonian form with J = JN +M ; then the above condition on G is simply that it is real-valued for real Qn and Pn . However, the partially complex form is more convenient here. The time discretization procedure introduced here works bes ...
Document
... General solution : looking for the unknown function of a differential equation Particular solution (Initial Value Problem) : looking for the unknown function of a differential equation where the values of the unknown function and its derivatives at some ...
... General solution : looking for the unknown function of a differential equation Particular solution (Initial Value Problem) : looking for the unknown function of a differential equation where the values of the unknown function and its derivatives at some ...
Full-Text PDF
... global philosophy of natural sciences. Even more interesting is the statement in the subtitle in [22], concerning the interdisciplinary aspects of physics and biology. What is most relevant to a theoretical physical approach to biology is not the usual reductionist-mechanicist-deterministic scheme o ...
... global philosophy of natural sciences. Even more interesting is the statement in the subtitle in [22], concerning the interdisciplinary aspects of physics and biology. What is most relevant to a theoretical physical approach to biology is not the usual reductionist-mechanicist-deterministic scheme o ...
Optimal Inequalities for State-Independent Contextuality Linköping University Post Print
... find that, up to symmetries, 4;7 is the only context that can be omitted while still preserving optimality. In order to demonstrate the practical advantage, let us discuss the recent experimental values obtained for the Yu-Oh scenario ([19], Fig. 2). For those values, the original Yu-Oh inequality ...
... find that, up to symmetries, 4;7 is the only context that can be omitted while still preserving optimality. In order to demonstrate the practical advantage, let us discuss the recent experimental values obtained for the Yu-Oh scenario ([19], Fig. 2). For those values, the original Yu-Oh inequality ...
The mathematics of PDEs and the wave equation
... So for instance, Laplace’s equation is elliptic, the heat equation is parabolic, and the wave equation is hyperbolic. It is useful to classify equations because the solution techniques, and properties of the solutions are different, depending on whether the equation is elliptic, parabolic, or hyperb ...
... So for instance, Laplace’s equation is elliptic, the heat equation is parabolic, and the wave equation is hyperbolic. It is useful to classify equations because the solution techniques, and properties of the solutions are different, depending on whether the equation is elliptic, parabolic, or hyperb ...
Maxflow-PF
... Objective function: maximize xmax Capacity constraints: x12 ≤ 4, x13 ≤ 5, x14 ≤ 4, x25 ≤ 4, x34 ≤ 4, x35 ≤ 6, x45 ≤ 5, x56 ≤ 5 Conservation-of-flow constraint: x12 = x25, x13 = x34+x35, x14+x34=x46, x24+x35=x56 Constraint for the sourse and sink node: x12+x13+x14=x46+x56=xmax Non-negativity constrai ...
... Objective function: maximize xmax Capacity constraints: x12 ≤ 4, x13 ≤ 5, x14 ≤ 4, x25 ≤ 4, x34 ≤ 4, x35 ≤ 6, x45 ≤ 5, x56 ≤ 5 Conservation-of-flow constraint: x12 = x25, x13 = x34+x35, x14+x34=x46, x24+x35=x56 Constraint for the sourse and sink node: x12+x13+x14=x46+x56=xmax Non-negativity constrai ...
