Results 1 - 10 of 66
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[en] Many systems are composed of multiple, interacting subsystems, where the dynamics of each subsystem only depends on the states of a subset of the other subsystems, rather than on all of them. I analyze how such constraints on the dependencies of each subsystem’s dynamics affects the thermodynamics of the overall, composite system. Specifically, I derive a strictly nonzero lower bound on the minimal achievable entropy production rate of the overall system in terms of these constraints. The bound is based on constructing counterfactual rate matrices, in which some subsystems are held fixed while the others are allowed to evolve. This bound is related to the ‘learning rate’ of stationary bipartite systems, and more generally to the ‘information flow’ in bipartite systems. It can be viewed as a strengthened form of the second law, applicable whenever there are constraints on which subsystem within an overall system can directly affect which other subsystem. (paper)
[en] Generative models in deep learning allow for sampling probability distributions that approximate data distributions. We propose using generative models for making approximate statistical predictions in the string theory landscape. For vacua admitting a Lagrangian description this can be thought of as learning random tensor approximations of couplings. As a concrete proof-of-principle, we demonstrate in a large ensemble of Calabi-Yau manifolds that Kähler metrics evaluated at points in Kähler moduli space are well-approximated by ensembles of matrices produced by a deep convolutional Wasserstein GAN. Accurate approximations of the Kähler metric eigenspectra are achieved with far fewer than Gaussian draws. Accurate extrapolation to values of outside the training set are achieved via a conditional GAN. Together, these results implicitly suggest the existence of strong correlations in the data, as might be expected if Reid's fantasy is correct. (© 2020 WILEY‐VCH Verlag GmbH and Co. KGaA, Weinheim)
[en] This book gives an introduction to quantum mechanics with the matrix method. Heisenberg's matrix mechanics is described in detail. The fundamental equations are derived by algebraic methods using matrix calculus. Only a brief description of Schrödinger's wave mechanics is given (in most books exclusively treated), to show their equivalence to Heisenberg's matrix method. In the first part the historical development of Quantum theory by Planck, Bohr and Sommerfeld is sketched, followed by the ideas and methods of Heisenberg, Born and Jordan. Then Pauli's spin and exclusion principles are treated. Pauli's exclusion principle leads to the structure of atoms. Finally, Dirac´s relativistic quantum mechanics is shortly presented. Matrices and matrix equations are today easy to handle when implementing numerical algorithms using standard software as MAPLE and Mathematica.
[de]Das Buch gibt eine Einführung in die Quantenmechanik mittels Matrizenrechnung. Heisenbergs Matrizenmechanik ist darin ausführlich beschrieben und die grundlegenden Gleichungen werden mit algebraischen Methoden und Matrizen berechnet. Während in vielen Lehrbüchern die Quantenmechanik mittels Schrödingers Wellenmechanik behandelt wird, findet sich in diesem Werk nur eine kurze Einführung in diese, um ihre Äquivalenz zu Heisenbergs Matrizenmethode zu zeigen. Im ersten Teil des Buches wird die historische Entwicklung der Quantentheorie durch Planck, Bohr und Sommerfeld beschrieben, gefolgt von den Ideen und Methoden von Heisenberg, Born und Jordan. Anschließend wird auf Paulis Spintheorie und auf sein Ausschließungsprinzip eingegangen, welches letztlich zur Struktur von Atomen führt. Abschließend wird Diracs relativistische Quantenmechanik kurz beschrieben. Die vorkommenden Matrizen und Matrizengleichungen können heutzutage leicht mittels numerischer Computeralgorithmen, wie z.B. MAPLE oder Mathematica gehandhabt werden.
[en] In Walter et al. (Science 340:1205, 2013), they gave a sufficient condition for genuinely entangled pure states and discussed SLOCC classification via polytopes and the eigenvalues of the single-particle states. In this paper, for 4n qubits, we show the invariance of algebraic multiplicities (AMs) and geometric multiplicities (GMs) of eigenvalues and the invariance of sizes of Jordan blocks (JBs) of the coefficient matrices under SLOCC. We explore properties of spectra, eigenvectors, generalized eigenvectors, standard Jordan normal forms (SJNFs), and Jordan chains of the coefficient matrices. The properties and invariance permit a reduction in SLOCC classification of 4n qubits to integer partitions (in number theory) of the number and the AMs.
[en] The stiffened structure has a complex effect on signal propagation and poses difficulties in leakage location technology. In order to solve this problem, this paper proposes a frequency energy ratio mapping method (FERMM). The method divides the grid on the structure in advance, compares the signal of the distributed sensor with the reference signal to generate a mapping matrix frome the energy ratio vector. When a leak at an unknown location occurs, the energy ratio vector is formed by the same method and matched with the mapping matrix to locate the unknown leakage. The energy ratio vector of this method are only related to the propagation path and are independent of the spectral characteristics of the leakage and the frequency response characteristics of the receiving sensor. FERMM has the adaptability to complex structures and can locate continuous signals for a fast real-time process. The FERMM was verified by 120 sets of experiments. The results show that the average positioning error of FERMM is 25.5 mm, which can reach 14.4 mm error under the optimal setting of grid coincidence. (paper)
[en] Traditional applications of the Judd-Ofelt (JO) theory to the analysis of the Eu3+ optical spectra make use of the emission transitions originating from the 5D0 manifold. In the present paper, we report an alternative method of evaluating the JO intensity parameters from the Eu3+ emission spectra based on the 5D1 → 7F0,1 transitions. The reduced matrix elements of the unit tensor operators are re-calculated for the 5D0,1,2 → 7F0,1,…,6 Eu3+ transitions in the intermediate coupling approximation using the average electrostatic and spin-orbit coupling parameters. The suggested method was tested by analyzing the emission spectra of the Eu3+ doped GdAlO3, LaF3, NaYF4, Y2O3, ZrO2, YNbO4, ZBLA and PIGLZ hosts. It is shown that the developed method is more accurate for the hosts with relatively high 5D1 level population, which emphasizes its high potential and applicability. In addition to the JO analysis, the CIE chromaticity coordinates are calculated for the investigated spectra. © 2019 Elsevier B.V.
[en] A full-Stokes polarization imaging method was introduced by using a liquid crystal variable retarder (LCVR) and the metallic nanograting arrays. The linear polarization was detected based on the dichroic transmission of the metallic nanograting. The circular polarization was retrieved from two successive measurements with different retardance or orientation of LCVR. The determinant of data retrieve matrix was analyzed for the LCVR optimization. A full-Stokes imaging setup was built, calibrated, and proof-of-principle verified through imaging of radially polarized beams. (paper)
[en] Although great achievements have been obtained in metasurfaces so far, the functionalities of these devices are almost static. The dynamically adjustable devices are far less explored. Here we theoretically and numerically demonstrate a veritable reconfigurable terahertz wavefront modulator (TWM). The designed TWM can dynamically shape the wavefront at will via imposing different Fermi levels on the constituent graphene ribbons. By adopting the Dirac brackets and Matrix analyze method, the correlation between the phase shift and Fermi level is theoretically established, which offers a general scheme for designing dynamically switchable devices. As a proof of concept, three different sets of pre-calculated Fermi levels are imposed on the graphene ribbons. The TWM can be dynamically switched among back reflector, varifocal metalens and Airy beam generator, which has never been demonstrated before as far as we know. The proposed reconfigurable TWM owns the capability of dynamically steering terahertz wavefront, indicating great significance for the development of THz reconfigurable devices. (paper)
[en] In this work we establish universal ensemble independent bounds on the mean and variance of the mutual information and channel capacity for imaging through a complex medium. Both upper and lower bounds are derived and are solely dependent on the mean transmittance of the medium and the number of degrees of freedom N. In the asymptotic limit of large N, upper bounds on the channel capacity are shown to be well approximated by that of a bimodal channel with independent identically Bernoulli distributed transmission eigenvalues. Reflection based imaging modalities are also considered and permitted regions in the transmission-reflection information plane defined. Numerical examples drawn from the circular and DMPK random matrix ensembles are used to illustrate the validity of the derived bounds. Finally, although the mutual information and channel capacity are shown to be non-linear statistics of the transmission eigenvalues, the existence of central limit theorems is demonstrated and discussed. (paper)
[en] We develop a scheme for the detection of entanglement in any continuous variable system, by constructing an optimal entanglement witness from random homodyne measurements. To this end, we introduce a set of linear constraints that guarantee the necessary properties of a witness and allow for its optimisation via a semidefinite program. We test our method on the class of squeezed vacuum states and study the efficiency of entanglement detection in general unknown covariance matrices. The results show that we can detect entanglement, including bound entanglement, in arbitrary continuous variable states with fewer measurements than in full tomography. The statistical analysis of our method shows a good robustness to statistical errors in experiments. (paper)