Search results for "Linear Algebra"
showing 10 items of 552 documents
A Temperature Dependent Non-Linear Inductor Model for a DC/DC Boost Converter
2018
This paper is focused on the use of non-linear inductors in DC/DC switching converters, as well as their behaviour due to changes in current and temperature. The model of an inductor is set up on the basis of experimental data, which are automatically acquired by a virtual instrument; from those data, a polynomial curve describing the inductance variations is obtained. The analysis of the converter, performed by including the proposed model, is validated by experimental tests.
Oscillatory Localization of Quantum Walks Analyzed by Classical Electric Circuits
2016
We examine an unexplored quantum phenomenon we call oscillatory localization, where a discrete-time quantum walk with Grover's diffusion coin jumps back and forth between two vertices. We then connect it to the power dissipation of a related electric network. Namely, we show that there are only two kinds of oscillating states, called uniform states and flip states, and that the projection of an arbitrary state onto a flip state is bounded by the power dissipation of an electric circuit. By applying this framework to states along a single edge of a graph, we show that low effective resistance implies oscillatory localization of the quantum walk. This reveals that oscillatory localization occ…
Analytic estimation of transition between instantaneous eigenstates of quantum two-level system
2018
AbstractTransition amplitudes between instantaneous eigenstates of a quantum two-level system are evaluated analytically on the basis of a new parametrization of its evolution operator, which has recently been proposed to construct exact solutions. In particular, the condition under which the transitions are suppressed is examined analytically. It is shown that the analytic expression of the transition amplitude enables us, not only to confirm the adiabatic theorem, but also to derive the necessary and sufficient condition for quantum two-level system to remain in one of the instantaneous eigenstates.
Entanglement in Gaussian matrix-product states
2006
Gaussian matrix product states are obtained as the outputs of projection operations from an ancillary space of M infinitely entangled bonds connecting neighboring sites, applied at each of N sites of an harmonic chain. Replacing the projections by associated Gaussian states, the 'building blocks', we show that the entanglement range in translationally-invariant Gaussian matrix product states depends on how entangled the building blocks are. In particular, infinite entanglement in the building blocks produces fully symmetric Gaussian states with maximum entanglement range. From their peculiar properties of entanglement sharing, a basic difference with spin chains is revealed: Gaussian matrix…
Scale-free relaxation of a wave packet in a quantum well with power-law tails
2013
We propose a setup for which a power-law decay is predicted to be observable for generic and realistic conditions. The system we study is very simple: A quantum wave packet initially prepared in a potential well with (i) tails asymptotically decaying like ~ x^{-2} and (ii) an eigenvalues spectrum that shows a continuous part attached to the ground or equilibrium state. We analytically derive the asymptotic decay law from the spectral properties for generic, confined initial states. Our findings are supported by realistic numerical simulations for state-of-the-art expansion experiments with cold atoms.
Including Tetraquark Operators in the Low-Lying Scalar Meson Sectors in Lattice QCD
2019
Lattice QCD allows us to probe the low-lying hadron spectrum in finite-volume using a basis of single- and multi-hadron interpolating operators. Here we examine the effect of including tetraquark operators on the spectrum in the scalar meson sectors containing the $K_0^*(700)$ ($\kappa$) and the $a_0(980)$ in $N_f = 2 + 1$ QCD, with $m_\pi \approx 230$ MeV. Preliminary results of additional finite-volume states found using tetraquark operators are shown, and possible implications of these states are discussed.
Decoherence effects in the Stern-Gerlach experiment using matrix Wigner functions
2016
We analyze the Stern-Gerlach experiment in phase space with the help of the matrix Wigner function, which includes the spin degree of freedom. Such analysis allows for an intuitive visualization of the quantum dynamics of the device. We include the interaction with the environment, as described by the Caldeira-Leggett model. The diagonal terms of the matrix provide us with information about the two components of the state that arise from interaction with the magnetic field gradient. In particular, from the marginals of these components, we obtain an analytical formula for the position and momentum probability distributions in the presence of decoherence that shows a diffusive behavior for l…
Color-singlet states in a hadronic quark-cluster basis
1987
We prove that any physical (color-singlet) state can be expanded in terms of a basis constructed by direct product from baryonic and/or mesonic states. The proof is based on a group-theoretical representation method due to Hund. The application of the procedure to the color degrees of freedom leads to known results, which we generalize to more complex situations. The joint application of the method to the color and flavor degrees of freedom results in our initial statement. In this way one is able to give physical meaning to a mathematical procedure. The physics behind our calculation is intimately connected with the concepts of elementarity of constituents and the spinstatistics theorem. T…
Four-time rotational correlation functions
1998
A scheme to analyze four-time rotational correlation functions of any rank is developed and details for rank L = 1 and 2 are given. The scheme provides a transparent way for identifying deviations from simple Markovian dynamics as observed, e.g., in complex liquids close to the glass transition. The method should be applicable to NMR and optical multiple-pulse techniques as well as to photon correlation spectroscopy. Results are given for 2H-NMR multiple-pulse data in supercooled glycerol. We identify and analyze the dynamical heterogeneity of molecular reorientation in a range of 205 − 215 K close to the glass temperature Tg = 190 K.
Stochastic models for heterogeneous relaxation: Application to inhomogeneous optical lineshapes
2001
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale. Starting from the most simple Gaussian Markov process we model the exchange between 'slow' and 'fast' environments by treating the fluctuating single-particle variable as a projection from a higher-dimensional Markov process. The moments of the resulting stochastic process are calculated from the corresponding Master equations or Langevin equations, depending on the model. The calculations show the importance of the way to treat exchange processes. The result…