Search results for "Matrix"

2019

The in-medium dynamics of heavy particles are governed by transport coefficients. The heavy quark momentum diffusion coefficient, $\ensuremath{\kappa}$, is an object of special interest in the literature, but one which has proven notoriously difficult to estimate, despite the fact that it has been computed by weak-coupling methods at next-to-leading order accuracy, and by lattice simulations of the pure SU(3) gauge theory. Another coefficient, $\ensuremath{\gamma}$, has been recently identified. It can be understood as the dispersive counterpart of $\ensuremath{\kappa}$. Little is known about $\ensuremath{\gamma}$. Both $\ensuremath{\kappa}$ and $\ensuremath{\gamma}$ are, however, of foremo…

Continuous-Variable Tomography of Solitary Electrons

2019

A method for characterising the wave-function of freely-propagating particles would provide a useful tool for developing quantum-information technologies with single electronic excitations. Previous continuous-variable quantum tomography techniques developed to analyse electronic excitations in the energy-time domain have been limited to energies close to the Fermi level. We show that a wide-band tomography of single-particle distributions is possible using energy-time filtering and that the Wigner representation of the mixed-state density matrix can be reconstructed for solitary electrons emitted by an on-demand single-electron source. These are highly localised distributions, isolated fro…

Fast evaluation of a linear number of local exchange matrices

2002

A fast method is described for evaluating multiple exchange matrices in a Gaussian atomic orbital basis. For insulators, it is asymptotically linear scaling, and is a generalization of the linear scaling exchange (LinK) method, which was formulated for a single exchange matrix [J. Chem. Phys. 109 (1998) 1663]. It is employed to evaluate exchange-type contractions of all derivative density matrices with two-electron integrals for a series of linear alkanes, linear polyacenes, and water clusters using STO-3G, 3-21G, and 6-31G* basis sets. Significant computational savings are obtained for molecules with as few as 10 non-hydrogen atoms.

High-field nuclear spin relaxation in liquids and solids

1990

The authors generalise the standard theory of nuclear spin relaxation to situations in which the Markovian approximation is not applicable. Expressions for generalised frequency-dependent spin relaxation functions are presented. They show that under high-field conditions the relaxation of longitudinal magnetisation is exponential independent of the particular time dependence of the correlation functions.

Time-dependent Landauer-B\"uttiker formalism for superconducting junctions at arbitrary temperatures

2015

We discuss an extension of our earlier work on the time-dependent Landauer--B\"uttiker formalism for noninteracting electronic transport. The formalism can without complication be extended to superconducting central regions since the Green's functions in the Nambu representation satisfy the same equations of motion which, in turn, leads to the same closed expression for the equal-time lesser Green's function, i.e., for the time-dependent reduced one-particle density matrix. We further write the finite-temperature frequency integrals in terms of known special functions thereby considerably speeding up the computation. Numerical simulations in simple normal metal -- superconductor -- normal m…

Adiabatic Elimination and Sub-space Evolution of Open Quantum Systems

2020

Efficient descriptions of open quantum systems can be obtained by performing an adiabatic elimination of the fast degrees of freedom and formulating effective operators for the slow degrees of freedom in reduced dimensions. Here, we perform the construction of effective operators in frequency space, and using the final value theorem or alternatively the Keldysh theorem, we provide a correction for the trace of the density matrix which takes into account the non trace-preserving character of the evolution. We illustrate our results with two different systems, ones where the eliminated fast subspace is constituted by a continuous set of states and ones with discrete states. Furthermore, we sh…

Multiple scattering theory for non-local and multichannel potentials.

2012

International audience; Methodological advances in multiple scattering theory (MST) in both wave and Green's function versions are reported for the calculation of electronic ground and excited state properties of condensed matter systems with an emphasis on core-level photoemission and absorption spectra. Full-potential MST is reviewed and extended to non-local potentials. Multichannel MST is reformulated in terms of the multichannel density matrix whereby strong electron correlation of atomic multiplet type can be accounted for in both ground and excited states.

Oscillator Strengths of Electronic Excitations with Response Theory using Phase Including Natural Orbital Functionals

2013

The key characteristics of electronic excitations of many-electron systems, the excitation energies ωα and the oscillator strengths fα, can be obtained from linear response theory. In one-electron models and within the adiabatic approximation, the zeros of the inverse response matrix, which occur at the excitation energies, can be obtained from a simple diagonalization. Particular cases are the eigenvalue equations of time-dependent density functional theory (TDDFT), time-dependent density matrix functional theory, and the recently developed phase-including natural orbital (PINO) functional theory. In this paper, an expression for the oscillator strengths fα of the electronic excitations is…

Dynamic chemical devices: photoinduced electron transfer and its ion-triggered switching in nanomechanical butterfly-type bis(porphyrin)terpyridines.

2005

A series of butterfly-type molecular constructs has been prepared in good yield by using a double Stille coupling synthetic protocol. They are composed of a terpyridine (terpy) scaffold and two wings composed of appended porphyrins that are capable of switching from an extended W geometry to a compact U geometry upon cation coordination of the terpy unit. The porphyrin moieties exist in the constructs either as free bases or they can be sequentially metallated, thus giving rise to wings of different "colours". Stationary and time-resolved emission studies of the HZn, ZnAu and Zn2Au constructs show that the electronic properties are strongly dependent on the geometry. In the extended W confo…

A new interface to couple thin-layer chromatography with laser desorption/atmospheric pressure chemical ionization mass spectrometry for plate scanni…

2005

An interface to allow on-line qualitative and quantitative full-plate detection and analysis of compounds separated by thin-layer chromatography (TLC) is presented. A continuous wave diode laser is employed as a desorption source. Atmospheric pressure chemical ionization mass spectrometry ionizes and subsequently identifies the desorbed sample molecules. Besides direct laser desorption on untreated TLC plates, graphite particles were used as a matrix to couple in the laser power and improve the efficiency of desorption.