Detlef Mentrup

Spin dynamics of quantum and classical Heisenberg dimers

Analytical solutions for the time-dependent autocorrelation function of the classical and quantum mechanical spin dimer with arbitrary spin are presented and compared. For large spin quantum numbers or high temperature the classical and the quantum dimer become more and more similar, yet with the major difference that the quantum autocorrelation function is periodic in time whereas the classical is not.

Transition from quantum to classical Heisenberg trimers: thermodynamics and time correlation functions

We focus on the transition from quantum to classical behavior in thermodynamic functions and time correlation functions of a system consisting of three identical quantum spins s that interact via isotropic Heisenberg exchange. The partition function and the zero-field magnetic susceptibility are readily shown to adopt their classical forms with increasing s. The behavior of the spin autocorrelation function (ACF) is more subtle. Unlike the classical Heisenberg trimer where the ACF approaches a unique non-zero limit for long times, for the quantum trimer the ACF is periodic in time. We present exact values of the time average over one period of the quantum trimer for s⩽7 and for infinite temperature. These averages differ from the long-time limit, (940)ln3+(730), of the corresponding classical trimer by terms of order 1/s2. However, upon applying the Levin u-sequence acceleration method to our quantum results we can reproduce the classical value to six significant figures.

ITERATIVE SCATTER CORRECTION FOR GRID-LESS BEDSIDE CHEST RADIOGRAPHY: PERFORMANCE FOR A CHEST PHANTOM

The aim of this work was to experimentally compare the contrast improvement factors (CIFs) of a newly developed software-based scatter correction to the CIFs achieved by an antiscatter grid. To this end, three aluminium discs were placed in the lung, the retrocardial and the abdominal areas of a thorax phantom, and digital radiographs of the phantom were acquired both with and without a stationary grid. The contrast generated by the discs was measured in both images, and the CIFs achieved by grid usage were determined for each disc. Additionally, the non-grid images were processed with a scatter correction software. The contrasts generated by the discs were determined in the scatter-corrected images, and the corresponding CIFs were calculated. The CIFs obtained with the grid and with the software were in good agreement. In conclusion, the experiment demonstrates quantitatively that software-based scatter correction allows restoring the image contrast of a non-grid image in a manner comparable with an antiscatter grid.

A MONTE-CARLO SIMULATION FRAMEWORK FOR JOINT OPTIMISATION OF IMAGE QUALITY AND PATIENT DOSE IN DIGITAL PAEDIATRIC RADIOGRAPHY

In paediatric radiography, according to the as low as reasonably achievable (ALARA) principle, the imaging task should be performed with the lowest possible radiation dose. This paper describes a Monte-Carlo simulation framework for dose optimisation of imaging parameters in digital paediatric radiography. Patient models with high spatial resolution and organ segmentation enable the simultaneous evaluation of image quality and patient dose on the same simulated radiographic examination. The accuracy of the image simulation is analysed by comparing simulated and acquired images of technical phantoms. As a first application example, the framework is applied to optimise tube voltage and pre-filtration in newborn chest radiography. At equal patient dose, the highest CNR is obtained with low-kV settings in combination with copper filtration.

Nosé–Hoover dynamics for coherent states

The popular method of Nose and Hoover to create canonically distributed positions and momenta in classical molecular dynamics simulations is generalized to a genuine quantum system of infinite dimensionality. We show that for the quantum harmonic oscillator, the equations of motion in terms of coherent states can easily be modified in an analogous manner to mimic the coupling of the system to a thermal bath and create a quantum canonical ensemble. Possible applications to more complex systems, especially interacting Fermion systems, are proposed.

Almost-Periodic Wave Packets and Wave Packets of Invariant Shape

Wave packets of one-dimensional, single-particle quantum systems exhibit a rich diversity of dynamical behavior. We focus on confining potentials where the entire energy spectrum is discrete so that wave packets do not spread indefinitely with time and instead exhibit characteristics of almost-periodic functions. For the harmonic oscillator, for which all wave packets are necessarily strictly periodic, Senitzky has shown that is possible to construct an infinite class of normalized wave packets that maintain a fixed shape while oscillating sinusoidally with time. We present two alternate and instructive methods for deriving this result using coherent states and the displacement operator.

Nosé–Hoover sampling of quantum entangled distribution functions

While thermostated time evolutions stand on firm grounds and are widely used in classical molecular dynamics (MD) simulations (J. Phys. Chem. B 104 (2000) 159), similar methods for quantum MD schemes are still lacking. In the special case of a quantum particle in a harmonic potential, it has been shown that the framework of coherent states permits to set up equations of motion for an isothermal quantum dynamics (Physica A 297 (2001) 337). In the present article, these results are generalized to indistinguishable quantum particles. We investigate the consequences of the (anti-)symmetry of the many-particle wavefunction which leads to quantum entangled distribution functions. The resulting isothermal equations of motion for bosons and fermions contain new terms which cause Bose-attraction and Pauli-blocking. Questions of ergodicity are discussed for different coupling schemes.

Isothermal Molecular Dynamics in Classical and Quantum Mechanics

The typical problem in statistical physics is the determination of ensemble averages given in terms of phase-space integrals (classical case) or traces of the density matrix (quantum case). Especially for strongly correlated, i.e. interacting many-body systems, the direct evaluation of these averages is usually impossible. Therefore, a large number of different approaches has been developed. In this contribution, we will focus on finite temperature or canonical ensemble properties.