Linear Continuum Mechanics for Quantum Many-Body Systems

We develop the continuum mechanics of quantum many-body systems in the linear response regime. The basic variable of the theory is the displacement field, for which we derive a closed equation of motion under the assumption that the time-dependent wave function in a locally co-moving reference frame can be described as a geometric deformation of the ground-state wave function. We show that this equation of motion is exact for systems consisting of a single particle, and for all systems at sufficiently high frequency, and that it leads to an excitation spectrum that has the correct integrated strength. The theory is illustrated by simple model applications to one- and two-electron systems.Comment: 4 pages, 1 figure, 1 tabl

Spectroscopy on two coupled flux qubits

We have performed spectroscopy measurements on two coupled flux qubits. The qubits are coupled inductively, which results in a $\sigma_1^z\sigma_2^z$ interaction. By applying microwave radiation, we observe resonances due to transitions from the ground state to the first two excited states. From the position of these resonances as a function of the magnetic field applied we observe the coupling of the qubits. The coupling strength agrees well with calculations of the mutual inductance

Kurt Symanzik - a stable fixed point beyond triviality

In 1970 Kurt Symanzik proposed a "precarious" phi**4-theory with a negative quartic coupling constant as a valid candidate for an asymptotically free theory of strong interactions. Symanzik's deep insight in the non-trivial properties of this theory has been overruled since then by the Hermitian intuition of generations of scientists, who considered or consider this actually non-Hermitian highly important theory to be unstable. This short - certainly controversial - communication tries to shed some light on the historical and formalistic context of Symanzik's theory in order to sharpen our (quantum) intuition about non-perturbative theoretical physics between (non)triviality and asymptotic freedom.Comment: 6 pages, no figures, new style files, revised for typos, improved discussion, new references adde

Continuum Mechanics for Quantum Many-Body Systems: The Linear Response Regime

We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave function. By describing the many-body system in terms of a single collective field we provide an alternative to traditional approaches, which emphasize one-particle orbitals. We refer to our approach as continuum mechanics for quantum many-body systems. In the linear response regime, the equation of motion for the displacement field becomes a linear fourth-order integro-differential equation, whose only inputs are the one-particle density matrix and the pair correlation function of the ground-state. The complexity of this equation remains essentially unchanged as the number of particles increases. We show that our equation of motion is a hermitian eigenvalue problem, which admits a complete set of orthonormal eigenfunctions under a scalar product that involves the ground-state density. Further, we show that the excitation energies derived from this approach satisfy a sum rule which guarantees the exactness of the integrated spectral strength. Our formulation becomes exact for systems consisting of a single particle, and for any many-body system in the high-frequency limit. The theory is illustrated by explicit calculations for simple one- and two-particle systems.Comment: 23 pages, 4 figures, 1 table, 6 Appendices This paper is a follow-up to PRL 103, 086401 (2009

Multilinear Wavelets: A Statistical Shape Space for Human Faces

We present a statistical model for $3$D human faces in varying expression, which decomposes the surface of the face using a wavelet transform, and learns many localized, decorrelated multilinear models on the resulting coefficients. Using this model we are able to reconstruct faces from noisy and occluded $3$D face scans, and facial motion sequences. Accurate reconstruction of face shape is important for applications such as tele-presence and gaming. The localized and multi-scale nature of our model allows for recovery of fine-scale detail while retaining robustness to severe noise and occlusion, and is computationally efficient and scalable. We validate these properties experimentally on challenging data in the form of static scans and motion sequences. We show that in comparison to a global multilinear model, our model better preserves fine detail and is computationally faster, while in comparison to a localized PCA model, our model better handles variation in expression, is faster, and allows us to fix identity parameters for a given subject.Comment: 10 pages, 7 figures; accepted to ECCV 201

Relativistic Structure of the Nucleon Self-Energy in Asymmetric Nuclei

The Dirac structure of the nucleon self-energy in asymmetric nuclear matter cannot reliably be deduced from the momentum dependence of the single-particle energies. It is demonstrated that such attempts yield an isospin dependence with even a wrong sign. Relativistic studies of finite nuclei have been based on such studies of asymmetric nuclear matter. The effects of these isospin components on the results for finite nuclei are investigated.Comment: 9 pages, Latex 4 figures include

On the effect of image denoising on galaxy shape measurements

Weak gravitational lensing is a very sensitive way of measuring cosmological parameters, including dark energy, and of testing current theories of gravitation. In practice, this requires exquisite measurement of the shapes of billions of galaxies over large areas of the sky, as may be obtained with the EUCLID and WFIRST satellites. For a given survey depth, applying image denoising to the data both improves the accuracy of the shape measurements and increases the number density of galaxies with a measurable shape. We perform simple tests of three different denoising techniques, using synthetic data. We propose a new and simple denoising method, based on wavelet decomposition of the data and a Wiener filtering of the resulting wavelet coefficients. When applied to the GREAT08 challenge dataset, this technique allows us to improve the quality factor of the measurement (Q; GREAT08 definition), by up to a factor of two. We demonstrate that the typical pixel size of the EUCLID optical channel will allow us to use image denoising.Comment: Accepted for publication in A&A. 8 pages, 5 figure

Relativistic Brueckner-Hartree-Fock calculations with explicit intermediate negative energy states

In a relativistic Brueckner-Hartree-Fock calculation we include explicit negative-energy states in the two-body propagator. This is achieved by using the Gross spectator-equation, modified by medium effects. Qualitatively our results compare well with other RBHF calculations. In some details significant differences occur, e.g, our equation of state is stiffer and the momentum dependence of the self-energy components is stronger than found in a reference calculation without intermediate negative energy states.Comment: 13 pages Revtex, 5 figures included seperatel