arXiv subjects

Cord A. Müller

Publications and source records attributed to Cord A. Müller.

At least 19 recordsLinked to original sources

arXiv2026

Finite-temperature superfluid depletion of disordered Bose gases

At zero temperature, homogeneous interacting Bose-condensed fluids are entirely superfluid, with remarkable transport properties. A non-superfluid, normal component is induced by finite temperatures and spatial inhomogeneity, the combined effects of which are rather intriguing, and difficult to describe quantitatively. By inhomogeneous Bogoliubov theory, applicable to weakly interacting condensed Bose gases in static external potentials with arbitrary spatial correlations, we calculate the normal fluid density via the transverse current-current correlation. We obtain finite-temperature disorder corrections to the normal fraction known since Laudau's seminal two-fluid theory, using diagrammatic perturbation theory for systems of any dimensionality, with closed analytical expressions to leading, quadratic order in disorder strength.

cond-mat.quant-gas↗

arXiv2021

Hypothesis-based acceptance sampling for modules F and F1 of the European Measuring Instruments Directive

Millions of measuring instruments are verified each year before being placed on the markets worldwide. In the EU, such initial conformity assessments are regulated by the Measuring Instruments Directive (MID). The MID modules F and F1 on product verification allow for statistical acceptance sampling, whereby only random subsets of instruments need to be inspected. This paper re-interprets the acceptance sampling conditions formulated by the MID. The new interpretation is contrasted with the one advanced in WELMEC guide 8.10, and three advantages have become apparent. Firstly, an economic advantage of the new interpretation is a producers' risk bounded from above, such that measuring instruments with sufficient quality are accepted with a guaranteed probability of no less than 95 %. Secondly, a conceptual advantage is that the new MID interpretation fits into the well-known, formal framework of statistical hypothesis testing. Thirdly, the new interpretation applies unambiguously to finite-sized lots, even very small ones. We conclude that the new interpretation is to be preferred and suggest re-formulating the statistical sampling conditions in the MID. Re-interpreting the MID conditions implies that currently available sampling plans are either not admissible or not optimal. We derive a new acceptance sampling scheme and recommend its application.

stat.AP↗

arXiv2019

Optimal acceptance sampling for modules F and F1 of the European Measuring Instruments Directive

Acceptance sampling plans offered by ISO 2859-1 are far from optimal under the conditions for statistical verification in modules F and F1 as prescribed by Annex II of the Measuring Instruments Directive (MID) 2014/32/EU, resulting in sample sizes that are larger than necessary. An optimised single-sampling scheme is derived, both for large lots using the binomial distribution and for finite-sized lots using the exact hypergeometric distribution, resulting in smaller sample sizes that are economically more efficient while offering the full statistical protection required by the MID.

stat.AP↗

arXiv2017

Weak localization of magnons in chiral magnets

We report on the impact of the Dzyaloshinskii-Moriya interaction on the coherent backscattering of spin waves in a disordered magnetic material. This interaction breaks the inversion symmetry of the spin-wave dispersion relation, such that $ω_\mathbf{k} = ω_{2\mathbf{K}^\mathrm{I}-\mathbf{k}} \neq ω_{-\mathbf{k}}$, where $\mathbf{K}^\mathrm{I}$ is related to the Dzyaloshinskii-Moriya vectors. As a result of numerical investigations we find that the backscattering peak of a wave packet with initial wave vector $\mathbf{k}_0$ shifts from $-\mathbf{k}_0$ to $2\mathbf{K}^\mathrm{I}-\mathbf{k}_0$, such that the backscattering wave vector and the initial wave vector are in general no longer antiparallel. The shifted coherence condition is explained by a diagrammatic approach and opens up an avenue to measure sign and magnitude of the Dzyaloshinskii-Moriya interaction in weakly disordered chiral magnets.

cond-mat.mes-hall↗

arXiv2016

Coherent back and forward scattering peaks in the quantum kicked rotor

We propose and analyze an experimental scheme using the quantum kicked rotor to observe the newly-predicted coherent forward scattering peak together with its long-known twin brother, the coherent backscattering peak. Contrary to coherent backscattering, which arises already under weak-localization conditions, coherent forward scattering is only triggered by Anderson or strong localization. So far, coherent forward scattering has not been observed in conservative systems with elastic scattering by spatial disorder. We propose to turn to the quantum kicked rotor, which has a long and succesful history as an accurate experimental platform to observe dynamical localization, i.e., Anderson localization in momentum space. We analyze the coherent forward scattering effect for the quantum kicked rotor by extensive numerical simulations, both in the orthogonal and unitary class of disordered quantum systems, and show that an experimental realization involving phase-space rotation techniques is within reach of state-of-the-art cold-atom experiments.

cond-mat.quant-gas↗

arXiv2016

Critical dynamics at the Anderson localization mobility edge

We study the critical dynamics of matter waves at the 3D Anderson mobility edge in cold-atom disorder quench experiments. General scaling arguments are supported by precision numerics for the spectral function, diffusion coefficient, and localization length in isotropic blue-detuned speckle potentials. We discuss signatures of critical slowdown in the time-dependent central column density of a spreading wave packet, and evaluate the prospects of observing anomalous diffusion right at criticality.

cond-mat.quant-gas↗

arXiv2016

Disorder and interference: localization phenomena

The specific problem we address in these lectures is the problem of transport and localization in disordered systems, when interference is present, as characteristic for waves, with a focus on realizations with ultracold atoms.

cond-mat.dis-nn↗

arXiv2015

Spin-wave localization in disordered magnets

The effect of disorder on magnonic transport in low-dimensional magnetic materials is studied in the framework of a classical spin model. Numerical investigations give insight into scattering properties of the systems and show the existence of Anderson localization in 1D and weak localization in 2D, potentially affecting the functionality of magnonic devices.

cond-mat.mes-hall↗

arXiv2015

Speckle intensity correlations of photons scattered by cold atoms

The irradiation of a dilute cloud of cold atoms with a coherent light field produces a random intensity distribution known as laser speckle. Its statistical fluctuations contain information about the mesoscopic scattering processes at work inside the disordered medium. Following up on earlier work by Assaf and Akkermans [Phys.\ Rev.\ Lett.\ \textbf{98}, 083601 (2007)], we analyze how static speckle intensity correlations are affected by an internal Zeeman degeneracy of the scattering atoms. It is proven on general grounds that the speckle correlations cannot exceed the standard Rayleigh law. On the contrary, because which-path information is stored in the internal atomic states, the intensity correlations suffer from strong decoherence and become exponentially small in the diffusive regime applicable to an optically thick cloud.

cond-mat.dis-nn↗

arXiv2015

Semiclassical spectral function for matter waves in random potentials

An $\hbar$-expansion is presented for the ensemble-averaged spectral function of noninteracting matter waves in random potentials. We obtain the leading quantum corrections to the deep classical limit at high energies by the Wigner-Weyl formalism. The analytical results are checked with success against numerical data for Gaussian and laser speckle potentials with Gaussian spatial correlation in two dimensions.

cond-mat.quant-gas↗

arXiv2015

Josephson relation for disordered superfluids

The Josephson sum rule relates the superfluid density to the condensate order parameter, via the infrared residue of the single-particle Green's function. We establish an effective Josephson relation for disordered condensates valid upon ensemble averaging. This relation has the merit to show explicitly how superfluidity links to the coherent density, i.e., the density of particles with zero momentum. Detailed agreement is reached with perturbation theory for weak disorder.

cond-mat.quant-gas↗

arXiv2015

Anderson localization of Bogoliubov excitations on quasi-1D strips

Anderson localization of Bogoliubov excitations is studied for disordered lattice Bose gases in planar quasi-one-dimensional geometries. The inverse localization length is computed as function of energy by a numerical transfer-matrix scheme, for strips of different widths. These results are described accurately by analytical formulas based on a weak-disorder expansion of backscattering mean free paths.

cond-mat.quant-gas↗

arXiv2014

Diffusive density profiles in a cold-atom expansion experiment

In a recent experiment [McGehee et al., Phys. Rev. Lett. 111, 145303 (2013)], the expansion of non-interacting ultracold fermions was studied in a random speckle potential, and the observed density profiles were interpreted based on 3D Anderson localization. The purpose of this note is to demonstrate that slow diffusion of particles with a broad energy distribution and an energy-dependent diffusion coefficient leads to density profiles that agree with the measured data, but not with the behavior expected for 3D Anderson localization.

cond-mat.quant-gas↗

arXiv2014

A grand-canonical approach to the disordered Bose gas

We study the problem of disordered interacting bosons within grand-canonical thermodynamics and Bogoliubov theory. We compute the fractions of condensed and non-condensed particles and corrections to the compressibility and the speed of sound due to interaction and disorder. There are two small parameters, the disorder strength compared to the chemical potential and the dilute-gas parameter.

cond-mat.quant-gas↗

arXiv2014

Optimal Control of Effective Hamiltonians

We present a systematic scheme for optimization of quantum simulations. Specifically, we show how polychromatic driving can be used to significantly improve the driving of Raman transitions in the Lambda system, which opens new possibilities for controlled driven-induced effective dynamics.

quant-ph↗

arXiv2013

Bogoliubov theory on the disordered lattice

Quantum fluctuations of Bose-Einstein condensates trapped in disordered lattices are studied by inhomogeneous Bogoliubov theory. Weak-disorder perturbation theory is applied to compute the elastic scattering rate as well as the renormalized speed of sound in lattices of arbitrary dimensionality. Furthermore, analytical results for the condensate depletion are presented, which are in good agreement with numerical data.

cond-mat.quant-gas↗

arXiv2012

Coherent Backscattering of Ultracold Matter Waves: Momentum Space Signatures

Using analytical and numerical methods, it is shown that the momentum distribution of a matter wave packet launched in a random potential exhibits a pronounced coherent backscattering (CBS) peak. By analyzing the momentum distribution, key transport times can be directly measured. The CBS peak can be used to prove that transport occurs in the phase-coherent regime, and measuring its time dependence permits monitoring the transition from classical diffusion to Anderson localization.

cond-mat.dis-nn↗

arXiv2011

Stability and decay of Bloch oscillations in presence of time-dependent nonlinearity

We consider Bloch oscillations of Bose-Einstein condensates in presence of a time-modulated s-wave scattering length. Generically, interaction leads to dephasing and decay of the wave packet. Based on a cyclic-time argument, we find---additionally to the linear Bloch oscillation and a rigid soliton solution---an infinite family of modulations that lead to a periodic time evolution of the wave packet. In order to quantitatively describe the dynamics of Bloch oscillations in presence of time-modulated interactions, we employ two complementary methods: collective-coordinates and the linear stability analysis of an extended wave packet. We provide instructive examples and address the question of robustness against external perturbations.

cond-mat.quant-gas↗