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Thomas Wolf

Publications and source records attributed to Thomas Wolf.

At least 127 records · Page 7Linked to original sources
arXiv2014

The ADI iteration for Lyapunov equations implicitly performs H2 pseudo-optimal model order reduction

Two approaches for approximating the solution of large-scale Lyapunov equations are considered: the alternating direction implicit (ADI) iteration and projective methods by Krylov subspaces. A link between them is presented by showing that the ADI iteration can always be identified by a Petrov-Galerkin projection with rational block Krylov subspaces. Then a unique Krylov-projected dynamical system can be associated with the ADI iteration, which is proven to be an H2 pseudo-optimal approximation. This includes the generalization of previous results on H2 pseudo-optimality to the multivariable case. Additionally, a low-rank formulation of the residual in the Lyapunov equation is presented, which is well-suited for implementation, and which yields a measure of the "obliqueness" that the ADI iteration is associated with.

math.NA↗
arXiv2014

High-Pressure Evolution of the Specific Heat of a Strongly Underdoped Ba(Fe0.963Co0.037)As2 Iron-Based Superconductor

We report specific-heat experiments under the influence of high pressure on a strongly underdoped Co-substituted BaFe2As2 single crystal. This allows us to study the phase diagram of this iron pnictide superconductor with a bulk thermodynamic method and pressure as a clean control parameter. The data show large specific-heat anomalies at the superconducting transition temperature, which proves the bulk nature of pressure-induced superconductivity. The transitions in the specific heat are sharper than in resistivity, which demonstrates the necessity of employing bulk thermodynamic methods to explore the exact phase diagram of pressure-induced Fe-based superconductors. The Tc at optimal pressure and the superconducting condensation energy are found to be larger than in optimally Co-doped samples at ambient pressure, which we attribute to a weak pair breaking effect of the Co ions.

cond-mat.supr-con↗
arXiv2014

Large enhancement of emergent magnetic fields in MnSi with impurities and pressure

We report a study of the topological Hall effect (THE) in Fe-doped MnSi and compare with results from pure MnSi under pressure. We find that Fe doping increases the THE, indicating an enhancement of the magnitude of the emergent gauge field. This is consistent with the concurrent reduction in the length scale of the skyrmion lattice. For both pressurized and doped samples, we calculate the emergent magnetic field based on the size of the measured THE, and compare it with a theoretical upper-bound. We find that the ratio of these two remains more or less constant with pressure or Fe doping, but differs greatly from that of pure MnSi at ambient pressure. We discuss the implications of this ratio with respect to trends in the saturated magnetic moment and helical pitch length as T_C \rightarrow 0 via doping and pressure, respectively.

cond-mat.str-el↗
arXiv2013

ADI iteration for Lyapunov equations: a tangential approach and adaptive shift selection

A new version of the alternating directions implicit (ADI) iteration for the solution of large-scale Lyapunov equations is introduced. It generalizes the hitherto existing iteration, by incorporating tangential directions in the way they are already available for rational Krylov subspaces. Additionally, first strategies to adaptively select shifts and tangential directions in each iteration are presented. Numerical examples emphasize the potential of the new results.

math.NA↗
arXiv2013

Multiband Superconductivity in KFe2As2: Evidence for one Isotropic and several Liliputian Energy Gaps

We report a detailed low-temperature thermodynamic investigation (heat capacity and magnetization) of the superconducting state of KFe2As2 for H || c axis. Our measurements reveal that the properties of KFe2As2 are dominated by a relatively large nodeless energy gap (Delta?0 = 1.9 kBTc) which excludes dx2-y2 symmetry. We prove the existence of several additional extremely small gaps (?Delta0 < 1.0 kBTc) that have a profound impact on the low-temperature and low-field behavior, similar to MgB2, CeCoIn5 and PrOs4Sb12. The zero-field heat capacity is analyzed in a realistic self-consistent 4-band BCS model which qualitatively reproduces the recent laser ARPES results of Okazaki et al. (Science 337 (2012) 1314). Our results show that extremely low-temperature measurements, i.e. T < 0.1 K, will be required in order to resolve the question of the existence of line nodes in this compound.

cond-mat.supr-con↗
arXiv2013

Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction

A novel symmetry method for finding exact solutions to nonlinear PDEs is illustrated by applying it to a semilinear reaction-diffusion equation in multi-dimensions. The method uses a separation ansatz to solve an equivalent first-order group foliation system whose independent and dependent variables respectively consist of the invariants and differential invariants of a given one-dimensional group of point symmetries for the reaction-diffusion equation. With this group-foliation reduction method, solutions of the reaction-diffusion equation are obtained in an explicit form, including group-invariant similarity solutions and travelling-wave solutions, as well as dynamically interesting solutions that are not invariant under any of the point symmetries admitted by this equation.

math-ph↗
arXiv2013

High precision nano scale temperature sensing using single defects in diamond

Measuring local temperature with a spatial resolution on the order of a few nanometers has a wide range of applications from semiconductor industry over material to life sciences. When combined with precision temperature measurement it promises to give excess to small temperature changes caused e.g. by chemical reactions or biochemical processes. However, nanoscale temperature measurements and precision have excluded each other so far owing to the physical processes used for temperature measurement of limited stability of nanoscale probes. Here we experimentally demonstrate a novel nanoscale temperature sensing technique based on single atomic defects in diamonds. Sensor sizes range from millimeter down to a few tens of nanometers. Utilizing the sensitivity of the optically accessible electron spin level structure to temperature changes we achieve a temperature noise floor of 5 mK Hz$^{-1/2}$ for single defects in bulk sensors. Using doped nanodiamonds as sensors yields temperature measurement with 130 mK Hz$^{-1/2}$ noise floor and accuracies down to 1 mK at length scales of a few ten nanometers. The high sensitivity to temperature changes together with excellent spatial resolution combined with outstanding sensor stability allows for nanoscale precision temperature determination enough to measure chemical processes of few or single molecules by their reaction heat even in heterogeneous environments like cells.

quant-ph↗
arXiv2012

The Two-Component Camassa-Holm Equations CH(2,1) and CH(2,2): First-Order Integrating Factors and Conservation Laws

Recently, Holm and Ivanov, proposed and studied a class of multi-component generalisations of the Camassa-Holm equations [D D Holm and R I Ivanov, Multi-component generalizations of the CH equation: geometrical aspects, peakons and numerical examples, J. Phys A: Math. Theor. 43, 492001 (20pp), 2010]. We consider two of those systems, denoted by Holm and Ivanov by CH(2,1) and CH(2,2), and report a class of integrating factors and its corresponding conservation laws for these two systems. In particular, we obtain the complete sent of first-order integrating factors for the systems in Cauchy-Kovalevskaya form and evaluate the corresponding sets of conservation laws for CH(2,1) and CH(2,2).

nlin.SI↗
arXiv2012

Coherent excitations and electron phonon coupling in Ba/EuFe_2As_2 compounds investigated by femtosecond time- and angle-resolved photoemission spectroscopy

We employed femtosecond time- and angle-resolved photoelectron spectroscopy to analyze the response of the electronic structure of the 122 Fe-pnictide parent compounds Ba/EuFe_2As_2 and optimally doped BaFe_{1.85}Co_{0.15}As_2 near the Γpoint to femtosecond optical excitation. We identify pronounced changes of the electron population within several 100 meV above and below the Fermi level, which we explain as combination of (i) coherent lattice vibrations, (ii) a hot electron and hole distribution, and (iii) transient modifications of the chemical potential. The response of the three different materials is very similar. In the Fourier transformation of the time-dependent photoemission intensity we identify three modes at 5.6, 3.3, and 2.6 THz. While the highest frequency mode is safely assigned to the A_{1g} mode, the other two modes require a discussion in comparison to literature. The time-dependent evolution of the hot electron distribution follows a simplified description of a transient three temperature model which considers two heat baths of lattice vibrations, which are more weakly and strongly coupled to transiently excited electron population. Still the energy transfer from electrons to the strongly coupled phonons results in a rather weak, momentum-averaged electron-phonon coupling quantified by values for λ<ω^2> between 30 and 70 meV^2. The chemical potential is found to present a transient modulation induced by the coherent phonons. This change in the chemical potential is particularly strong in a two band system like in the 122 Fe-pnictide compounds investigated here due to the pronounced variation of the electrons density of states close to the equilibrium chemical potential.

cond-mat.mtrl-sci↗
arXiv2012

Travelling waves and conservation laws for complex mKdV-type equations

Travelling waves and conservation laws are studied for a wide class of U(1)-invariant complex mKdV equations containing the two known integrable generalizations of the ordinary (real) mKdV equation. The main results on travelling waves include deriving new complex solitary waves and kinks that generalize the well-known mKdV $\sech$ and $\tanh$ solutions. The main results on conservation laws consist of explicitly finding all 1st order conserved densities that yield phase-invariant counterparts of the well-known mKdV conserved densities for momentum, energy, and Galilean energy, and a new conserved density describing the angular twist of complex kink solutions

math-ph↗
arXiv2011

Thermal expansion and Grüneisen parameters of Ba(Fe1-xCox)2As2 - a thermodynamic quest for quantum criticality

Thermal expansion data are used to study the uniaxial pressure dependence of the electronic/magnetic entropy of Ba(Fe1-xCox)2As2. Uniaxial pressure is found to be proportional to doping and, thus, also an appropriate tuning parameter in this system. Many of the features predicted to occur for a pressure-tuned quantum critical system, in which superconductivity is an emergent phase hiding the critical point, are observed. The electronic/magnetic Grüneisen parameters associated with the spin-density wave and superconducting transitions further demonstrate an intimate connection between both ordering phenomena.

cond-mat.supr-con↗
arXiv2011

Solving large linear algebraic systems in the context of integrable non-abelian Laurent ODEs

The paper reports on a computer algebra program LSSS (Linear Selective Systems Solver) for solving linear algebraic systems with rational coefficients. The program is especially efficient for very large sparse systems that have a solution in which many variables take the value zero. The program is applied to the symmetry investigation of a non-abelian Laurent ODE introduced recently by M. Kontsevich. The computed symmetries confirmed that a Lax pair found for this system earlier generates all first integrals of degree at least up to 14.

cs.SC↗
arXiv2011

The Parametric Solution of Underdetermined linear ODEs

The purpose of this paper is twofold. An immediate practical use of the presented algorithm is its applicability to the parametric solution of underdetermined linear ordinary differential equations (ODEs) with coefficients that are arbitrary analytic functions in the independent variable. A second conceptual aim is to present an algorithm that is in some sense dual to the fundamental Euclids algorithm, and thus an alternative to the special case of a Groebner basis algorithm as it is used for solving linear ODE-systems. In the paper Euclids algorithm and the new `dual version' are compared and their complementary strengths are analysed on the task of solving underdetermined ODEs. An implementation of the described algorithm is interactively accessible under http://lie.math.brocku.ca/crack/demo.

cs.SC↗
arXiv2011

On integrability of the Kontsevich non-abelian ODE system

We consider systems of ODEs with the right hand side being Laurent polynomials in several non-commutative unknowns. In particular, these unknowns could be matrices of arbitrary size. An important example of such a system was proposed by M. Kontsevich. We prove the integrability of the Kontsevich system by finding a Lax pair, corresponding first integrals and commuting flows. We also provide a pre-Hamiltonian operator which maps gradients of integrals for the Kontsevich system to symmetries.

nlin.SI↗
arXiv2011

A Dynamical Systems Approach for Static Evaluation in Go

In the paper arguments are given why the concept of static evaluation has the potential to be a useful extension to Monte Carlo tree search. A new concept of modeling static evaluation through a dynamical system is introduced and strengths and weaknesses are discussed. The general suitability of this approach is demonstrated.

cs.AI↗
arXiv2011

Sensing electric fields using single diamond spins

The ability to sensitively detect charges under ambient conditions would be a fascinating new tool benefitting a wide range of researchers across disciplines. However, most current techniques are limited to low-temperature methods like single-electron transistors (SET), single-electron electrostatic force microscopy and scanning tunnelling microscopy. Here we open up a new quantum metrology technique demonstrating precision electric field measurement using a single nitrogen-vacancy defect centre(NV) spin in diamond. An AC electric field sensitivity reaching ~ 140V/cm/\surd Hz has been achieved. This corresponds to the electric field produced by a single elementary charge located at a distance of ~ 150 nm from our spin sensor with averaging for one second. By careful analysis of the electronic structure of the defect centre, we show how an applied magnetic field influences the electric field sensing properties. By this we demonstrate that diamond defect centre spins can be switched between electric and magnetic field sensing modes and identify suitable parameter ranges for both detector schemes. By combining magnetic and electric field sensitivity, nanoscale detection and ambient operation our study opens up new frontiers in imaging and sensing applications ranging from material science to bioimaging.

quant-ph↗
arXiv2011

Symmetry analysis and exact solutions of semilinear heat flow in multi-dimensions

A symmetry group method is used to obtain exact solutions for a semilinear radial heat equation in $n>1$ dimensions with a general power nonlinearity. The method involves an ansatz technique to solve an equivalent first-order PDE system of similarity variables given by group foliations of this heat equation, using its admitted group of scaling symmetries. This technique yields explicit similarity solutions as well as other explicit solutions of a more general (non-similarity) form having interesting analytical behavior connected with blow up and dispersion. In contrast, standard similarity reduction of this heat equation gives a semilinear ODE that cannot be explicitly solved by familiar integration techniques such as point symmetry reduction or integrating factors.

math.AP↗