Searcharxiv⌕ Search

arXiv subjects

H. Lange

Publications and source records attributed to H. Lange.

At least 19 recordsLinked to original sources
arXiv2023

Time-resolved single-particle x-ray scattering reveals electron-density as coherent plasmonic-nanoparticle-oscillation source

Dynamics of optically-excited plasmonic nanoparticles are presently understood as a series of sequential scattering events, involving thermalization processes after pulsed optical excitation. One important step is the initiation of nanoparticle breathing oscillations. According to established experiments and models, these are caused by the statistical heat transfer from thermalized electrons to the lattice. An additional contribution by hot electron pressure has to be included to account for phase mismatches that arise from the lack of experimental data on the breathing onset. We used optical transient-absorption spectroscopy and time-resolved single-particle x-ray-diffractive imaging to access the excited electron system and lattice. The time-resolved single-particle imaging data provided structural information directly on the onset of the breathing oscillation and confirmed the need for an additional excitation mechanism to thermal expansion, while the observed phase-dependence of the combined structural and optical data contrasted previous studies. Therefore, we developed a new model that reproduces all our experimental observations without using fit parameters. We identified optically-induced electron density gradients as the main driving source.

cond-mat.mes-hall↗
arXiv2021

Polarized phonons carry the missing angular momentum in femtosecond demagnetization

Magnetic phenomena are ubiquitous in our surroundings and indispensable for modern science and technology, but it is notoriously difficult to change the magnetic order of a material in a rapid way. However, if a thin nickel film is subjected to ultrashort laser pulses, it can lose its magnetic order almost completely within merely femtosecond times. This phenomenon, in the meantime also observed in many other materials, has connected magnetism with femtosecond optics in an efficient, ultrafast and complex way, offering opportunities for rapid information processing or ultrafast spintronics at frequencies approaching those of light. Consequently, the physics of ultrafast demagnetization is central to modern material research, but a crucial question has remained elusive: If a material loses its magnetization within only femtoseconds, where is the missing angular momentum in such short time? Here we use ultrafast electron diffraction to reveal in nickel an almost instantaneous, long-lasting, non-equilibrium population of anisotropic high-frequency phonons that appear as quickly as the magnetic order is lost. The anisotropy plane is perpendicular to the direction of the initial magnetization and the atomic oscillation amplitude is 2 pm. We explain these observations by means of circularly polarized phonons that quickly absorb the missing angular momentum of the spin system before the slower onset of a macroscopic sample rotation. The time that is needed for demagnetization is related to the time it takes to accelerate the atoms. These results provide an atomistic picture of ultrafast demagnetization under adherence to all conservation laws but also demonstrate the general importance of polarized phonons for non-equilibrium dynamics and provide innovative ways for controlling materials on atomic dimensions.

cond-mat.mtrl-sci↗
arXiv2018

Higher rank BN-theory for curves of genus 6

Higher rank Brill-Noether theory for genus 6 is especially interesting as, even in the general case, some unexpected phenomena arise which are absent in lower genus. Moreover, it is the first case for which there exist curves of Clifford dimension greater than 1 (smooth plane quintics). In all cases, we obtain new upper bounds for non-emptiness of Brill-Noether loci and construct many examples which approach these upper bounds more closely than those that are well known. Some of our examples of non-empty Brill-Noether loci have negative Brill-Noether numbers.

math.AG↗
arXiv2016

Higher rank BN-theory for curves of genus 4

Higher rank Brill-Noether theory is completely known for curves of genus $\leq 3$. In this paper, we investigate the theory for curves of genus 4. Some of our results apply to curves of arbitrary genus.

math.AG↗
arXiv2016

Higher rank BN-thory for curves of genus 5

In this paper, we consider higher rank Brill-Noether theory for smooth curves of genus 5, obtaining new upper bounds for non-emptiness of Brill-Noether loci and many new examples.

math.AG↗
arXiv2015

Non-emptiness of Brill-Noether loci in M(2,L)

Let $C$ be a smooth projective complex curve of genus $g \geq 2$. We investigate the Brill-Noether locus consisting of stable bundles of rank 2 and determinant $L$ of odd degree $d$ having at least $k$ independent sections. This locus possesses a virtual fundamental class. We show that in many cases this class is non-zero, which implies that the Brill-Noether locus is non-empty. For many values of $d$ and $k$ the result is best possible. We obtain more precise results for $k\le5$. An appendix contains the proof of a combinatorial lemma which we need.

math.AG↗
arXiv2013

Bundles of rank 3 on curves of Clifford index 3

Two definitions of the Clifford index for vector bundles on a smooth projective curve $C$ of genus $g\ge4$ were introduced in a previous paper by the authors. In another paper the authors obtained results on one of these indices for bundles of rank 3. In this paper we extend these results in the case where $C$ has classical Clifford index 3. In particular we prove Mercat's conjecture for bundles of rank 3 for $g \leq 8$ and $g \geq 13$ when $C$ has classical Clifford index 3. We obtain complete results in the case of genus 7.

math.AG↗
arXiv2012

On bundles of rank 3 computing Clifford indices

Let $C$ be a smooth irreducible projective algebraic curve defined over the complex numbers. The notion of the Clifford index of $C$ was extended a few years ago to semistable bundles of any rank. Recent work has been focussed mainly on the rank-2 Clifford index, although interesting results have also been obtained for the case of rank 3. In this paper we extend this work, obtaining improved lower bounds for the rank-3 Clifford index. This allows the first computations of the rank-3 index in non-trivial cases and examples for which the rank-3 index is greater than the rank-2 index.

math.AG↗
arXiv2012

Vector bundles of rank 2 computing Clifford indices

Clifford indices of vector bundles on algebraic curves were introduced in a previous paper of the authors. In this paper we study bundles of rank 2 which compute these Clifford indices. This is of particular interest in the light of recently discovered counterexamples to a conjecture of Mercat.

math.AG↗
arXiv2011

On an example of Mukai

In this note we use an example of Mukai to construct semistable bundles of rank 3 with 6 independent sections on a curve of genus 9 or 11 with Clifford index strictly less than the Clifford index of the curve. The example also allows us to show the non-emptiness of some Brill-Noether loci with negative expected dimension.

math.AG↗
arXiv2010

Further examples of stable bundles of rank 2 with 4 sections

In this paper we construct new examples of stable bundles of rank 2 of small degree with 4 sections on a smooth irreducible curve of maximal Clifford index. The corresponding Brill-Noether loci have negative expected dimension of arbitrarily large absolute value.

math.AG↗
arXiv2010

On the gonality sequence of an algebraic curve

For any smooth irreducible projective curve $X$, the gonality sequence $\{d_r \;| \; r \in \mathbb N \}$ is a strictly increasing sequence of positive integer invariants of $X$. In most known cases $d_{r+1}$ is not much bigger than $d_r$. In our terminology this means the numbers $d_r$ satisfy the slope inequality. It is the aim of this paper to study cases when this is not true. We give examples for this of extremal curves in $\PP^r$, for curves on a general K3-surface in $\PP^r$ and for complete intersections in $\PP^3$.

math.AG↗
arXiv2010

Generation of vector bundles computing Clifford indices

Clifford indices for semistable vector bundles on a smooth projective curve of genus at least 4 were defined in a previous paper of the authors. The present paper studies bundles which compute these Clifford indices. We show that under certain conditions on the curve all such bundles and their Serre duals are generated.

math.AG↗
arXiv2009

Lower bounds for Clifford indices in rank three

Clifford indices for semistable vector bundles on a smooth projective curve of genus at least 4 were defined in previous papers of the authors. In the present paper, we establish lower bounds for the Clifford indices for rank 3 bundles. As a consequence we show that, on smooth plane curves of degree at least 10, there exist non-generated bundles of rank 3 computing one of the Clifford indices.

math.AG↗
arXiv2009

Clifford indices for vector bundles on curves

For smooth projective curves the Clifford index is an important invariant which provides a bound for the dimension of the space of sections of a line bundle. This is the first step in distinguishing curves of the same genus. In this paper we generalise this to introduce Clifford indices for semistable vector bundles on curves. We study these invariants, giving some basic properties and carrying out some computations for small ranks and for general and some special curves. For curves whose classical Clifford index is two, we compute all values of our new Clifford indices.

math.AG↗