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Martin Andersson

Publications and source records attributed to Martin Andersson.

36 records · Page 2Linked to original sources
arXiv2022

Historic behaviour vs. physical measures for irrational flows with multiple stopping points

We study Birkhoff averages along trajectories of smooth reparameterizations of irrational linear flows of the two torus with two stopping points, say $\mathbf p$ and $\mathbf q$, of quadratic order. The limiting behaviour of such averages is independent of the starting point in a set of full Haar-Lebesgue measure and depends in an intricate way on the Diophantine properties of both the slope $α$ of the linear flow as well as the relative position of $\mathbf p$ and $\mathbf q$. In particular, if $α$ is Diophantine, then Birkhoff limits diverge almost everywhere (historic behaviour) and if $α$ is sufficiently Liouville, then there exists some $\mathbf p$ and $\mathbf q$ such that the Birkhoff averages converge almost everywhere (unique physical measure).

math.DS↗
arXiv2021

A Hybrid Quantum-Classical Heuristic to solve large-scale Integer Linear Programs

We present a method that integrates any quantum algorithm capable of finding solutions to integer linear programs into the Branch-and-Price algorithm, which is regularly used to solve large-scale integer linear programs with a specific structure. The role of the quantum algorithm is to find integer solutions to subproblems appearing in Branch-and-Price. Obtaining optimal or near-optimal integer solutions to these subproblems can increase the quality of solutions and reduce the depth and branching factor of the Branch-and-Price algorithm and hence reduce the overall running time. We investigate the viability of the approach by considering the Tail Assignment problem and the Quantum Approximate Optimization Algorithm (QAOA). Here, the master problem is the optimization problem Set Partitioning or its decision version Exact Cover and can be expressed as finding the ground state of an Ising spin glass Hamiltonian. For Exact Cover, our numerical results indicate that the required algorithm depth decreases with the number of feasible solutions for a given success probability of finding a feasible solution. For Set Partitioning, on the other hand, we find that for a given success probability of finding the optimal solution, the required algorithm depth can increase with the number of feasible solutions if the Hamiltonian is balanced poorly, which in the worst case is exponential in the problem size. We therefore address the importance of properly balancing the objective and constraint parts of the Hamiltonian. We empirically find that the approach is viable with QAOA if polynomial algorithm depth can be realized on quantum devices.

quant-ph↗
arXiv2020

Illuminating a Blind Spot in Digitalization -- Software Development in Sweden's Private and Public Sector

As Netscape co-founder Marc Andreessen famously remarked in 2011, software is eating the world - becoming a pervasive invisible critical infrastructure. Data on the distribution of software use and development in society is scarce, but we compile results from two novel surveys to provide a fuller picture of the role software plays in the public and private sectors in Sweden, respectively. Three out of ten Swedish firms, across industry sectors, develop software in-house. The corresponding figure for Sweden's government agencies is four out of ten, i.e., the public sector should not be underestimated. The digitalization of society will continue, thus the demand for software developers will further increase. Many private firms report that the limited supply of software developers in Sweden is directly affecting their expansion plans. Based on our findings, we outline directions that need additional research to allow evidence-informed policy-making. We argue that such work should ideally be conducted by academic researchers and national statistics agencies in collaboration.

cs.CY↗
arXiv2020

Applying the Quantum Approximate Optimization Algorithm to the Tail Assignment Problem

Airlines today are faced with a number of large scale scheduling problems. One such problem is the tail assignment problem, which is the task of assigning individual aircraft to a given set of flights, minimizing the overall cost. Each aircraft is identified by the registration number on its tail fin. In this article, we simulate the Quantum Approximate Optimization Algorithm (QAOA) applied to instances of this problem derived from real world data. The QAOA is a variational hybrid quantum-classical algorithm recently introduced and likely to run on near-term quantum devices. The instances are reduced to fit on quantum devices with 8, 15 and 25 qubits. The reduction procedure leaves only one feasible solution per instance, which allows us to map the tail assignment problem onto the Exact Cover problem. We find that repeated runs of the QAOA identify the feasible solution with close to unit probability for all instances. Furthermore, we observe patterns in the variational parameters such that an interpolation strategy can be employed which significantly simplifies the classical optimization part of the QAOA. Finally, we empirically find a relation between the connectivity of the problem graph and the single-shot success probability of the algorithm.

quant-ph↗
arXiv2019

Statistical stability of mostly expanding diffeomorphisms

We study how physical measures vary with the underlying dynamics in the open class of $C^r$, $r>1$, strong partially hyperbolic diffeomorphisms for which the central Lyapunov exponents of every Gibbs $u$-state is positive. If transitive, such a diffeomorphism has a unique physical measure that persists and varies continuously with the dynamics. A main ingredient in the proof is a new Pliss-like Lemma which, under the right circumstances, yields frequency of hyperbolic times close to one. Another novelty is the introduction of a new characterization of Gibbs $cu$-states. Both of these may be of independent interest. The non-transitive case is also treated: here the number of physical measures varies upper semi-continuously with the diffeomorphism, and physical measures vary continuously whenever possible.

math.DS↗
arXiv2018

Transitivity of conservative toral endomorphisms

It is shown that if a non-invertible area preserving local homeomorphism on $\mathbb{T}^2$ is homotopic to a linear expanding or hyperbolic endomorphism, then it must be topologically transitive. This gives a complete characterization, in any smoothness category, of those homotopy classes of conservative endomorphisms that consist entirely of transitive maps.

math.DS↗
arXiv2016

On mostly expanding diffeomorphisms

In this work we study the class of mostly expanding partially hyperbolic diffeomorphisms. We prove that such class is $C^r$-open, $r>1$, among the partially hyperbolic diffeomorphisms (in the narrow sense) and we prove that the mostly expanding condition guarantee the existence of physical measures and provide more information about the statistics of the system. Mañé's classical derived-from-Anosov diffeomorphism on $\mathbb{T}^3$ belongs to this set.

math.DS↗
arXiv2014

Hyperfine dependent $gf$-values of Mn I lines in the 1.49 $-$ 1.80 $μ$m H-band

The three Mn I lines at 17325, 17339 and 17349 Å~are among the 25 strongest lines ($\log(gf)>0.5$) in the H-band. They are all heavily broadened due to hyperfine structure and the profiles of these lines have so far not been understood. Earlier studies of these lines even suggested that they were blended. In this work, the profiles of these three infra-red (IR) lines have been studied theoretically and compared to experimental spectra to assist in the complete understanding of the solar spectrum in the IR. It is shown that the structure of these lines can not be described in the conventional way by the diagonal $A$ and $B$ hyperfine interaction constants. The off-diagonal hyperfine interaction not only has large impact on the energies of the hyperfine levels, but also introduces a large intensity redistribution among the hyperfine lines, changing the line profiles dramatically. By performing large-scale calculations of the diagonal and off-diagonal hyperfine interaction and $gf$-values between the upper and lower hyperfine levels and using a semi-empirical fitting procedure, agreement between our synthetic and experimental spectra was achieved. Furthermore, we compare our results with observations of stellar spectra. The spectra of the Sun and the K1.5 III red giant star Arcturus were modelled in the relevant region, $1.73-1.74$ $μ$m using our theoretically predicted $gf$-values and energies for each individual hyperfine line. Satisfactory fits were obtained and clear improvements were found using our new data compared with the old available Mn I data. A complete list of energies and $gf$-values for all the $3d^54s({^7S})4d$ e$^{6}$D $-$ $3d^54s({^7S})4f$ w$^{6}$F hyperfine lines are available as supplementary material online, whereas only the stronger lines are presented and discussed in detail in this paper.

astro-ph.SR↗
arXiv2013

Ergodic theory of generic continuous maps

We study the ergodic properties of generic continuous dynamical systems on compact manifolds. As a main result we prove that generic homeomorphisms have convergent Birkhoff averages under continuous observables at Lebesgue almost every point. In spite of this, when the underlying manifold has dimension greater than one, generic homeomorphisms have no physical measure --- a somewhat strange result which stands in sharp contrast to current trends in generic differentiable dynamics. Similar results hold for generic continuous maps. To further explore the mysterious behaviour of $C^0$ generic dynamics, we also study the ergodic properties of continuous maps which are conjugated to expanding circle maps. In this context, generic maps have divergent Birkhoff averages along orbits starting from Lebesgue almost every point.

math.DS↗
arXiv2013

Theoretical investigations on magnetic field induced $2p^53s^3P_{0,2} - 2p^6^1S_0$ transitions in Ne-like ions without nuclear spin

We report theoretical results for magnetic field induced $2p^53s^3P_{0,2} - 2p^6^1S_0$ E1 transitions in Ne-like ions with zero nuclear spin (I=0) between Mg III and Zn XXI as well as in Ne I. We demonstrate that it is important to include both ``perturber'' states $2p^53s^1P_1$ and $2p^53s^3P_1$ in order to produce reliable transition rates. Furthermore, we investigate the trends of the rates along the isoelectronic sequence of the $2p^53s^3P_{0,2} - 2p^6^1S_0$ transitions and their competition with the $2p^53s^3P_0 - 2p^53s^3P_1$ M1 and the $2p^53s^3P_2 - 2p^6^1S_0$ M2 decays. For the $2p^53s^3P_0$ state the magnetic field induced transition becomes the dominant decay channel for the light elements even in a relatively weak magnetic field, and it will therefore prove useful in diagnostics of the strength of magnetic fields in different plasmas. The influence of an external magnetic field on the lifetime of the $2p^53s^3P_2$ state is much smaller but still observable for the ions near the neutral end of the sequence. As a special case, the magnetic field effect on the lifetimes of $2p^53s^3P_{0,2}$ states of neutral $^{20}$Ne is discussed. It is found that the lifetimes are drastically reduced by a magnetic field, which may be an underlying reason for the discrepancies in the lifetime of the $2p^53s^3P_2$ state between experiment (14.73(14) s) and theory (17.63 s).

physics.atom-ph↗
arXiv2008

Stable ergodicity of dominated systems

We provide a new approach to stable ergodicity of systems with dominated splittings, based on a geometrical analysis of global stable and unstable manifolds of hyperbolic points. Our method suggests that the lack of uniform size of Pesin's local stable and unstable manifolds - a notorious problem in the theory of non-uniform hyperbolicity - is often less severe than it appeas to be.

math.DS↗
arXiv2008

Robust ergodic properties in partially hyperbolic dynamics

We study ergodic properties of partially hyperbolic systems whose central direction is mostly contracting. Earlier work of Bonatti, Viana about existence and finitude of physical measures is extended to the case of local diffeomorphisms. Moreover, we prove that such systems constitute a C^2-open set in which statistical stability is a dense property. In contrast, all mostly contracting systems are shown to be stable under small random perturbations.

math.DS↗
arXiv2002

Staggered flux and stripes in doped antiferromagnets

We have numerically investigated whether or not a mean-field theory of spin textures generate fictitious flux in the doped two dimensional $t-J$-model. First we consider the properties of uniform systems and then we extend the investigation to include models of striped phases where a fictitious flux is generated in the domain wall providing a possible source for lowering the kinetic energy of the holes. We have compared the energetics of uniform systems with stripes directed along the (10)- and (11)-directions of the lattice, finding that phase-separation generically turns out to be energetically favorable. In addition to the numerical calculations, we present topological arguments relating flux and staggered flux to geometric properties of the spin texture. The calculation is based on a projection of the electron operators of the $t-J$ model into a spin texture with spinless fermions.

cond-mat.str-el↗
arXiv2001

Fictitious fluxes in doped antiferromagnets

In a tight binding model of charged spin-1/2 electrons on a square lattice, a fully polarized ferromagnetic spin configuration generates an apparent U(1) flux given by $2π$ times the skyrmion charge density of the ferromagnetic order parameter. We show here that for an antiferromagnet, there are two ``fictitious'' magnetic fields, one staggered and one unstaggered. The staggered topological flux per unit cell can be varied between $-π\leΦ\leπ$ with a negligible change in the value of the effective nearest neighbor coupling constant whereas the magnitude of the unstaggered flux is strongly coupled to the magnitude of the second neighbor effective coupling.

cond-mat.str-el↗
arXiv1998

Density Matrix Renormalization Group of Gapless Systems

We investigate convergence of the density matrix renormalization group (DMRG) in the thermodynamic limit for gapless systems. Although the DMRG correlations always decay exponentially in the thermodynamic limit, the correlation length at the DMRG fixed-point scales as $ξ\sim m^{1.3}$, where $m$ is the number of kept states, indicating the existence of algebraic order for the exact system. The single-particle excitation spectrum is calculated, using a Bloch-wave ansatz, and we prove that the Bloch-wave ansatz leads to the symmetry $E(k)=E(π-k)$ for translationally invariant half-integer spin-systems with local interactions. Finally, we provide a method to compute overlaps between ground states obtained from different DMRG calculations.

cond-mat.str-el↗
arXiv1998

Anytime Coalition Structure Generation with Worst Case Guarantees

Coalition formation is a key topic in multiagent systems. One would prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow exhaustive search for the optimal one. But then, can the coalition structure found via a partial search be guaranteed to be within a bound from optimum? We show that none of the previous coalition structure generation algorithms can establish any bound because they search fewer nodes than a threshold that we show necessary for establishing a bound. We present an algorithm that establishes a tight bound within this minimal amount of search, and show that any other algorithm would have to search strictly more. The fraction of nodes needed to be searched approaches zero as the number of agents grows. If additional time remains, our anytime algorithm searches further, and establishes a progressively lower tight bound. Surprisingly, just searching one more node drops the bound in half. As desired, our algorithm lowers the bound rapidly early on, and exhibits diminishing returns to computation. It also drastically outperforms its obvious contenders. Finally, we show how to distribute the desired search across self-interested manipulative agents.

cs.MA↗