arXiv subjects

M. Ogren

Publications and source records attributed to M. Ogren.

At least 19 recordsLinked to original sources

arXiv2026

Heterosymmetric states of rotating quantum droplets under confinement

We investigate the rotational response of a confined, two-dimensional quantum droplet, which emerges in an attractive binary Bose mixture that is stabilized against collapse by beyond-mean-field effects. We consider both a harmonic and an anharmonic form for the external confining potential. We go beyond the widely employed ``phase-locked" single-order-parameter model, maintaining two separate order parameters for the two components, and calculating the lowest-energy state for various values of the angular momentum. For a population-balanced quantum droplet and sufficiently tight confinement, we find that near certain half-integer values of the angular momentum the droplet is excited in a ``heterosymmetric" manner, with the two components carrying different vorticities. This mode is naturally missed by the single-order-parameter model. We additionally investigate the effects of a small population imbalance in the droplet. Apart from an energy increase associated with the population difference, the imbalance also lifts the double degeneracy of the heterosymmetric states, which characterizes the $\mathbb{Z}_2$-symmetric balanced droplet. The heterosymmetric mode is found to be favored by the energy term which captures the beyond-mean-field effects in the mixture.

cond-mat.quant-gas↗

arXiv2024

Rapidly-rotating quantum droplets confined in a harmonic potential

We consider a "symmetric" quantum droplet in two spatial dimensions, which rotates in a harmonic potential, focusing mostly on the limit of "rapid" rotation. We examine this problem using a purely numerical approach, as well as a semi-analytic Wigner-Seitz approximation (first developed by Baym, Pethick et al.) for the description of the state with a vortex lattice. Within this approximation we assume that each vortex occupies a cylindrical cell, with the vortex-core size treated as a variational parameter. Working with a fixed angular momentum, as the angular momentum increases and depending on the atom number, the droplet accommodates none, few, or many vortices, before it turns to center-of-mass excitation. For the case of a "large" droplet, working with a fixed rotational frequency of the trap $\Omega$, as $\Omega$ approaches the trap frequency $\omega$, a vortex lattice forms, the number of vortices increases, the mean spacing between them decreases, while the "size" of each vortex increases as compared to the size of each cell. In contrast to the well-known problem of contact interactions, where we have melting of the vortex lattice and highly-correlated many-body states, here no melting of the vortex lattice is present, even when $\Omega = \omega$. This difference is due to the fact that the droplet is self-bound. Actually, for $\Omega = \omega$, the "smoothed" density distribution becomes a flat top, very much like the static droplet. When $\Omega$ exceeds $\omega$, the droplet maintains its shape and escapes to infinity, via center-of-mass motion.

cond-mat.quant-gas↗

arXiv2023

Rotating quantum droplets confined in an anharmonic potential

We investigate the rotational properties of quantum droplets, which form in a mixture of two Bose-Einstein condensates, in the presence of an anharmonic trapping potential. We identify various phases as the atom number and the angular momentum/angular velocity of the trap vary. These phases include center-of-mass-like excitation (without, or with vortices), vortices of single and multiple quantization, etc. Finally, we compare our results with those of the single-component problem.

cond-mat.quant-gas↗

arXiv2023

Nonlinearity managed vector solitons

The evolution of vector solitons under nonlinearity management is studied. The averaged over strong and rapid modulations in time of the inter-species interactions vector Gross-Pitaevskii equation (GPE) is derived. The averaging gives the appearance of the effective nonlinear quantum pressure depending on the population of the other component. Using this system of equations, the existence and stability of the vector solitons under the action of the strong nonlinearity management (NM) is investigated. Using a variational approach the parameters of NM vector solitons are found. The numerical simulations of the full time-dependent coupled GPE confirms the theoretical predictions.

nlin.PS↗

arXiv2023

Rotating quantum droplets confined in a harmonic potential

We investigate the rotational properties of a two-component, two-dimensional self-bound quantum droplet, which is confined in a harmonic potential and compare them with the well-known problem of a single-component atomic gas with contact interactions. For a fixed value of the trap frequency, choosing some representative values of the atom number, we determine the lowest-energy state, as the angular momentum increases. For a sufficiently small number of atoms, the angular momentum is carried via center-of-mass excitation. For larger values, when the angular momentum is sufficiently small, we observe vortex excitation instead. Depending on the actual atom number, one or more vortices enter the droplet. Beyond some critical value of the angular momentum, however, the droplet does not accommodate more vortices and the additional angular momentum is carried via center-of-mass excitation in a "mixed" state. Finally, the excitation spectrum is also briefly discussed.

cond-mat.quant-gas↗

arXiv2022

Management of solitons in medium with competing cubic and quadratic nonlinearities

Management of solitons in media with competing quadratic and cubic nonlinearities is investigated. Two schemes, using rapid modulations of a mismatch parameter, and of the Kerr nonlinearity parameter are studied. For both cases, the averaged in time wave equations are derived. In the case of mismatch management, the region of the parameters where stabilization is possible is found. In the case of Kerr nonlinearity management, it is shown that the effective $\chi^{(2)}$ nonlinearity depends on the intensity imbalance between fundamental (FH) and second (SH) harmonics. Predictions obtained from the averaged equations are confirmed by numerical simulations of the full PDE's.

nlin.PS↗

arXiv2022

Correlated quantum dynamics of graphene

Phase-space representations are a family of methods for dynamics of both bosonic and fermionic systems, that work by mapping the system's density matrix to a quasi-probability density and the Liouville-von Neumann equation of the Hamiltonian to a corresponding density differential equation for the probability. We investigate here the accuracy and the computational efficiency of one approximate phase-space representation, called the fermionic Truncated Wigner Approximation (fTWA), applied to the Fermi-Hubbard model. On a many-body 2D system, with hopping strength and Coulomb $U$ tuned to represent the electronic structure of graphene, the method is found to be able to capture the time evolution of first-order (site occupation) and second-order (correlation functions) moments significantly better than the mean-field, Hartree-Fock method. The fTWA was also compared to results from the exact diagonalization method for smaller systems, and in general the agreement was found to be good. The fully parallel computational requirement of fTWA scales in the same order as the Hartree-Fock method, and the largest system considered here contained 198 lattice sites.

cond-mat.quant-gas↗

arXiv2020

Stochastic solutions of Stefan problems

This work deals with the one-dimensional Stefan problem with a general time-dependent boundary condition at the fixed boundary. Stochastic solutions are obtained using discrete random walks, and the results are compared with analytic formulae when they exist, otherwise with numerical solutions from a finite difference method. The innovative part is to model the moving boundary with a random walk method. The results show statistical convergence for many random walkers when $\Delta x \rightarrow 0$. Stochastic methods are very competitive in large domains in higher dimensions and has the advantages of generality and ease of implementation. The stochastic method suffers from that longer execution times are required for increased accuracy. Since the code is easily adapted for parallel computing, it is possible to speed up the calculations. Regarding applications for Stefan problems, they have historically been used to model the dynamics of melting ice, and we give such an example here where the fixed boundary condition follows data from observed day temperatures at \"{O}rebro airport. Nowadays, there are a large range of examples of applications, such as climate models, the diffusion of lithium-ions in lithium-ion batteries and modelling steam chambers for petroleum extraction.

math.AP↗

arXiv2020

A numerical damped oscillator approach to constrained Schr\"{o}dinger equations

This article explains and illustrates the use of a set of coupled dynamical equations, second order in a fictitious time, which converges to solutions of stationary Schr\"{o}dinger equations with additional constraints. We include three qualitative different numerical examples: the radial Schr\"{o}dinger equation for the hydrogen atom; the two-dimensional harmonic oscillator with degenerate excited states; and finally a non-linear Schr\"{o}dinger equation for rotating states. The presented method is intuitive, with analogies in classical mechanics for damped oscillators, and easy to implement, either in own coding, or with software for dynamical systems. Hence, we find it suitable to introduce it in a continuation course in quantum mechanics or generally in applied mathematics courses which contain computational parts.

physics.comp-ph↗

arXiv2019

Numerical simulations of NMR relaxation in chalk using local Robin boundary conditions

The interpretation of nuclear magnetic resonance (NMR) data is of interest in a number of fields. In \"{O}gren [Eur. Phys. J. B (2014) 87: 255] local boundary conditions for random walk simulations of NMR relaxation in digital domains were presented. Here, we have applied those boundary conditions to large, three-dimensional (3D) porous media samples. We compared the random walk results with known solutions and then applied them to highly structured 3D domains, from images derived using synchrotron radiation CT scanning of North Sea chalk samples. As expected, there were systematic errors caused by digitalization of the pore surfaces so we quantified those errors, and by using linear local boundary conditions, we were able to significantly improve the output. We also present a technique for treating numerical data prior to input into the ESPRIT algorithm for retrieving Laplace components of time series from NMR data (commonly called $T$-inversion).

physics.geo-ph↗

arXiv2019

Collective dynamics of Fermi-Bose mixtures with an oscillating scattering length

Collective oscillations of superfluid mixtures of ultra cold fermionic and bosonic atoms are investigated while varying the fermion-boson scattering length. We study the dynamics with respect to excited center of mass modes and breathing modes in the mixture. Parametric resonances are also analyzed when the scattering length varies periodically in time, by comparing partial differential equation (PDE) models and ordinary differential equation (ODE) models for the dynamics. An application to the recent experiment with fermionic $^{6}$Li and bosonic $^{7}$Li atoms, which approximately have the same masses, is discussed.

cond-mat.quant-gas↗

arXiv2017

Solitons in a ${\cal PT}$- symmetric $\chi^{(2)}$ coupler

We consider the existence and stability of solitons in a $\chi^{(2)}$ coupler. Both the fundamental and second harmonics undergo gain in one of the coupler cores and are absorbed in the other one. The gain and losses are balanced creating a parity-time (${\cal PT}$) symmetric configuration. We present two types of families of ${\cal PT}$-symmetric solitons, having equal and different profiles of the fundamental and second harmonics. It is shown that gain and losses can stabilize solitons. Interaction of stable solitons is shown. In the cascading limit the model is reduced to the ${\cal PT}$-symmetric coupler with effective Kerr-type nonlinearity and balanced nonlinear gain and losses.

physics.optics↗

arXiv2017

There's more to the multimedia effect than meets the eye: is seeing pictures believing?

Textbooks in applied mathematics often use graphs to explain the meaning of formulae, even though their benefit is still not fully explored. To test processes underlying this assumed multimedia effect we collected performance scores, eye movements, and think-aloud protocols from students solving problems in vector calculus with and without graphs. Results showed no overall multimedia effect, but instead an effect to confirm statements that were accompanied by graphs, irrespective of whether these statements were true or false. Eye movement and verbal data shed light on this surprising finding. Students looked proportionally less at the text and the problem statement when a graph was present. Moreover, they experienced more mental effort with the graph, as indicated by more silent pauses in thinking aloud. Hence, students actively processed the graphs. This, however, was not sufficient. Further analysis revealed that the more students looked at the statement, the better they performed. Thus, in the multimedia condition the graph drew students' attention and cognitive capacities away from focusing on the statement. A good alternative strategy in the multimedia condition was to frequently look between graph and problem statement, and thus to integrate their information. In conclusion, graphs influence where students look and what they process, and may even mislead them into believing accompanying information. Thus, teachers and textbook designers should be very critical on when to use graphs and carefully consider how the graphs are integrated with other parts of the problem.

physics.ed-ph↗

arXiv2017

The Dynamics of Magnetic Vortices in Type II Superconductors with Pinning Sites Studied by the Time Dependent Ginzburg-Landau Model

We investigate the dynamics of magnetic vortices in type II superconductors with normal state pinning sites using the Ginzburg-Landau equations. Simulation results demonstrate hopping of vortices between pinning sites, influenced by external magnetic fields and external currents. The system is highly nonlinear and the vortices show complex nonlinear dynamical behaviour.

cond-mat.supr-con↗

arXiv2015

Numerical solution of the stationary multicomponent nonlinear Schr\"{o}dinger equation with a constraint on the angular momentum

We formulate a damped oscillating particle method to solve the stationary nonlinear Schr\"{o}dinger equation (NLSE). The ground state solutions are found by a converging damped oscillating evolution equation that can be discretized with symplectic numerical techniques. The method is demonstrated for three different cases: for the single-component NLSE with an attractive self-interaction, for the single-component NLSE with a repulsive self interaction and a constraint on the angular momentum, and for the two-component NLSE with a constraint on the total angular momentum. We reproduce the so called yrast curve for the single-component case, described in [A. D. Jackson et al., Europhys. Lett. 95, 30002 (2011)], and produce for the first time an analogous curve for the two-component NLSE. The numerical results are compared with analytic solutions and competing numerical methods. Our method is well suited to handle a large class of equations and can easily be adapted to further constraints and components.

physics.comp-ph↗

arXiv2014

Local boundary conditions for NMR-relaxation in digitized porous media

We narrow the gap between simulations of nuclear magnetic resonance dynamics on digital domains (such as CT-images) and measurements in D-dimensional porous media. We point out with two basic domains, the ball and the cube in D dimensions, that due to a digital uncertainty in representing the real pore surfaces of dimension D-1, there is a systematic error in simulated dynamics. We then reduce this error by introducing local Robin boundary conditions.

physics.comp-ph↗

arXiv2013

Perturbative Semiclassical Trace Formulae for Harmonic Oscillators

In this article we extend previous semiclassical studies by including more general perturbative potentials of the harmonic oscillator in arbitrary spatial dimensions. Our starting point is a radial harmonic potential with an arbitrary even monomial perturbation, which we use to study the resulting $\mathrm{U}(D)$ to $\mathrm{O}(D)$ symmetry breaking. We derive the gross structure of the semiclassical spectrum from periodic orbit theory, in the form of a perturbative ($\hbar \rightarrow 0$) trace formula. We then show how to apply the results to even order polynomial potentials, possibly including mean-field terms. We have drawn the conclusion that the gross structure of the quantum spectrum is determined from only classical circular- and diameter-orbits for this class of systems.

math-ph↗

arXiv2013

Faraday waves in quasi-one-dimensional superfluid Fermi-Bose mixtures

Generation of Faraday waves in superfluid Fermi-Bose mixtures in elongated traps is investigated. The generation of waves is achieved by periodically changing a parameter of the system in time. Two types of modulations of parameters are considered, first a variation of the fermion-bosons scattering length, and secondly the boson-boson scattering length. We predict the properties of the generated Faraday patterns and study the parameter regions where they can be excited.

nlin.PS↗