| 1. |
- Ögren, Magnus, 1977-, et al.
(författare)
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A numerical damped oscillator approach to constrained Schrödinger equations
- 2020
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Ingår i: European journal of physics. - : Institute of Physics (IOP). - 0143-0807 .- 1361-6404. ; 41:6
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Tidskriftsartikel (refereegranskat)abstract
- 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 Schrödinger equations with additional constraints. In fact, the method is general and can solve constrained minimization problems in many fields. We present the method for introductory applications in quantum mechanics including three qualitative different numerical examples: the radial Schrödinger equation for the hydrogen atom; the two-dimensional harmonic oscillator with degenerate excited states; and a non-linear Schrödinger 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. The undergraduate student can for example use our derived results and the code (supplemental material) to study the Schrödinger equation in 1D for any potential. The graduate student and the general physicist can work from our three examples to derive their own results for other models including other global constraints.
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| 2. |
- Lin, G., et al.
(författare)
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A regularizing Kohn-Vogelius formulation for the model-free adsorption isotherm estimation problem in chromatography
- 2018
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Ingår i: Applicable Analysis. - : Informa UK Limited. - 0003-6811 .- 1563-504X. ; 97:1, s. 13-40
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Tidskriftsartikel (refereegranskat)abstract
- Competitive adsorption isotherms must be estimated in order to simulate and optimize modern continuous modes of chromatography in situations where experimental trial-and-error approaches are too complex and expensive. The inverse method is a numeric approach for the fast estimation of adsorption isotherms directly from overloaded elution profiles. However, this identification process is usually ill-posed. Moreover, traditional model-based inverse methods are restricted by the need to choose an appropriate adsorption isotherm model prior to estimate, which might be very hard for complicated adsorption behavior. In this study, we develop a Kohn-Vogelius formulation for the model-free adsorption isotherm estimation problem. The solvability and convergence for the proposed inverse method are studied. In particular, using a problem-adapted adjoint, we obtain a convergence rate under substantially weaker and more realistic conditions than are required by the general theory. Based on the adjoint technique, a numerical algorithm for solving the proposed optimization problem is developed. Numerical tests for both synthetic and real-world problems are given to show the efficiency of the proposed regularization method.
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| 3. |
- Dmytryshyn, Andrii, 1986-, et al.
(författare)
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Miniversal deformations of matrices of bilinear forms
- 2012
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Ingår i: Linear Algebra and its Applications. - : Elsevier. - 0024-3795 .- 1873-1856. ; 436:7, s. 2670-2700
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Tidskriftsartikel (refereegranskat)abstract
- Arnold [V.I. Arnold, On matrices depending on parameters, Russian Math. Surveys 26 (2) (1971) 29–43] constructed miniversal deformations of square complex matrices under similarity; that is, a simple normal form to which not only a given square matrix A but all matrices B close to it can be reduced by similarity transformations that smoothly depend on the entries of B. We construct miniversal deformations of matrices under congruence.
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| 4. |
- Zhang, Ye, 1984-, et al.
(författare)
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Reconstructing gas distribution maps via an adaptive sparse regularization algorithm
- 2016
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Ingår i: Inverse Problems in Science and Engineering. - : Taylor & Francis. - 1741-5977 .- 1741-5985. ; 24:7, s. 1186-1204
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we present an algorithm to be used by an inspectionrobot to produce a gas distribution map and localize gas sources ina large complex environment. The robot, equipped with a remotegas sensor, measures the total absorption of a tuned laser beam andreturns integral gas concentrations. A mathematical formulation ofsuch measurement facility is a sequence of Radon transforms,which isa typical ill-posed problem. To tackle the ill-posedness, we developa new regularization method based on the sparse representationproperty of gas sources and the adaptive finite-element method. Inpractice, only a discrete model can be applied, and the quality ofthe gas distributionmap depends on a detailed 3-D world model thatallows us to accurately localize the robot and estimate the paths of thelaser beam. In this work, using the positivity ofmeasurements and theprocess of concentration, we estimate the lower and upper boundsof measurements and the exact continuous model (mapping fromgas distribution to measurements), and then create a more accuratediscrete model of the continuous tomography problem. Based onadaptive sparse regularization, we introduce a new algorithm thatgives us not only a solution map but also a mesh map. The solutionmap more accurately locates gas sources, and the mesh map providesthe real gas distribution map. Moreover, the error estimation of theproposed model is discussed. Numerical tests for both the syntheticproblem and practical problem are given to show the efficiency andfeasibility of the proposed algorithm.
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| 5. |
- Aksteiner, S., et al.
(författare)
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New identities for linearized gravity on the Kerr spacetime
- 2019
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Ingår i: Physical Review D. - : American Physical Society. - 2470-0010 .- 2470-0029. ; 99:4
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we derive a differential identity for linearized gravity on the Kerr spacetime and more generally on vacuum spacetimes of Petrov type D. We show that a linear combination of second derivatives of the linearized Weyl tensor can be formed into a complex symmetric 2-tensor M-ab which solves the linearized Einstein equations. The identity makes this manifest by relating M-ab to two terms solving the linearized Einstein equations by construction. The self-dual Weyl curvature of M-ab gives a covariant version of the Teukolsky-Starobinsky identities for linearized gravity which, in addition to the two classical identities for linearized Weyl scalars with extreme spin weights, includes three additional equations. In particular, they are not consequences of the classical Teukolsky-Starobinsky identities, but are additional integrability conditions for linearized gravity. The result has direct application in the construction of symmetry operators and also yields a set of nontrivial gauge invariants for linearized gravity.
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| 6. |
- Roussou, Alexandra, et al.
(författare)
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Excitation spectrum of a mixture of two Bose gases confined in a ring potential with interaction asymmetry
- 2018
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Ingår i: New Journal of Physics. - : Institute of Physics (IOP). - 1367-2630. ; 20
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Tidskriftsartikel (refereegranskat)abstract
- We study the rotational properties of a two-component Bose-Einstein condensed gas of distinguishable atoms which are confined in a ring potential using both the mean-field approximation, as well as the method of diagonalization of the many-body Hamiltonian. We demonstrate that the angular momentum may be given to the system either via single-particle, or "collective" excitation. Furthermore, despite the complexity of this problem, under rather typical conditions the dispersion relation takes a remarkably simple and regular form. Finally, we argue that under certain conditions the dispersion relation is determined via collective excitation. The corresponding many-body state, which, in addition to the interaction energy minimizes also the kinetic energy, is dictated by elementary number theory.
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| 7. |
- Rousse, François, 1989-, et al.
(författare)
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Simulations of quantum dynamics with fermionic phase-space representations using numerical matrix factorizations as stochastic gauges
- 2024
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Ingår i: Journal of Physics A. - : Institute of Physics (IOP). - 1751-8113 .- 1751-8121. ; 57:1
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Tidskriftsartikel (refereegranskat)abstract
- The Gaussian phase-space representation can be used to implement quantum dynamics for fermionic particles numerically. To improve numerical results, we explore the use of dynamical diffusion gauges in such implementations. This is achieved by benchmarking quantum dynamics of few-body systems against independent exact solutions. A diffusion gauge is implemented here as a so-called noise-matrix, which satisfies a matrix equation defined by the corresponding Fokker-Planck equation of the phase-space representation. For the physical systems with fermionic particles considered here, the numerical evaluation of the new diffusion gauges allows us to double the practical simulation time, compared with hitherto known analytic noise-matrices. This development may have far reaching consequences for future quantum dynamical simulations of many-body systems.
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| 8. |
- Sandin, Patrik, 1980-, et al.
(författare)
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Dimensional reduction in Bose-Einstein condensed clouds of atoms confined in tight potentials of any geometry and any interaction strength
- 2017
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Ingår i: Physical Review E. - : American Physical Society. - 2470-0045 .- 2470-0053. ; 95:1
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Tidskriftsartikel (refereegranskat)abstract
- Motivated by numerous experiments on Bose-Einstein condensed atoms which have been performed in tight trapping potentials of various geometries (elongated and/or toroidal/annular), we develop a general method which allows us to reduce the corresponding three-dimensional Gross-Pitaevskii equation for the order parameter into an effectively one-dimensional equation, taking into account the interactions (i.e., treating the width of the transverse profile variationally) and the curvature of the trapping potential. As an application of our model we consider atoms which rotate in a toroidal trapping potential. We evaluate the state of lowest energy for a fixed value of the angular momentum within various approximations of the effectively one-dimensional model and compare our results with the full solution of the three-dimensional problem, thus getting evidence for the accuracy of our model.
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| 9. |
- Ögren, Magnus, 1977-, et al.
(författare)
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Numerical simulations of NMR relaxation in chalk using local Robin boundary conditions
- 2019
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Ingår i: Journal of magnetic resonance. - : Elsevier. - 1090-7807 .- 1096-0856. ; 308
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Tidskriftsartikel (refereegranskat)abstract
- The interpretation of nuclear magnetic resonance (NMR) data is of interest in a number of fields. In Ögren [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).
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| 10. |
- Ögren, Magnus, 1977-, et al.
(författare)
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On the dynamics of the Fermi-Bose model
- 2013
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Ingår i: Journal of Physics A. - : Institute of Physics (IOP). - 1751-8113 .- 1751-8121. ; 46:1
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Tidskriftsartikel (refereegranskat)abstract
- We consider the exponential matrix representing the dynamics of the Fermi-Bose model in an undepleted bosonic field approximation. A recent application of this model is molecular dimers dissociating into its atomic compounds. The problem is solved in D spatial dimensions by dividing the system matrix into blocks with generalizations of Hankel matrices, here referred to as D-block-Hankel matrices. The method is practically useful for treating large systems, i.e. dense computational grids or higher spatial dimensions, either on a single standard computer or a cluster. In particular the results can be used for studies of three-dimensional physical systems of arbitrary geometry. We illustrate the generality of our approach by giving numerical results for the dynamics of Glauber type atomic pair correlation functions for a non-isotropic three-dimensional harmonically trapped molecular Bose-Einstein condensate.
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