Vasile Catrinel Gradinaru


Last Name

Gradinaru

First Name

Vasile Catrinel

ORCID

0000-0002-7762-7894

Organisational unit

03632 - Hiptmair, Ralf / Hiptmair, Ralf

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2012 - 201932020 - 20245
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Publications 1 - 8 of 8
  • Hagedorn wavepackets and Schrödinger equation with time-dependent, homogeneous magnetic field
    Item type: Journal Article
    Gradinaru, Vasile Catrinel; Rietmann, Oliver (2021)
    Journal of Computational Physics
    Certain generalized coherent states, so-called Hagedorn wavepackets, have been used to numerically solve the standard Schrödinger equation. We extend this approach and its recent enhancements to the magnetic Schrödinger equation for a time-dependent, spatially homogeneous magnetic field. We explain why Hagedorn wavepackets are naturally compatible with the aforementioned physical system. In numerical experiments we examine the order of convergence and the preservation of norm and energy. We use this method to simulate a Penning trap as proposed in recent work on quantum computing.
  • A high-order semiclassical splitting for the Schroedinger Equation for nuclei
    Item type: Other Conference Item
    Gradinaru, Vasile Catrinel; Blanes, Sergio (2014)
    The 10th AIMS Conference on Dynamical Systems Differential Equations and Applications. Abstracts
  • High Order Efficient Splittings for the Semiclassical Time–Dependent Schrödinger Equation
    Item type: Report
    Blanes, Sergio; Gradinaru, Vasile Catrinel (2019)
    SAM Research Report
  • Spawning semiclassical wavepackets
    Item type: Journal Article
    Gradinaru, Vasile Catrinel; Rietmann, Oliver (2024)
    Journal of Computational Physics
    The semiclassical (or Hagedorn) wavepackets depending on a fixed set of parameters are an orthonormal L²-basis of generalized coherent states. They have been used to solve numerically the time-dependent Schrödinger equation in its semiclassical formulation, yet their localization property makes them inefficient in case of non-local phenomena such as quantum tunneling. In order to overcome this difficulty, we use simultaneously several bases with different parameters. We propose an algorithm to expand a given wavefunction in terms of multiple families of Hagedorn wavepackets; each family can then be accurately and efficiently propagated using modern semiclassical time-splittings.
  • Numerical Semiclassical Quantum Dynamics with Wavepackets
    Item type: Conference Poster
    Gradinaru, Vasile Catrinel (2012)
  • High order efficient splittings for the semiclassical time–dependent Schrödinger equation
    Item type: Journal Article
    Blanes, Sergio; Gradinaru, Vasile Catrinel (2020)
    Journal of Computational Physics
  • A High-Order Integrator for the Schrödinger Equation with Time-Dependent, Homogeneous Magnetic Field
    Item type: Journal Article
    Gradinaru, Vasile Catrinel; Rietmann, Oliver (2020)
    The SMAI Journal of Computational Mathematics
    We construct a family of numerical methods for the Pauli equation of charged particles in a time-dependent, homogeneous magnetic field. These methods are described in a general setting comprising systems of multiple particles and extend the usual splitting and Fourier grid approach. The issue is that the magnetic field causes charged particles to rotate. The corresponding rotations of the wave function are highly incompatible with the Fourier grid approach used for the standard Schrödinger equation. Motivated by the theory of Lie algebras and their representations, our new approach approximates the exact flow map in terms of rotated potentials and rotated initial data, and thereby avoids this issue. Finally, we provide numerical examples to examine convergence and preservation of norm and energy.
  • Spawning Semiclassical Wavepackets
    Item type: Report
    Gradinaru, Vasile Catrinel; Rietmann, Oliver (2022)
    SAM Research Report
    The semiclassical (or Hagedorn) wavepackets depending on a fixed set of parameters are an orthonormal L2-basis of generalized coherent states. They have been used to solve numerically the time-dependent Schrödinger equation in its semiclassical formulation, yet their localization property makes them inefficient in case of non-local phenomena such as quantum tunneling. In order to overcome this difficulty, we use simultaneously a few members of several bases with different parameters. We propose an algorithm to expand a given wavefunction in terms of multiple families of Hagedorn wavepackets; each family can then be accurately and efficiently propagated using modern semiclassical time-splittings.
Publications 1 - 8 of 8