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Showing 1 to 20 of 20 for “"Gross-Pitaevskii equation"”.
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Dynamics of the Gross-Pitaevskii Equation and Shortcuts to Adiabaticity
Procedures which vary the parameters of a model in an adiabatic way have applications in many areas of quantum technology. However, explicitly employing adiabatic evolution often leads to decoherence issues due to systems interacting with their environment. For this reason, there has been much …
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Numerical Solutions to the Gross-Pitaevskii Equation for Bose-Einstein Condensates
… potential operators for the two-dimensional (2D) Gross-Pitaevskii equation (GPE) for Bose-Einstein condensates. Both the 2D and the 1D models are scaled to get a three parameter model. Smoothness of initial conditions is considered and choice of method (Split-Step Fourier method with Strang …
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Statistical Analysis of Highly Correlated Systems in Biology and Physics
… explore the limit of rapid rotations, where the Gross-Pitaevskii equation is no longer valid. Interestingly, the Gross-Pitaevskii equation seems to be valid for much higher densities than expected if properly renormalized. I show that, in accord with the prediction of the Gross-Pitaevskii …
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Rotating Nonlinear States in Gross-Pitaevskii Equations
… we consider a class of nonlinear Schr\"odinger equations with angular momentum rotation term, which is also known as the Gross-Pitaevskii equation in the physics literature. This equation is a well-known model for ultra-cold quantum gases in rotating traps. Our results include two main …
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Bounds on the growth of high Sobolev norms of solutions to nonlinear Schrödinger equations
… of solutions to nonlinear Schrödinger type equations which we can't bound from above by energy conservation. The growth of such norms gives a quantitative estimate on the low-to high frequency cascade which can occur due to the nonlinear evolution. In our work, we present two possible …
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Quasi-condensation in low-dimensional Bose gases
… on the basis of their excitation sprectum, equation of state, density fluctuations and related correlation functions. High-temperature expansions of the corresponding integrals are derived analytically for the numerical evaluation of the self-consistent integral equations. Apart from that, …
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On quantum vortex reconnections
… in Bose–Einstein condensates, governed by the Gross–Pitaevskii Equation (GPE). The investigation is applied to two distinct settings. First we study the reconnection between an inclined vortex ring and a straight vortex line, where the vortex ring inclination angle is varied. We analyze the …
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Tunneling Dynamics of a Bose-Einstein Condensate
… agreement with numerical solutions of the 3D Gross-Pitaevskii equation.
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Bogoliubov Excitations of Inhomogeneous Bose-Einstein Condensates
… the many-body problem is split into the Gross-Pitaevskii condensate (mean-field) and the Bogoliubov excitations, which are bosonic quasiparticles. The disorder potential causes an imprint in the condensate, which makes the Hamiltonian for the Bogoliubov excitations inhomogeneous. The …
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Multi-Symplectic Integrators for Nonlinear Wave Equations
… for Hamiltonian ordinary differential equations have shown to be robust, efficient and accurate in long-term calculations. In this thesis, we show how symplectic integrators have a natural generalization to Hamiltonian PDEs by introducing the concept of multi-symplectic partial …
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Dynamics and thermodynamics of strongly driven Bose gases
… (within the classical field approximation using Gross-Pitaevskii equation simulations). Here, the continuous energy input leads to a turbulent cascade, which reaches a steady-state with matching energy injection and dissipation rates. The turbulent state, although steady, is far from …
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Negative temperature states of bosons in triangular and kagome lattices
… such states using a Monte-Carlo method. The Gross-Pitaevskii equation provides another way to calculate the groundstates for the frustrated lattice and has the advantage of including the effects of both interaction and harmonic confinement. Although the resulting states from the calculation …
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Topics in the Theory of Quantum Degenerate Gases
… can be in two hyperfine states. We derive simple equations of motion for this system closely analogous to the Bloch equations. We also map the dynamics of the system onto those of a classical particle in a well. We find novel density and spin modes of oscillation and new stable equilibrium points …
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Topics in the theory of quantum degenerate gases
… can be in two hyperfine states. We derive simple equations of motion for this system closely analogous to the Bloch equations. We also map the dynamics of the system onto those of a classical particle in a well. We find novel density and spin modes of oscillation and new stable equilibrium points …
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Excitations in superfluids of atoms and polaritons
… satisfies a particular partial differential equation (PDE). These PDEs are discussed in the beginning of this thesis and justified in the context of the quantum many-body problem. For high occupation numbers and when neglecting quantum fluctuations the quantum field operator simplifies to a …
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Localisation of Bose-Einstein condensates in optical lattices
… well-described by a continuous model using the Gross-Pitaevskii equation in a modulated potential or, in the case of deep potentials, a discrete model using the Discrete Nonlinear Schrodinger equation. Spatially localised modes, known as lattice solitons in the continuous model, or discrete …
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Dynamics in Cold Atomic Gases: Resonant Behaviour of the Quantum Delta-Kicked Accelerator and Bose-Einstein Condensates in Ring Traps
… included via a mean-field description within the Gross-Pitaevskii equation. A broad regime of dynamical stability using a two-component BEC is identified, in which a typical implementation using Rb-87 is predicted to lie. A proof-of-principle Sagnac atom-interferometer using a two-component Rb-87 …
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Measurement of the density profile of quantized vortices and of the equation of state in a 3D interacting Bose gas
… been simulated with numerical solutions of the Gross-Pitaevskii equation. The same data analysis procedure has been applied to both the experimental images and to the density profiles computed with the simulations to ensure a faithful comparison. We were able to detail the evolution of the …
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Novel effects in self-interacting scalar field dark matter solitons
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms
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Dynamics and properties of massive quantum vortices in binary mixtures of Bose-Einstein condensates
L'abstract è presente nell'allegato / the abstract is in the attachment