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Showing 1 to 20 of 30 for “"Gross-Pitaevskii"”.
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Rotating Nonlinear States in Gross-Pitaevskii Equations
… 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 directions: (1) Approximate solutions known as semiclassical wave packets to weakly …
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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… explore the limit of rapid rotations, where the Gross-Pitaevskii equation is no longer valid.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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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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The dynamics of bose gases
We study the Gross-Pitaevskii (GP) hierarchy, which is an infinite sequence of coupled partial differential equations that models the dynamics of Bose gases and arises in the derivation of the cubic and quintic nonlinear Schrödinger equations from an N-body linear Schrödinger equation. In Chapter …
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Bounds on the growth of high Sobolev norms of solutions to nonlinear Schrödinger equations
… regular convolution potential, as well as the Gross-Pitaevskii equation for dipolar quantum gases in the physically relevant 3D setting. The other method is based on a rough cut-off in frequency and it allows us to bound the growth of fractional Sobolev norms of the completely integrable …
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Towards a holographic description of pulsar glitch mechanism
… The foundation of this work is built upon the Gross Pitaevskii (GP) model of super-fluidity applied to the interior matter of neutron stars, where the condensate wave function acts as the order parameter of the macroscopic coherence theory. The excitation modes of the field equations are found …
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Coupled mode reductions and rotating wave approximations in nonlinear equations
… in the cubic-quintic nonlinear Schrodinger/Gross Pitaevskii (NLS/GP) equation with a linear double-well potential and study justifications of the rotating wave approximations in lattice systems. First, we study the long-time dynamics near a symmetry breaking bifurcation point of the …
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Active flows and networks
… leads to persistent localization in a discrete Gross-Pitaevskii quantum network.
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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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Quasi-condensation in low-dimensional Bose gases
… equations. Apart from that, the Stochastic Gross-Pitaevskii equation (SGPE), a non-linear Langevin equation, is analysed numerically by means of Monte-Carlo simulations and the results are compared to those of the mean-field theories. In this context, a lot of attention is payed to 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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Spin and lattice properties of optically trapped exciton polaritons
… condensates is explained within a Gross-Pitaevskii model which accurately reproduces the influence of electric fields and condensate density. Under elliptically polarised pumping, two phenomena are observed: the formation of condensates with the opposite handedness to the pump and …
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Multi-Symplectic Integrators for Nonlinear Wave Equations
… Schrödinger and sine-Gordon equations and the 2D Gross-Pitaevskii equation. In sensitive regimes, the spectral MSIs are not only more accurate but are better at capturing the spatial features of the solutions. In particular, for the sine-Gordon equation we show that its phase space, as measured by …
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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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Ultrakalte Quantengase und Atomlaser
… Die zugehörige Physik wird durch die so genannte Gross-Pitaevskii-Gleichung beschrieben, einer Art nichtlinearen Schrödingergleichung für die Wellenfunktionen der beteiligten Hyperfeinzustände des Bose-Einstein-Kondensats aus 87Rb-Atomen. In der vorliegenden Arbeit wurden unter anderem die …
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Pattern-forming in non-equilibrium quantum systems and geometrical models of matter
… non-linear PDE which is strictly related to the Gross-Pitaevskii and the complex Ginzburg-Landau equations. Numerical simulations of this equation are used to investigate the robustness of the rotating vortex lattice which is predicted to spontaneously form in a non-equilibrium trapped …
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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
… fields are then evolved with the time dependent Gross-Pitaevskii equation. We illustrate the method with the damping of a collective excitation of a one dimensional Bose gas. The fourth part deals with inhomogeneous superconductivity in the presence of magnetic fields that couple only to the spin …
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