Kaleidoscope
![husimi_q_distribution The Husimi-Q distribution at different times allows for the investigation of phase space dynamics.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19090378/husimi-q-distribution-b7a220b88d4c46a4a770b8f1899885fb741c1d0d.png)
Photo: AG Schmelcher
The Husimi-Q distribution at different times allows for the investigation of phase space dynamics.
![natorb-phase-profile Phase profile evolution of a higher order natural orbital corresponding to an ab initio quantum dynamics simulation of a bosonic many-body system out of equilibrium.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19090650/natorb-phase-profile-a56603710fbb6e39eb89713412c1b0146179cb70.png)
Photo: AG Schmelcher
Phase profile evolution of a higher order natural orbital corresponding to an ab initio quantum dynamics simulation of a bosonic many-body system out of equilibrium.
![spatial-natural-geminal Spatial phase distribution of a certain natural geminal, i.e. eigenvector of the reduced 2-body density operator, for a bosonic many-body system in a non-equilibrium state.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19090688/spatial-natural-geminal-0c7bd4b7405ac2f1c34c17e1b6bbb3ec3ed67988.png)
Photo: AG Schmelcher
Spatial phase distribution of a certain natural geminal, i.e. eigenvector of the reduced 2-body density operator, for a bosonic many-body system in a non-equilibrium state.
![decaying-grey-soliton Two-body correlation function of a decaying grey matter-wave soliton.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19090756/decaying-grey-soliton-19a37af84ef4278da5bace84573d0c0924aa25ac.png)
Photo: AG Schmelcher
Two-body correlation function of a decaying grey matter-wave soliton.
![trilobite Trilobite state: The electron probability density of a 35s Rydberg molecule.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19090868/trilobite-0ee121f5567c9f372995a596092aad4068e159c3.png)
Photo: AG Schmelcher
Trilobite state: The electron probability density of a 35s Rydberg molecule.
![excited-chain-relaxation The relaxation of a nonlinearly excited chain of particles in a lattice towards its equilibrium configuration gives rise to collective behavior in terms of oscillation patterns. The figure shows extracts from the time-evolution of the chain's velocit](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19090964/excited-chain-relaxation-1148ba60bd8b474bcb087d2748bbe7c275a995ff.png)
Photo: AG Schmelcher
The relaxation of a nonlinearly excited chain of particles in a lattice towards its equilibrium configuration gives rise to collective behavior in terms of oscillation patterns. The figure shows extracts from the time-evolution of the chain's velocity distribution.
![one-body-lattice The fluctuations of the one-body density evolution for five repulsive bosons in a lattice potential with ten wells, after a sudden change in the interaction strength (quench).](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19091000/one-body-lattice-1eb36b9feaca71d5de4f6c05b9f54f25608ce7b7.png)
Photo: AG Schmelcher
The fluctuations of the one-body density evolution for five repulsive bosons in a lattice potential with ten wells, after a sudden change in the interaction strength (quench).
![one-body-lattice2 The fluctuations of the one-body density evolution (small time-scales) for four repulsive bosons in a lattice potential with three wells, after an abrupt change in the interaction strength (quench).](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19091033/one-body-lattice2-f015dbd192eac1715c704904afc9fb47a62feda0.png)
Photo: AG Schmelcher
The fluctuations of the one-body density evolution (small time-scales) for four repulsive bosons in a lattice potential with three wells, after an abrupt change in the interaction strength (quench).
![half-elliptical-quantum-billiard An electron wave flowing through an open, half-elliptical quantum billiard with four leads, in a strong magnetic field. Coming in through the leftmost lead, the electron forms an edge state which circulates around an obstacle in the middle.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19091066/half-elliptical-quantum-billiard-2123d39a1c549ac5346affc31ae9465cae96ea57.png)
Photo: AG Schmelcher
An electron wave flowing through an open, half-elliptical quantum billiard with four leads, in a strong magnetic field. Coming in through the leftmost lead, the electron forms an edge state which circulates around an obstacle in the middle.
![quantum-billiard-directed-current Directed current: Electron waves injected in each port of an open quantum billiard are transmitted selectively to other ports by tuning a perpendicular magnetic field from zero (top) via intermediate (middle) to high strength (bottom row).](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19091100/quantum-billiard-directed-current-88ad754b0f0920cb9f3fbfc23f3e59e30b49be96.png)
Photo: AG Schmelcher
Directed current: Electron waves injected in each port of an open quantum billiard are transmitted selectively to other ports by tuning a perpendicular magnetic field from zero (top) via intermediate (middle) to high strength (bottom row).
![quantum-billiard-spectrum Energy spectrum of a soft-wall elliptic quantum billiard as a function of magnetic field strength (horizontal axis), plotted on top of the transmission function for the same system attached to left and right leads.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19091169/quantum-billiard-spectrum-a75888e0ce22603536cb3c5e4a30bd6ee8291024.png)
Photo: AG Schmelcher
Energy spectrum of a soft-wall elliptic quantum billiard as a function of magnetic field strength (horizontal axis), plotted on top of the transmission function for the same system attached to left and right leads.
![quantum-billiard-densities Probability density and current density streamlines of electrons in an open soft-wall quantum billiard forwardly collimated in zero magnetic field (top) and backscattered at finite field strength (bottom), persistently in increasing energy (left to r](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19091136/quantum-billiard-densities-562681d5a4703b1c17a524e9128feaa48dd6d46e.png)
Photo: AG Schmelcher
Probability density and current density streamlines of electrons in an open soft-wall quantum billiard forwardly collimated in zero magnetic field (top) and backscattered at finite field strength (bottom), persistently in increasing energy (left to right).
![quantum-billiard-local-dos Local density of states for electron waves flowing through a four-terminal lattice of elliptic quantum dots (ingoing wave in the upper left lead), at different energies and applied magnetic field strengths.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19091201/quantum-billiard-local-dos-c70c8ed0b6c175823d366511905e44205747a91f.png)
Photo: AG Schmelcher
Local density of states for electron waves flowing through a four-terminal lattice of elliptic quantum dots (ingoing wave in the upper left lead), at different energies and applied magnetic field strengths.
![quantum-billiard-transmission Transmission as a function of energy (vertical axis) and magnetic field (horizontal axis) for electron waves flowing through a four-terminal lattice of elliptic quantum dots (see previous picture) from the upper left to the upper right lead.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19091239/quantum-billiard-transmission-111a1e333d96561fce6c894cba8feaf458ce7d35.png)
Photo: AG Schmelcher
Transmission as a function of energy (vertical axis) and magnetic field (horizontal axis) for electron waves flowing through a four-terminal lattice of elliptic quantum dots (see previous picture) from the upper left to the upper right lead.
![oscillating-lattice-phase-space Extract of the phase space portrait of two superimposed simultaneously oscillating lattices, with different lattice spacings.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19091275/oscillating-lattice-phase-space-303f5585e0c8f000355ce73d10b85bab7c708a0f.png)
Photo: AG Schmelcher
Extract of the phase space portrait of two superimposed simultaneously oscillating lattices, with different lattice spacings.
![quantum-billiard-100-modes A Quantum Billiard is a two-dimensional closed region where waves are confined. Here, the first hundred oscillation modes are shown for an oval quantum billiard with left and right stubs.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19091310/quantum-billiard-100-modes-ed8b88a66c566c624b115345782c6e60fa075286.png)
Photo: AG Schmelcher
A Quantum Billiard is a two-dimensional closed region where waves are confined. Here, the first hundred oscillation modes are shown for an oval quantum billiard with left and right stubs.
![ml-mcthdb-flow-chart Flow-chart of the multilayer-multiconfiguration time-dependent Hartree method for bosons.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19091353/ml-mcthdb-flow-chart-47aca2b907966b5e4d7354072dae6ddd4878b2ea.png)
Photo: AG Schmelcher
A Quantum Billiard is a two-dimensional closed region where waves are confined. Here, the first hundred oscillation modes are shown for an oval quantum billiard with left and right stubs.
![bec-vortices Stirring this superfluid excites quantized vortices. The picture shows the simulated density profile of a condensate cloud with four such vortices.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19091385/bec-vortices-8765e2234c5e256371656bba3df4aff4a3f953ba.png)
Photo: AG Schmelcher
In a Bose-Einstein condensate, millions of ultracold bosonic atoms cooperate to form a superfluid. Stirring this superfluid excites quantized vortices. The picture shows the simulated density profile of a condensate cloud with four such vortices.
![oscillating-lattice-phase-space2 Extract of the phase space portrait of an oscillating lattice.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19091421/oscillating-lattice-phase-space2-d187d0127eba80cd601c52613aa4090a7668a32d.png)
Photo: AG Schmelcher
Extract of the phase space portrait of an oscillating lattice.
![oscillating-barrier-scattering-function Scattering function of oscillating potential barrier.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19091464/oscillating-barrier-scattering-function-28ea774e73aca3eeb3830c2db44be872f729990a.png)
Photo: AG Schmelcher
Scattering function of oscillating potential barrier.
![driven-lattice-attraction Attraction to periodic orbits in the driven lattice.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19091510/driven-lattice-attraction-15d01907707649dc4fb5cbe8a2e52a8d408942c1.png)
Photo: AG Schmelcher
Attraction to periodic orbits in the driven lattice.
![driven-lattice-floquet Floquet Mode in a phase modulated driven lattice.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19091545/driven-lattice-floquet-0610c017ac82fd37d674c793dd281b036c8f9376.png)
Photo: AG Schmelcher
Floquet Mode in a phase modulated driven lattice.
![imperfect-lattice-local-invariants Local invariants in an imperfect lattice.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19091600/imperfect-lattice-local-invariants-8e6e71aeecebb4891541660f32e51db8ac533ae5.png)
Photo: AG Schmelcher
Local invariants in an imperfect lattice.
![ions-toroidal-helix Repulsive ions constrained to move on a toroidal helix can stabilize in many different configurations. Here eight such patterns are seen from above.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19091648/ions-toroidal-helix-25643d5e28c12d9c239b74db2667cf18df129335.png)
Photo: AG Schmelcher
Repulsive ions constrained to move on a toroidal helix can stabilize in many different configurations. Here eight such patterns are seen from above.
![inhomogeneous-helix-trajectories Trajectories resulting from the scattering of two charged particles confined on an inhomogeneous helix for various values of initial energy, as viewed in the relevant two-particle space.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19091697/inhomogeneous-helix-trajectories-6cd4a34ad631389eb74e65606fa354896bf7562c.png)
Photo: AG Schmelcher
Trajectories resulting from the scattering of two charged particles confined on an inhomogeneous helix for various values of initial energy, as viewed in the relevant two-particle space.
![bounded-trajectories Bounded trajectories resulting from the scattering of two charged particles confined on an inhomogeneous helix, as viewed in the relevant two-particle space, for a lower (upper) and a higher (lower) energy.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19091759/bounded-trajectories-662ff3a343435900d0a0bd8226cc68d0a7c97038.png)
Photo: AG Schmelcher
Bounded trajectories resulting from the scattering of two charged particles confined on an inhomogeneous helix, as viewed in the relevant two-particle space, for a lower (upper) and a higher (lower) energy.
![poincare-surfaces Poincaré surfaces of section for bounded trajectories resulting from the scattering of two charged particles confined on an inhomogeneous helix, for a lower (upper) and a higher (lower) energy.](https://assets.rrz.uni-hamburg.de/instance_assets/fakmin/19091792/poincare-surfaces-574cc5c4e3396cbcc549c5f8c547418434746a97.png)
Photo: AG Schmelcher
Poincaré surfaces of section for bounded trajectories resulting from the scattering of two charged particles confined on an inhomogeneous helix, for a lower (upper) and a higher (lower) energy.