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International audience; The self-consistent mean-fied Schrödinger-Poisson model of quantum-dot helium is described in the mixed-state approximation of a two-level nonlinear quantum system (G. Reinisch, M. Gazeau, Eur. Phys. J. Plus 131, 220 (2016)). We investigate the strong nonlinear limit of vanishing harmonic confinement. We find that the two corresponding trajectories in the appropriate phase-space bifurcate from the Thomas-Fermi fixed point to a final singular statistical equilibrium state that is defined by equal population of the two energy levels as a result of eigenstate overlap $ \sim 1/\sqrt{2}$ between their respective nonlinear eigenstates. Further increase of nonlinearity, i.e. of eigenstate overlap, yields population inversion and therefore instability. At equilibrium, a black-body residual photon field is set up when considering the single-photon lowest-order QED description of the Coulomb interaction between the two electrons. We point out the possible interest of such an equilibrium state in the search of the Cooper-pair “pairing glue” of bound electron pairs in the degenerate Fermi gas of high-temperature superconductors, as well as its link with a recently renewed debate about the physical existence of QED mediating virtual photons (G. Jaeger, Entropy 21, 141 (2019)).

The recent results on the linear breathing mode of the excitation spectrum of a quantum dot obtained by McDonald et. al [Phys. Rev. Lett. 111, 256801 (2013)] are extended to the nonlinear regime. To accomplish this and analyze the results the response of five different models of two interacting electrons in a quantum dot to an external short lived radial excitation that is strong enough to excite the system well beyond the linear response regime is compared. The models considered describe the Coulomb interaction between the electrons in different ways ranging from mean-field approaches to configuration interaction (CI) models, where the two-electron Hamiltonian is diagonalized in a large truncated Fock space. The radially symmetric excitation is selected in order to severely put to test the different approaches to describe the interaction and correlations of an electron system in a nonequilibrium state. As can be expected for the case of only two electrons none of the mean-field models can in full details reproduce the results obtained by the CI model. Nonetheless, some linear and nonlinear characteristics are reproduced reasonably well. All the models show activation of an increasing number of collective modes as the strength of the excitation is increased. By varying slightly the confinement potential of the dot it was observed how sensitive the properties of the excitation spectrum are to the Coulomb interaction and its correlation effects. In order to approach closer the question of nonlinearity one of the mean-field models has been solved directly in a nonlinear fashion without resorting to iterations.

In this paper we consider a basic two-level nonlinear quantum model consisting in a two-particle interacting bound-state system. It is described by means of two different approaches: i) the mean-field stationary nonlinear Schrodinger-Poisson equation with classical Coulomb interaction and harmonic potential; ii) the linear quantum electrodynamics Hamiltonian of a quantized field coupled to two fixed charges. Computing numerically the ground state and the first excited state about the maximum eigenstate overlap (which is not zero because of eigenstate non-orthogonality), we numerically demonstrate that these two descriptions coincide at first order. As a consequence, a specific definition of the fine-structure constant \( \alpha\) is provided within 99.95% accuracy by the present first-order non-relativistic and nonlinear quantum description. This result also means that the internal Coulomb interaction commutes with external particle confinement for the calculation of the ground state. Consequently peculiar nonlinear quantum properties become observable (an experiment with GaAs quantum-dot helium is suggested).

The 2D radial stationary nonlinear Schroedinger equation yields a new action-phase quantization of energy, in contrast with the linear case where the energy levels are degenerated with respect to the Ermakov constant. Characteristic values of radial energy quantization are given in the Gross–Pitaevskii mean-field description for the main vortex-nucleation experiments performed in rotating Bose–Einstein condensates. Finally, the link with Einstein's conjecture about non-quantizability of quasiperiodic orbits on a 2D torus is pointed out.

Two output beams of a Stern–Gerlach (SG) apparatus for spin 1/2 particles should not show interference when appropriately superposed (i.e. by means of a `half-reversible SG setup' that is described in this letter). The reason is that an entanglement between energy level and path selection occurs.

We consider the simplest quantum system, namely the two-level system with real matrix elements, and exhibit its specific phase properties related to the complex Hamiltonian formalism provided by a simple canonical transformation between the Schroedinger equation and a classical dynamical system that actually describes the dynamics of a spin 12. In the case of the quantum Zeno effect, it yields the provocative theoretical suggestion and experimental prediction that an energy measurement should always yield the same energy value (which is either the upper or the lower energy level, depending on the value of the energy expectation value), contrary to the standard quantum rule stating that an energy measurement should share the probabilities between the two energy levels (except for the eigenstates). This makes a quasi-continuously observed two-level quantum system very similar to a classical system from the point of view of energy measurements.

In the presence of resonant Rabi oscillations and depending on the amplitude of the periodic drive, the dynamics of the phase of a two-state quantum system is either fractal (i.e. aperiodic according to a random process) or phase-locked (i.e. quasiperiodic).

Originally proposed by Read [1] and Jain [2], the so-called "composite-fermion" is a phenomenological attachment of two infinitely thin local flux quanta seen as nonlocal vortices to two-dimensional (2D) electrons embedded in a strong orthogonal magnetic field. In this letter, it is described as a highly-nonlinear and coherent mean-field quantum process of the soliton type by use of a 2D stationary Schroedinger-Poisson differential model with only two Coulomb-interacting electrons. At filling factor $\nu={1}{3}$ of the lowest Landau level, it agrees with both the exact two-electron antisymmetric Schroedinger wave function and Laughlin's Jastrow-type guess for the fractional quantum Hall effect, hence providing this later with a tentative physical justification based on first principles., Comment: RevTeX, 5 pages with 3 included eps-figures

Using similar nonlinear stationary mean-field models for Bose-Einstein Condensation of cold atoms and interacting electrons in a Quantum Dot, we propose to describe the original many-particle ground state as a one-particle statistical mixed state of the nonlinear eigenstates whose weights are provided by the eigenstate non-orthogonality. We search for physical grounds in the interpretation of our two main results, namely, quantum-classical nonlinear transition and interference between nonlinear eigenstates., Comment: RevTeX (pdfLaTeX), 7 pages with 5 png-figures included

We use a nonlinear Schroedinger-Poisson equation to describe two interacting electrons with opposite spins confined in a parabolic potential, a quantum dot. We propose an effective form of the Poisson equation taking into account the dimensional mismatch of the two-dimensional electronic system and the three-dimensional electrostatics. The results agree with earlier numerical calculations performed in a large basis of two-body states and provide a simple model for continuous quantum-classical transition with increasing nonlinearity. Specific intriguing properties due to eigenstate non-orthogonality are emphasized., RevTeX, 8 pages with 6 included eps figures

By use of the Larmor equivalence between uniform rotation and a magnetic field, we consider in the strong-interaction Thomas-Fermi regime the single centered vortex as the first Zeeman-like excited state of the axisymmetric rotating Bose-Einstein condensate. This yields a resonant-drive nucleation mechanism whose threshold is in quite good agreement with ENS, MIT, and JILA experimental results.

We present a simple mechanical model, relevant to first order with respect to the perturbation, which accounts for plateau-tail generations and adiabatic dampings or growths of basic nonlinear solitary waves: the Korteweg de Vries, nonlinear Schrodinger, and Burgers shock wave. This theory gives most qualitative and quantitative properties of the plateau, i.e., its large width (which may extend over the mean free path of the pulse itself), its amplitude and its shape.

It is shown, by means of numerical experiments, that a sine-Gordon soliton trapped in a harmonic potential possesses an oscillatory structure of well-defined discrete energy levels. We then show up discrete energy exchanges between the system sine-Gordon soliton/harmonic potential , and an external driving oscillatory field. The theoretical analysis is sketched by means of usual linear perturbation technique.

To the extent that a sine-Gordon soliton may be viewed as a mass point in a given potential $V(x)$, we propose the resulting modified sine-Gordon equation which takes this potential into account and leads to a Newtonian dynamics of the kink in $V(x)$.

A one‐dimensional stochastic kinetic equation for the propagation of unstable plasmons (Langmuir modes) in the presence of large scale random spatial fluctuations is presented, within the frame of the WKB approximation, and then solved. Using probabilistic arguments, an effective growth rate is evaluated, which turns out to be much smaller than the plasmon growth rate in the absence of fluctuations. The theory is then applied to the beam‐plasma kinetic instability and to the stimulated photon‐plasmon interaction. The former case exhibits a shift of the turbulent plasmon spectrum toward larger wavenumbers. The latter case shows a strong reduction in the efficiency of the stimulated process (i.e., much smaller growth rate) and the removal of the strong asymmetry inherent in this problem.