We simulate the transformation of a classical fluid into a quantum-like (super)-fluid by the application of a generalized quantum potential through a retro-active loop. This numerical experiment is exemplified in the case of a non-spreading oscillating wave packet in a harmonic potential. We find signatures of a quantum-like behavior which are stable against various perturbations.
We simulate the transformation of a classical fluid into a quantum-like (super)-fluid by the application of a generalized quantum potential through a retro-active loop. This numerical experiment is exemplified in the case of a non-spreading oscillating wave packet in a harmonic potential. We find signatures of a quantum-like behavior which are stable against various perturbations.
We perform numerical simulations of a new proposal of laboratory experiment that would allow the transformation of a classical fluid into a quantum-type (super)fluid through the application of a generalized quantum potential. This quantum potential is simulated by using a real time retroactive loop involving a measurement of density, a calculation of the potential in function of the measured density, then an application of the calculated potential through a classical force. This general experimental concept is exemplified here by the case of a nonspreading oscillating wave packet in a harmonic oscillator potential. We find signatures of a quantum-like behavior which are stable against various perturbations. Finally, the feasability of a realization of this concept in an actual plasma experiment is analyzed.
We have recently proposed a new general concept of macroscopic quantum-type experiment. It amounts to transform a classical fluid into a quantum-type fluid by the application of a quantum-like potential, either directly in a stationary configuration, or through a retro-active loop to simulate the time evolution. In this framework, the amplitude of the quantum potential depends on a macroscopic generalization of the Planck constant, which can be changed during the experiment, therefore simulating a quantum to classical transition. The experiment is exemplified here by an application of this concept to gravity waves at the surface of an incompressible liquid in a basin of finite height, with particular emphasis on the quantized vortex. We construct a complex wave function with the height of the fluid in the basin as its square modulus and the velocity potential as its phase. This wave function is solution of a nonlinear Schrodinger equation typical of superfluids. The quantum potential is therefore defined here in terms of the square root of the fluid height. We suggest two methods for applying this quantum-like potential to the fluid: (i) by the action of a force on the surface (wind, blower, pressure, field, etc...); (ii) by a curvature of the basin ground. In this last case the ground profile yields the quantum potential itself, while usually only the quantum force is accessible, so that such an experiment is expected to provide one with a macroscopic model of a quantum-type vacuum energy. These results may also be relevant to the study of freak waves, which have already been described by nonlinear Schrodinger equations.
The problem investigated refers to periodically driven 1D quantum inverted harmonic oscillator (IHO) with the Hamiltonian of . The model is used widely in huge quantum applications concerned unstable molecular complexes and ions under laser light affection. Non-stationary Schrödinger equation (NSE) was solved analytically and numerically by means of Maple 17 with initial wave function (w.f.) of generalized Gaussian type. This one described the converging 1D probability flux and fitted well the quantum operator of initial conditions (IC). For the IC one can observe, first, the collapse of w.f. packet into extremely narrow 1D space interval of length and, second, its spreading back up to its starting half width, and all that - at dimensionless times. At certain phases j defined by W and s0 the wave packet center displayed nonharmonic oscillating behavior near some slowly drifting space position within this time interval and after that leaved onto infinity while the unlimited packet spreading. And the phases themselves served as bifurcation points separating the NSE solutions with the outgoing to from those with. In “resonant” case of the values obeyed an inverted Fermi-Dirac formula of; for differing the asymptotic of obeyed well classical law.
Wave packets of one-dimensional, single-particle quantum systems exhibit a rich diversity of dynamical behavior. We focus on confining potentials where the entire energy spectrum is discrete so that wave packets do not spread indefinitely with time and instead exhibit characteristics of almost-periodic functions. For the harmonic oscillator, for which all wave packets are necessarily strictly periodic, Senitzky has shown that is possible to construct an infinite class of normalized wave packets that maintain a fixed shape while oscillating sinusoidally with time. We present two alternate and instructive methods for deriving this result using coherent states and the displacement operator.
In this paper we numerically solve the time dependent Schrödinger equation for scenarios using wave packets. These examples include the free wave packet, which we use to show the difference between group and phase velocities, the packet in a harmonic oscillator potential with non-trivial initial conditions in one and two dimensions, which is compared with their classical analogs to show how Ehrenfest theorem holds. We also include simulations of the diffraction through the single and double slit potentials, the refraction with a step potential and the dispersion by a central potential. The aim of this paper is to illustrate with simulations, nowadays easy to implement, scenarios that can help explaining the basics of the wave-particle duality.