Bohm's quantum potential as an internal energy

We propose the notion of a classical/quantum duality in the gravitational case (it can be extended to other interactions). By this one means exchanging Bohm's quantum potential for the classical potential VQ↔V in the stationary quantum Hamilton–Jacobi equation (QHJE) so that VQ+V=−V0 (ground state energy). Despite that the corresponding Schrödinger equations, and their solutions differ, their associated quantum Hamilton–Jacobi equation, and ground state energy remains the same. This is how the classical/quantum duality is implemented. In this scenario Bohm's quantum potential (which coincides with the attractive Newtonian potential) is now correlated to a classical repulsive gravitational potential (plus a constant). These results suggest that there might be a quantum origin to the classical repulsive gravitational behavior (of the accelerated expansion) of the universe which is based on this notion of classical/quantum duality. We hope that the notion of classical/quantum duality raised in this work in connection to the QHJE may cast further light into the deep interplay between gravity and quantum mechanics.

Bohm's non-relativistic approach to quantum mechanics is generalized to the relativistic domain. The non-relativistic concept of a «quantum potential» is transcribed into the corresponding «quantum force». This quantum force can be deduced from the recently established theory of relativistic Schrodinger equations in a similar way as the original quantum potential is deduced from the ordinary Schrodinger equation. The leading term of the new quantum force turns out as the well-known classical Lorentz force of electrodynamics, but modified by some quantum corrections. In the non-relativistic limit, Bohm's result is recovered again for a scalar particle.

About the Different Approaches to Bohm's Quantum Potential in Non-Relativistic Quantum Mechanics

Here, the problem of the classical chaos effect on dissipation in nuclear many-body systems is addressed. To investigate this problem, the energy response on parametric driving of external confinement of the simplest interacting many-body system is studied: two identical like-charged particles moving on the plane in the field of a deformed harmonic oscillator, which shows a rich structure of the classical phase space. The parametric driving is represented by the slow periodic modulation of the deformation of confinement. Here, the focus is on how the driven dynamics of particles is defined by the structure of the unperturbed phase space of the system. It has been found that the rate at which the energy of the external driving is pumped into the energy of the interacting two-body system strongly depends on the driven dynamics of the regular orbits. A role of interaction for the energy absorption rate is also discussed.

The phase space structure and statistics of the photon added cat state are studied in the state's general form. Photon addition leads to a π phase shift at the origin in the observed phase space interference of the Wigner function, which may serve as an error syndrome detector. The maxima and minima of the sub-Planck tiles in the phase space of the kitten state are interchanged after photon addition, leading to their orthogonality. Interestingly, photon addition to the Yurke-Stoler state characterized by Poissonian statistics leads to a sub-Poissonian distribution, which may find potential use in quantum noise reduction.

A wavepacket model for a system of free pions, which takes into account the full permutation symmetry of the wavefunction and which is suitable for any phase space parametrization is developed. The properties of the resulting mixed ensembles and the two-particle correlation function are discussed. A physical interpretation of the chaoticity lambda as localizat of the pions in the source is presented. Two techniques to generate test-particles, which satisfy the probability densities of the wavepacket state, are studied: 1. A Monte Carlo procedure in momentum space based on the standard Metropolis technique. 2. A molecular dynamic procedure using Bohm's quantum theory of motion. In order to reduce the numerical complexity, the separation of the wavefunction into momentum space clusters is discussed. In this context th influence of an unauthorized factorization of the state, i. e. the omissio of interference terms, is investigated. It is shown that the correlation radius remains almost uneffected, but the chaoticity parameter decreases substantially. A similar effect is observed in systems with high multiplic where the omission of higher order corrections in the analysis of two-part correlations causes a reduction of the chaoticity and the radius. The approximative treatment of the Coulomb interaction between pions and source is investigated. The results suggest that Coulomb effects on the co radii are not symmetric for pion pairs of different charges. For negative the radius, integrated over the whole momentum spectrum, increases substan while for positive pions the radius remains almost unchanged.

We develop a framework for Large Scale Structure (LSS) perturbation theory, that solves the Vlasov-Poisson system of equations for the distribution function in full phase space. This approach relaxes the usual apriori assumption of negligible velocity dispersion underlying the Standard Perturbation Theory (SPT). We apply the new method to rederive the usual SPT kernels up to third order in the perturbative expansion. We also show that a counterterm, identical to the one introduced by standard Effective Field Theory (EFT) methods, naturally arises within our framework. We finish by making a precise connection to EFT techniques, which reveals the necessity of the EFTofLSS to self-consistently model the long-wavelength fluid, and illustrates the importance of having theoretical control over short distance fluctuations.

The structure of phase space is determined for spatially compact and locally homogeneous universe models with fluid. The analysis covers models with all possible space topologies, except for those covered by S3, H3 or S2×ℝ, which have no moduli freedom. We show that the space topology significantly affects the number of dynamical degrees of freedom of the system. In particular, we give a detailed proof of the result that for systems modeled on the Thurston types H2×ℝ and which locally possesses the Bianchi type III or VIII symmetry, the number of dynamical degrees of freedom increases without bound when the space topology becomes more and more complicated. This behavior was first pointed out by Koike, Tanimoto and Hosoya in an incomplete form.

Differential cross sections and escape plots for low-energy solitonic SU(2) BPS magnetic monopole dynamics

Chimera states—curious symmetry-broken states in systems of identical coupled oscillators—typically occur only for certain initial conditions. Here we analyze their basins of attraction in a simple system comprised of two populations. Using perturbative analysis and numerical simulation we evaluate asymptotic states and associated destination maps, and demonstrate that basins form a complex twisting structure in phase space. Understanding the basins’ precise nature may help in the development of control methods to switch between chimera patterns, with possible technological and neural system applications.

The chaotic advection of the interface between two miscible liquids inside a closed cavity, generated by a damped oscillatory buoyancy-driven (BD) regular flow field, is investigated experimentally for BD mixing. The Lagrangian history of interface motion, determined using the planar laser-induced fluorescence and the photographic full-field view method, is contrasted against the Eulerian flow field measured from particle image velocimetry. Chaotic advection stretches and folds the interface at an early stage to produce an asymmetric pairwise Rayleigh–Taylor (RT) morphology (RTM) structure from long wavelength RT instability and short-time Richtmyer–Meshkov instability and its fractal interface structure at a high impulsive-Reynolds number. The mechanism of folding, from global bifurcation of the flow field, caused by a hyperbolic point, served as an organizing center for multiple vortex interactions. The intermediate-stage kinematics of the RTM structure exhibits RT mixing and shows unfolding of the lamellar structure from the net effect of stretching, folding, and molecular diffusion prior to its breakdown; and it has a probabilistic outcome of exhibiting topological transitions through a breakup of the RTM structure in phase space from necking singularity and pinch-off, indicating sensitivity to the initial conditions. The effectiveness of mixing determined from mixing efficiency is contrasted against mechanical and lamellar models of mixing. The determination of topological entropy, from an approximate Gaussian distribution of the interface length stretch, yields time scale for information decay comparable to time scale for which a low-order horseshoe map emerges from flow, indicating local chaos of the interface. The late-stage breakdown of the RTM structure from internal and wall collision drives the interaction between advection and diffusion, which indicates that critical mixing time scales as the logarithmic of Peclet number, comparable to time-periodic sine flow and blinking vortex flow chaotic mapping models.

We find the existence of sub-Planck scale structures in the P{\"o}schl-Teller potential, which is an exactly solvable potential with both symmetric and asymmetric features. We analyze these structures in both cases by looking at the Wigner distribution of the state evolved from an initial coherent state up to various fractional revival times. We also investigate the sensitivity to perturbations of the P{\"o}schl-Teller potential and we verify that, similar to the harmonic oscillator, the presence of sub-Planck structure in phase space is responsible for a high sensitivity to phase-space displacements.

Hamiltonians which are inaccessible in static systems can be engineered in periodically driven many-body systems, i.e., Floquet many-body systems. We propose to use interacting particles in a one-dimensional (1D) harmonic potential with periodic kicking to investigate two-dimensional topological and many-body physics. Depending on the driving parameters, the Floquet Hamiltonian of single kicked harmonic oscillator has various lattice structures in phase space. The noncommutative geometry of phase space gives rise to the topology of the system. We investigate the effective interactions of particles in phase space and find that the point-like contact interaction in quasi-1D real space becomes a long-rang Coulomb-like interaction in phase space, while the hardcore interaction in pure-1D real space becomes a confinement quark-like potential in phase space. We also find that the Floquet exchange interaction does not disappear even in the classical limit, and can be viewed as an effective long-range spin–spin interaction induced by collision. Our proposal may provide platforms to explore new physics and exotic phases by Floquet many-body engineering.

Momentum diffusion of the quantum kicked rotor: Comparison of Bohmian and standard quantum mechanics

The classical electronic motion of the Rydberg hydrogen atom near a dielectric surface has been studied by using the Poincaré surfaces of section method and the closed orbit theory. The structure and evolution of the phase space as a function of the scaled energy is explored extensively by means of the Poincaré surfaces of section. The results suggest that when the scaled energy is less than the critical energy epsilon(s), the whole phase space structure is regular. However, when the energy is larger than epsilon(s), chaotic motions appear. The recurrence spectra of this system have also been calculated. The results show that, for a given scaled energy larger than the critical energy epsilon(s), when the dielectric constant alpha is small, the influence of the dielectric surface can be neglected and the number of closed orbits is very small. With the increase of the dielectric constant alpha, the effect of the dielectric surface becomes significant, the number of closed orbits increases, and there are more peaks in the recurrence spectra. When alpha = 1.0, the recurrence spectra approach the case of the Rydberg hydrogen atom near a metallic surface. This study provides a new method to explore the dynamic behavior of the Rydberg atom interacting with a dielectric surface.