Phase Space Dynamics Research Articles

Quantum diffusion in spin chains with phase space methods.

Connecting short-time microscopic dynamics with long-time hydrodynamics in strongly correlated quantum systems is one of the outstanding questions. In particular, it is hard to determine various hydrodynamic coefficients such as the diffusion constant or viscosity starting from a microscopic model: exact quantum simulations are limited to either small system sizes or to short times, which are insufficient to reach asymptotic behavior and so various approximations must be applied. We show that these difficulties, at least for particular models, can be circumvented by using the cluster truncated Wigner approximation (CTWA), which maps quantum Hamiltonian dynamics into classical Hamiltonian dynamics in auxiliary high-dimensional phase space. We apply CTWA to XXZ next-nearest-neighbor spin-1/2 chains and XY spin ladders, and find behavior consisting of short-time spin relaxation which gradually crosses over to emergent diffusive behavior at long times. For a random initial state, we show that CTWA correctly reproduces the whole spin spectral function. Necessary in this construction is sampling from properly fluctuating initial conditions: the Dirac mean-field (variational) ansatz, which neglects such fluctuations, leads to incorrect predictions.

Digital Proxy of a Bio-Reactor (DIYBOT) combines sensor data and data analytics to improve greywater treatment and wastewater management systems

Technologies to treat wastewater in decentralized systems are critical for sustainable development. Bioreactors are suitable for low-energy removal of inorganic and organic compounds, particularly for non-potable applications where a small footprint is required. One of the main problems associated with bioreactor use is sporadic spikes of chemical toxins, including nanoparticles. Here, we describe the development of DIYBOT (Digital Proxy of a Bio-Reactor), which enables remote monitoring of bioreactors and uses the data to inform decisions related to systems management. To test DIYBOT, a household-scale membrane aerated bioreactor with real-time water quality sensors was used to treat household greywater simulant. After reaching steady-state, silver nanoparticles (AgNP) representative of the mixture found in laundry wastewater were injected into the system to represent a chemical contamination. Measurements of carbon metabolism, effluent water quality, biofilm sloughing rate, and microbial diversity were characterized after nanoparticle exposure. Real-time sensor data were analyzed to reconstruct phase-space dynamics and extrapolate a phenomenological digital proxy to evaluate system performance. The management implication of the stable-focus dynamics, reconstructed from observed data, is that the bioreactor self-corrects in response to contamination spikes at AgNP levels below 2.0 mg/L. DIYBOT may help reduce the frequency of human-in-the-loop corrective management actions for wastewater processing.

Quantum and classical phase-space dynamics of a free-electron laser

In a quantum mechanical description of the free-electron laser (FEL) the electrons jump on discrete momentum ladders, while they follow continuous trajectories according to the classical description. In order to observe the transition from quantum to classical dynamics, it is not sufficient that many momentum levels are involved. Only if additionally the initial momentum spread of the electron beam is larger than the quantum mechanical recoil, caused by the emission and absorption of photons, the quantum dynamics in phase space resembles the classical one. Beyond these criteria, quantum signatures of averaged quantities like the FEL gain might be washed out.

Flow topology dynamics in a three-dimensional phase space for turbulent Rayleigh-Bénard convection

F.X.T., F.D. and A.O. are financially supported by the Ministerio de Economia y Competitividad, Spain (ENE2017-88697-R). F.X.T. is supported by a Ramon y Cajal postdoctoral contract (RYC-2012-11996). F.D. is supported by the Austrian Federal Ministry for Digital and Economic Affairs, the National Foundation for Research, Technology and Development, and the K1MET center for metallurgical research in Austria (www.k1-met.com). Calculations have been performed on the IBM MareNostrum 4 supercomputer at the BSC (PRACE 15th Call, Ref. 2016163972, \Exploring new frontiers in Rayleigh-Benard convection). Preliminary simulations were carried out using computational resources of MCC NRC \Kurchatov Institute, http://computing.nrcki.ru/. The authors thankfully acknowledge these institutions.

Sculpted ultracold neutral plasmas.

Ultracold neutral plasma (UNP) experiments allow for careful control of plasma properties across Coulomb coupling regimes. Here, we examine how UNPs can be used to study heterogeneous, nonequilibrium phenomena, including nonlinear waves, transport, hydrodynamics, kinetics, stopping power, and instabilities. Through a series of molecular dynamics simulations, we have explored UNPs formed with spatially modulated ionizing radiation. We have developed a computational model for such sculpted UNPs that includes an ionic screened Coulomb interaction with a spatiotemporal screening length, and Langevin-based spatial ion-electron and ion-neutral collisions. We have also developed a hydrodynamics model and have extracted its field quantities (density, flow velocity, and temperature) from the molecular dynamics simulation data, allowing us to investigate kinetics by examining moment ratios and phase-space dynamics; we find that it is possible to create UNPs that vary from nearly perfect fluids (Euler limit) to highly kinetic plasmas. We have examined plasmas in three geometries: a solid rod, a hollow rod, and a gapped slab; we have studied basic properties of these plasmas, including the spatial Coulomb coupling parameter. By varying the initial conditions, we find that we can design experimental plasmas that would allow the exploration of a wide range of phenomena, including shock and blast waves, stopping power, two-stream instabilities, and much more. Using an evaporative cooling geometry, our results suggest that much larger Coulomb couplings can be achieved, possibly in excess of 10.

The classical and quantum synchronization between two scattering modes in Bose–Einstein condensates

The classical and quantum synchronization between two nonlinear mechanical modes of Bose–Einstein condensates is investigated by different types of measures in order to reveal macroscopic and microscopic properties of synchronized behaviors in a closed quantum system. The classical measure synchronization (CMS) is studied by Pearson correlation coefficient, the orbital overlapping and covering areas in the phase space based on mean-value dynamical equations. The dynamical transitions of CMS are analyzed with phase diagrams in the parametric plane of population imbalance and phase difference between two modes in a wide range of mode coupling rate. Based on Husimi Q functions, the synchronized behaviors of quantum measure synchronization (QMS) are displayed by density overlapping and correlated probability dynamics in phase space, and further investigated by two quantum measures: Mari measure and mutual information. These results demonstrate that the “revival and collapse” of quantum fluctuations beyond mean-value dynamics discriminates QMS from CMS. The overwhelming dynamics of error fluctuations not only excludes complete CMS and perfect phase overlap in QMS, but also leads to upper bound to Mari measure and unceasing oscillations of mutual information. We reveal that the correlation between Mari measure and mutual information for QMS is derived from the similar dynamics of error fluctuations with respect to their opposite mean-value behaviors.

Fractal catastrophes

We analyse the spatial inhomogeneities (‘spatial clustering’) in the distribution of particles accelerated by a force that changes randomly in space and time. To quantify spatial clustering, the phase-space dynamics of the particles must be projected to configuration space. Folds of a smooth phase-space manifold give rise to catastrophes (‘caustics’) in this projection. When the inertial particle dynamics is damped by friction, however, the phase-space manifold converges towards a fractal attractor. It is believed that caustics increase spatial clustering also in this case, but a quantitative theory is missing. We solve this problem by determining how projection affects the distribution of finite-time Lyapunov exponents (FTLEs). Applying our method in one spatial dimension we find that caustics arising from the projection of a dynamical fractal attractor (‘fractal catastrophes’) make a distinct and universal contribution to the distribution of spatial FTLEs. Our results explain a projection formula for the spatial fractal correlation dimension, and how a fluctuation relation for the distribution of FTLEs for white-in-time Gaussian force fields breaks upon projection. We explore the implications of our results for heavy particles in turbulence, and for wave propagation in random media.

Dynamic magnetostriction for antiferromagnets

In this paper we study the switching properties of the dynamics of magnetic moments, that interact with an elastic medium. To do so we construct a Hamiltonian framework, that can take into account the dynamics in phase space of the variables that describe the magnetic moments in a consistent way. It is convenient to describe the magnetic moments as bilinears of anticommuting variables that are their own conjugates. However, we show how it is possible to avoid having to deal directly with the anticommuting variables themselves, only using them to deduce non-trivial constraints on the magnetoelastic couplings. We construct the appropriate Poisson bracket and a geometric integration scheme, that is symplectic in the extended phase space and that allows us to study the switching properties of the magnetization, that are relevant for applications, for the case of a toy model for antiferromagnetic NiO, under external stresses. In the absence of magnetoelastic coupling, we recover the results reported in the literature and in our previous studies. In the presence of the magnetoelastic coupling, the characteristic oscillations of the mechanical system have repercussions on the N\'eel order parameter dynamics. This is particularly striking for the spin accumulation which is more than doubled by the coupling to the strain ; here as well, the mechanical oscillations are reflected on the magnetic dynamics. As a consequence of such a stress induced strain, the switching time of the magnetization is slightly faster and the amplitude of the magnetization enhanced.

Phase-space dynamics of near-wall streaks in wall-bounded turbulence with spanwise oscillation

This work presents systematical investigations on the skin-friction drag reduction (DR) of turbulent channel flow subjected to spanwise wall oscillation using direct numerical simulation. Altogether 12 different oscillatory cases have been studied with a reference at Reτ = 200, varying the controlling parameters characterized by maximum wall velocity Wm+ and oscillation period T+. Some of the previously established facts have been reproduced by our analysis with a new focus on the phase-space dynamics of the near-wall streaks, on the basis of statistical data over entire oscillation periods and over phasewise variations. It is revealed that streamwise vortices are generated in the vicinity of oscillation walls, disrupting the formation of near-wall low-speed streaks. Although the overall turbulence is weakened, the Stokes layer is thicker within wall acceleration phases for larger Wm+, which causes the turbulence intensity to increase in the upper viscous sublayer. In addition, regarding the effect of T+, a long oscillation period promotes the formation of energetic near-wall structures, while for short T+, the streak-generation time scale preferentially restricts the growth of spanwise streaks. From a new vorticity-transport perspective of the Reynolds shear stress, our results further indicate that high drag-reducing phenomena are connected to the near-wall sweep events, and the shear stress variation is principally driven by the distortion of the spanwise transport of wall-normal vorticity, i.e., vortex tilting/stretching. The DR process is seen to be linked to the increase in enstrophy and turbulence-energy dissipation in the near-wall region.

Electronic current in a nano-mechanical kicked electron shuttle

Abstract We have studied the phase-space dynamics and rectified current of a nano-electromechanical shuttle with two types of time-periodic potentials. By applying only sinusoidal voltage with frequency ω at one lead, regular shuttle motion constructs Arnold’s tongues in parameter space, where the motion in each tongue has a period of π ∕ ω or 2 π ∕ ω . The rectified current in each tongue is finite for the 2 π ∕ ω period but zero for the π ∕ ω period. We then apply discrete kicks, the periods of which modify the period of motion in the tongues. We find that it is important to the rectified current whether the integer of the lowest common multiple between the two periods is even or odd. Specifically, the rectified current is finite in the tongues when the lowest common multiple integer is even, while the current is zero when the integer is odd.

Towards a semiclassical understanding of chaotic single- and many-particle quantum dynamics at post-Heisenberg time scales.

Despite considerable progress during the past decades in devising a semiclassical theory for classically chaotic quantum systems a quantitative semiclassical understanding of their dynamics at late times (beyond the so-called Heisenberg time T_{H}) is still missing. This challenge, corresponding to resolving spectral structures on energy scales below the mean level spacing, is intimately related to the quest for semiclassically restoring unitary quantum evolution. Guided through insights for quantum graphs we devise a periodic-orbit resummation procedure for spectra of quantum chaotic systems invoking periodic-orbit self-encounters as the structuring element of a hierarchical phase space dynamics. Quantum unitarity is reflected in real-valued spectral determinants with zeros giving discrete energy levels. We propose a way to purely semiclassically construct such real spectral determinants based on two major underlying mechanisms. (i) Complementary contributions to the spectral determinant from regrouped pseudo-orbits of duration T<T_{H} and T_{H}-T are complex conjugate to each other. (ii) Contributions from long periodic orbits involving multiple traversals along shorter orbits cancel out. We furthermore discuss implications for interacting N-particle quantum systems with a chaotic classical large-N limit that have recently attracted particular interest in the context of many-body quantum chaos.

Hamiltonian formalism and gauge-fixing conditions for cosmological perturbation theory

We apply the Dirac procedure for constrained systems to the Arnowitt–Deser–Misner formalism linearized around the Friedmann–Lemaitre universe. We explain and employ some basic concepts such as Dirac observables, Dirac brackets, gauge-fixing conditions, reduced phase space, physical Hamiltonian and physical dynamics. In particular, we elaborate on the key concept which is the canonical isomorphism between different gauge-fixing surfaces. We apply our formalism to describe the reduced phase space of cosmological perturbations in some popular in the literature gauges. Our formalism is first developed for the universe with a single fluid and then extended to the multi-fluid case. The obtained results are a starting point for complete quantization of the cosmological perturbations and the cosmological background. Our approach may be used in future to derive the reduced phase space of higher order perturbations and in more generic cosmological spacetimes.

Dissipative Bose-Josephson junction coupled to bosonic baths.

We investigate the effect of dissipation in a Bose-Josephson junction (BJJ) coupled to baths of bosons at its two sites. Apart from the dynamical transition due to repulsive interactions, the BJJ undergoes a quantum phase transition by increasing the coupling strength with the bath modes. We analyze this system by mapping to an equivalent spin model coupled to the bosonic modes. The excitation energies and fluctuation of number imbalance are obtained within a Holstein-Primakoff approximation, which exhibits vanishing of the energy gap and enhanced quantum fluctuations at the critical point. We study the dynamics of BJJ using a time-dependent variational method and analyze stability of different types of steady states. As a special case we study in detail the phase space dynamics of BJJ coupled to a single mode, which reveals diffusive and incoherent behavior with increasing coupling to the bath mode. The dynamical steady states corresponding to the π oscillation and self-trapped state become unstable when their oscillation frequencies are in resonance with the bath modes. We study the Josephson dynamics in the presence of an Ohmic bath with Gaussian noise to incorporate the thermal fluctuations and obtain the Josephson oscillation frequency and damping analytically. We also observe the transition to the symmetry-broken state for strong coupling as well as decay of π oscillation and a self-trapped state to the ground state due to dissipation. Variation of the phase fluctuation with temperature of the bath shows similar behavior as observed in experiment. Finally we discuss the experimental setup to study the observable effects of dissipation in BJJ.

Dynamic Behavior of Arc Voltage and Electro-thermal Efficiency in Atmospheric Pressure Non-transferred Arc Plasma Torches under Different Degrees of Anode Cooling

Unusually, high electro-thermal efficiency, observed under certain cooling rates of the anode boundary layer in a typical non-transferred arc argon plasma torch, is reported. The behavior is reproducible at different arc currents and gas flow rates. To understand the origin of such behavior, total arc voltage, which bears an overall signature of the internal arc dynamics, has been analyzed using tools of dynamical analysis such as frequency space behavior, phase space dynamics, correlation dimension and Lyapunov exponent under different rates of anode cooling. Simultaneous emission spectroscopic investigation of the plasma temperature at the nozzle exit and fast photographic study of the anode boundary layer have been carried out for better insight. Observed significant variation in the dominant frequency components with change in cooling rates gives concrete signature of onset on new dynamics induced by anode cooling. Vivid differences in the dynamics are brought out in phase space representations. True natures of the dynamics are obtained through the estimated values of correlation dimension and Lyapunov exponents.

An Algorithmic Information Calculus for Causal Discovery and Reprogramming Systems.

SummaryWe introduce and develop a method that demonstrates that the algorithmic information content of a system can be used as a steering handle in the dynamical phase space, thus affording an avenue for controlling and reprogramming systems. The method consists of applying a series of controlled interventions to a networked system while estimating how the algorithmic information content is affected. We demonstrate the method by reconstructing the phase space and their generative rules of some discrete dynamical systems (cellular automata) serving as controlled case studies. Next, the model-based interventional or causal calculus is evaluated and validated using (1) a huge large set of small graphs, (2) a number of larger networks with different topologies, and finally (3) biological networks derived from a widely studied and validated genetic network (E. coli) as well as on a significant number of differentiating (Th17) and differentiated human cells from a curated biological network data.

Two ways for finding the thermal decay rate at weak friction

We model the thermal decay of a metastable state at weak friction (the underdamped regime), the phenomenon which might be met in many branches of natural and technical sciences. The profile of the metastable state is considered as a pure parabola. We quantitatively compare the decay rate obtained from the phase space dynamics with the rate coming from the approximate energy diffusion approach which should be correct in the case of relatively weak friction. Both the phase space and energy diffusion dynamics employ the Langevin-type equations, however for the different stochastic variables. The results of the comparison reveal that the level of agreement between these two approaches depends not only upon the damping parameter (as qualitatively expected) but also upon the thermal energy.

The role of electrostatic waves in the formation of thermal front in solar flares: 1-D PIC simulation

The electrostatic waves excited during the formation of the thermal front are studied using a one-dimensional electromagnetic particle-in-cell simulation. The thermal front is defined as a sudden decrease in the local electron temperature. The results suggest that the beam mode and the electron acoustic waves are first excited, and then ion acoustic waves are produced. The thermal front just forms in the region of the plasma density depression. The nonlinear evolution of ion acoustic waves can be a potential mechanism for the formation of the thermal front which confines hot electrons and reduces their cooling time. According to the evolution of electron dynamics in phase space, the thermal front actually reflects hot electrons with low kinetic energy through the double layer which is driven by the ion-acoustic waves. That is, the thermal front is actually a double layer.

Longitudinal phase space dynamics of witness bunch during the Trojan Horse injection for plasma-based particle accelerators

In the Trojan Horse injection process for plasma-based particle accelerators, we have investigated how the longitudinal phase space of the witness bunch would be governed by the parameters of the ionization laser and background plasma in the limit of quasistatic wakefield approximation. The tunneling ionization rate distribution by the laser pulse is introduced to describe the ionization time interval and initial distribution of the witness electrons. The quasilinear (or equivalently quasistatic) regime of the charged particle beam-driven wakefield is considered to make the phase of the wake potential constant in time in the driver beam frame. In the simulations, it is shown that the ionization laser phase on the quasistatic wake potential determines the longitudinal space-charge field of the witness bunch. We also find that the relative energy spread of the witness bunch can be estimated by the sum of three effects: The ionization time interval, wakefield slope, and space-charge fields of the witness bunch. Analytical expressions for the characteristic distance from the ionization to trapping positions, rms length, and relative energy spread of the witness bunch are obtained approximately and compared with the particle-in-cell simulations.

A Branching Random Walk Method for Many-Body Wigner Quantum Dynamics

A branching random walk algorithm for the many-body Wigner equation and its numerical applications for quantum dynamics in phase space are proposed and analyzed. After introducing an auxiliary function, the (truncated) Wigner equation is cast into the integral formulation as well as its adjoint correspondence, both of which can be reformulated into the renewal-type equations and have transparent probabilistic interpretation. We prove that the first moment of a branching random walk happens to be the solution for the adjoint equation. More importantly, we detail that such stochastic model, associated with both importance sampling and resampling, paves the way for a numerically tractable scheme, within which the Wigner quantum dynamics is simulated in a time-marching manner and the complexity can be controlled with the help of an (exact) estimator of the growth rate of particle number. Typical numerical experiments on the Gaussian barrier scattering and a Helium-like system validate our theoretical findings, as well as demonstrate the accuracy, the efficiency and thus the computability of the Wigner branching random walk algorithm.

Boltzmann stochastic thermodynamics.

The Boltzmann kinetic equation is obtained from an integrodifferential master equation that describes a stochastic dynamics in phase space of an isolated thermodynamic system. The stochastic evolution yields a generation of entropy, leading to an increase of Gibbs entropy, in contrast to a Hamiltonian dynamics, described by the Liouville equation, for which the entropy is constant in time. By considering transition rates corresponding to collisions of two particles, the Boltzmann equation is attained. When the angle of the scattering produced by collisions is small, the master equation is shown to be reduced to a differential equation of the Fokker-Planck type. When the dynamics is of the Hamiltonian type, the master equation reduces to the Liouville equation. The present approach is understood as a stochastic interpretation of the reasonings employed by Maxwell and Boltzmann in the kinetic theory of gases regarding the microscopic time evolution.