Entire Phase Space Research Articles

Topological pressure of simultaneous level sets

Multifractal analysis studies level sets of asymptotically defined quantities in a topological dynamical system. We consider the topological pressure function on such level sets, relating it both to the pressure on the entire phase space and to a conditional variational principle. We use this to recover information on the topological entropy and Hausdorff dimension of the level sets.Our approach is thermodynamic in nature, requiring only existence and uniqueness of equilibrium states for a dense subspace of potential functions. Using an idea of Hofbauer, we obtain results for all continuous potentials by approximating them with functions from this subspace.This technique allows us to extend a number of previous multifractal results from the C1+ε case to the C1 case. We consider ergodic ratios Snφ/Snψ where the function ψ need not be uniformly positive, which lets us study dimension spectra for non-uniformly expanding maps. Our results also cover coarse spectra and level sets corresponding to more general limiting behaviour.

Mutual influence of locality and chaotic dynamics on quantum controllability

Quantum control tasks are classified either as classical-like or as quantum requiring interference of pathways. We study the generation of interference pathways and relate them to the fidelity of the control target at a fixed time for various tasks. The model drift Hamiltonian studied is the two-dimensional Henon-Heiles (HH) potential. This system shows regular classical dynamics for low energies and chaotic dynamics for higher energies. A control operator supported by the whole momentum space and therefore connecting the entire Hilbert phase space is a random spiky potential. The other extreme is a smooth control potential. Intermediate cases are obtained by filtering the random spiky potential in momentum space. The fidelity of achieving a control task was related to the connectivity in phase space of the control operators. Typical quantum tasks such as generating a superposition of generalized coherent states rely on interfering pathways. For these cases the nonlinearity in the drift or control Hamiltonian is a necessary requirement for creating interferences. Control over rapidly diverging components of the wave function is achieved by the use of highly nonlocal control operators. Quantum control under chaotic drift was found to give a better yield than control under regular dynamics for such cases. For classical tasks we study the transformation of an initial generalized coherent state to another one. The best fidelity is obtained for regular or harmonic regions of the potential and smooth control operators. The approach to the classical limit is checked by decreasing the effective value of $\ensuremath{\hbar}$. Control under both quantum and classical tasks suffered from the decrease of $\ensuremath{\hbar}$ and the approach to classical proximity. Classical control tasks which rely heavily on maintaining a generalized coherent state throughout the evolution were found to be dysfunctional and lead to a completely uncontrolled situation once the classical chaos starts to appear.

The dependence of Bose–Einstein correlations, on energy, multiplicity and hadronic jets

The dependence of the one-dimensional Bose–Einstein correlation R1D derived from proton–proton collisions is examined in terms of energy, hadron multiplicity and number of emerging hadronic jets. It is argued that the observed rise of R1D with energy is the result of the increase of the average number of hadronic jets. It is further shown that by the relatively straightforward measurements of R1D and its chaoticity parameter λ one should be able to estimate the average number of outgoing hadronic jets emitted over the entire final state phase space without the need to rely on a particular jet finding algorithm and its associated parameters.

The great escape - II. Exoplanet ejection from dying multiple-star systems

Extrasolar planets and belts of debris orbiting post-main-sequence single stars may become unbound as the evolving star loses mass. In multiple star systems, the presence or co-evolution of the additional stars can significantly complicate the prospects for orbital excitation and escape. Here, we investigate the dynamical consequences of multi-phasic, nonlinear mass loss and establish a criterion for a system of any stellar multiplicity to retain a planet whose orbit surrounds all of the parent stars. For single stars which become white dwarfs, this criterion can be combined with the Chandrasekhar Limit to establish the maximum allowable mass loss rate for planet retention. We then apply the criterion to circumbinary planets in evolving binary systems over the entire stellar mass phase space. Through about 10^5 stellar evolutionary track realizations, we characterize planetary ejection prospects as a function of binary separation, stellar mass and metallicity. This investigation reveals that planets residing at just a few tens of AU from a central concentration of stars are susceptible to escape in a wide variety of multiple systems. Further, planets are significantly more susceptible to ejection from multiple star systems than from single star systems for a given system mass. For system masses greater than about 2 Solar masses, multiple star systems represent the greater source of free-floating planets.

Computations of the collapse of a stellar iron core allowing for the absorption, emission, and scattering of electron neutrinos and anti-neutrinos

The collapse of the iron core of a star with mass 1.4M⊙ is computed. The initial model was chosen to be polytropic, P ∝ ρ1+1/n, with n = 3. The equation of state takes into account the equilibrium radiation of photons, a mixture of Fermi gases comprised of free nucleons and ideal gases comprised of nuclei (Fe, He) in equilibrium with respect to nuclear reactions, and electron-positron gas. The transport equation for electron neutrinos and anti-neutrinos is also included. The absorption and emission of neutrinos and anti-neutrinos with the participation of free nucleons and nuclei is taken into account, as well as scattering on electrons. The main goal of this study is to develop a numerical method for the joint solution of the gas-dynamical equations formatter and the Boltzmann kinetic equations for the distribution functions of various types of neutrinos in both optically thin and optically thick regions. The spherically symmetrical case is considered, but the dependences of the distribution functions on all the phase-space variables—the mass coordinate, particle energy, cosine of the angle between the radius vector and the particle momentum, and time, (m, e, µ, t)—are retained in the description of the neutrino transport. When computing reaction rates, the exact quantum-mechanical expressions for the probabilities of processes are used, with integration over the entire momentum phase space. The gas-dynamical variables depend on the mass coordinate and time, (m, t). The solution yields neutrino light curves, which have narrow maximum with characteristic widths ≈10 ms. This makes it possible to place constraints on the mass of the electron neutrino based on the detection of short bursts of radiation, ≲4 eV. Part of the neutrino energy is absorbed in the envelope of the stellar core (∼1050 erg). This is associated with the higher mean neutrino energies in this model, which is more exact than models with neutrino thermal conductivity. This approach is of interest for the application of multi-dimensional models taking into account large-scale convection.

Characterization of a π-phase shift quantum gate for coherent-state qubits

We discuss the characterization of a π-phase shift quantum gate acting on a qubit encoded in superpositions of coherent states. We adopt a technique relying on some a priori knowledge about the physics underlying the functioning of the device. A parameter summarizing the global quality of the quantum gate is obtained by ‘virtually’ processing an entangled state. With such an approach, we can facilitate the characterization of our gate, focusing on the useful subspace rather than on the entire phase space.

Relation Between the Information Carrier in Nervous Systems and the Dependence of a Neuron Model Behavior on the Past Activity

A neuron or neural network is in the transient regime if its input changes much faster than the convergence speed to its asymptotic dynamics. Transient dynamics are also related to the problem about the information carriers in nervous systems since spikes contain encoded information in the transient regime. Some studies have showed that neurons or neural networks function in the transient regime. Since transient dynamics can occur far from the invariant structure of a neuron or neural network, it is necessary to understand the dynamics of the entire phase space.In this study, we analyze the global dynamics of an impulse-driven radial isochron clock, which is one of the canonical models of neuronal oscillators. We analyze the dynamics of the entire phase space using the Markov operator, denoting the density evolution of the neuronal oscillator. To construct the Markov operator, we use the asymptotic expansion of stochastic processes. We show that the Markov operator can successfully approximate the density evolution of the neuronal oscillator. We analyze the dynamics of the neuronal oscillator using the transient and the stationary properties of the Markov operator. We show that the second eigenvalue of the product of the Markov operators reflects the past activity of the neuronal oscillator; in other words, it describes the degree to which the current state of the neuronal oscillator is affected by past activity and how the model conveys this historical information.

On codings and dynamics of planar piecewise rotations

In this paper, we investigate codings and dynamics of the piecewise rotations belonging to a sub-class of piecewise isometries. We show that the irrational set is empty for some piecewise rational rotations under some assumptions, while a piecewise irrational rotation has at least one irrational coding by extending the definition of the coding map onto the entire phase space. We further prove that the cell corresponding to irrational coding is a single point set for a piecewise irrational rotation.

Bulk density of small meteoroids

Aims. Here we report on precise metric and photometric observations of 107 optical meteors, which were simultaneously recorded at multiple stations using three different intensified video camera systems. The purpose is to estimate bulk meteoroid density, link small meteoroids to their parent bodies based on dynamical and physical density values expected for different small body populations, to better understand and explain the dynamical evolution of meteoroids after release from their parent bodies. Methods. The video systems used had image sizes ranging from 640 × 480 to 1360 × 1036 pixels, with pixel scales from 0.01 ◦ per pixel to 0.05 ◦ per pixel, and limiting meteor magnitudes ranging from Mv =+ 2.5 to +6.0. We find that 78% of our sample show noticeable deceleration, allowing more robust constraints to be placed on density estimates. The density of each meteoroid is estimated by simultaneously fitting the observed deceleration and lightcurve using a model based on thermal fragmentation, conservation of energy and momentum. The entire phase space of the model free parameters is explored for each event to find ranges of parameters which fit the observations within the measurement uncertainty. Results. (a) We have analysed our data by first associating each of our events with one of the five meteoroid classes. The average density of meteoroids whose orbits are asteroidal and chondritic (AC) is 4200 kg m −3 suggesting an asteroidal parentage, possibly related to the high-iron content population. Meteoroids with orbits belonging to Jupiter family comets (JFCs) have an average density of 3100 ± 300 kg m −3 . This high density is found for all meteoroids with JFC-like orbits and supports the notion that the refractory material reported from the Stardust measurements of 81P/Wild 2 dust is common among the broader JFC population. This high density is also the average bulk density for the 4 meteoroids with orbits belonging to the Ecliptic shower-type class (ES) also related to JFCs. Both categories we suggest are chondritic based on their high bulk density. Meteoroids of HT (Halley type) orbits have a minimum bulk density value of 360 +400 −900 kg m −3 . This is consistent with many previous works which suggest bulk cometary meteoroid density is low. SA (Sun-approaching)-type meteoroids show a density spread from 1000 kg m −3 to 4000 kg m −3 , reflecting multiple origins. (b) We found two different meteor showers in our sample: Perseids (10 meteoroids, ∼11% of our sample) with an average bulk density of 620 kg m −3 and Northern Iota Aquariids (4 meteoroids) with an average bulk density of 3200 kg m −3 , consistent with the notion that the NIA derive from 2P/Encke.

Characterization of an ArF excimer laser beam from measurements of the Wigner distribution function

An ArF excimer laser beam at a wavelength of 193 nm has been characterized by a quantitative determination of the Wigner distribution function. The setup, comprising a spherical lens, a rotating cylindrical lens and a moveable ultraviolet-sensitive CCD detector, enabled the mapping of the entire four-dimensional phase space within less than 20 min. Experiments yielded complete information about second-order moment-based parameters, spatial coherence, wavefront, beam profiles, as well as beam propagation and local distributions of radiant intensities.

An Empirical Modification of Classical Mixing Rule for the Cohesive Parameter: The Triple Interactions in Binary Systems Considered

The proposed mixing rule can be formally interpreted as an approach considering the triple cohesive interactions of a part of the molecules in a mixture as follows: a = k∑i=12∑j=12xixjaij(1 − kij(T)) + (1 − κ)∑i=12∑j=12∑k=12xixjxkaijk, where kij(T) and κ are the system-dependent adjustable parameters. Regardless of its possible theoretical justification, the proposed mixing rule is equivalent to the classical mixing rule with the composition-dependent adjustable parameter kij(T), and this dependence follows the regularities typically required for an accurate modeling of experimental data. This study demonstrates that the proposed mixing rule allows an accurate description of the entire thermodynamic phase space involving liquid−liquid−vapor equilibria, vapor−liquid equilibria, and the high pressure liquid−liquid equilibria. However in some complex cases it still may not cancel a need of evaluating the binary parameter l12.

Strange attractors in dissipative Nambu mechanics: classical and quantum aspects

We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation in $R^{3}$ phase space. We demonstrate that it accommodates the phase space dynamics of low dimensional dissipative systems such as the much studied Lorenz and R\"{o}ssler Strange attractors, as well as the more recent constructions of Chen and Leipnik-Newton. The rotational, volume preserving part of the flow preserves in time a family of two intersecting surfaces, the so called {\em Nambu Hamiltonians}. They foliate the entire phase space and are, in turn, deformed in time by Dissipation which represents their irrotational part of the flow. It is given by the gradient of a scalar function and is responsible for the emergence of the Strange Attractors. Based on our recent work on Quantum Nambu Mechanics, we provide an explicit quantization of the Lorenz attractor through the introduction of Non-commutative phase space coordinates as Hermitian $ N \times N $ matrices in $ R^{3}$. They satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its volume phase space contraction it violates the quantum commutation relations. We demonstrate that the Heisenberg-Nambu evolution equations for the Quantum Lorenz system give rise to an attracting ellipsoid in the $3 N^{2}$ dimensional phase space.

Measurements of scattering observables for thepdbreak-up reaction

High-precision measurements of the scattering observables such as cross sections and analyzing powers for the proton-deuteron elastic and break-up reactions have been performed at KVI in the last two decades and elsewhere to investigate various aspects of the three-nucleon force (3NF) effects simultaneously. In 2006 an experiment was performed to study these effects in $\vec{p}+d$ break-up reaction at 135 MeV with the detection system, Big Instrument for Nuclear polarization Analysis, BINA. BINA covers almost the entire kinematical phase space of the break-up reaction. The results are interpreted with the help of state-of-the-art Faddeev calculations and are partly presented in this contribution.

Dynamical behaviors and codings of invertible planar piecewise isometric systems

In this paper, the authors discuss some important sets, including singular sets, exceptional sets, irrational sets, etc., generated by invertible planar piecewise isometric maps. They first extend the coding map onto the entire phase space and characterize singular sets and exceptional sets by the number of codings. Then they reveal the relation among these sets, and show that an irrational set is contained in an exceptional set. And they confirm the existence of admissible rational codings under some conditions (including a necessary and sufficient condition and a sufficient condition). They also discuss dynamical properties of the discontinuity line segments which determine the dynamics of a piecewise isometric system. Finally, they list some open problems for further research.

Multi-electron continua in strongly perturbing collisions of ions with atoms

We have measured doubly differential cross sections(DDCS) d2σ/dvedΩe for single and multiple electron emission for the collision systems p, F8+,9+ and I23+25+ + He and Ar via electron recoil coincidences. For the first time the entire relevant phase space 00≤θe≤360° and 0<ve/vproj≤2 was covered. We observe that for a large perturbation strength q/vproj the ve=vproj cusp is originating dominantly from multiple ionization of the target and not single ionization as is commonly believed. It is to be noted that the projectile centered continuum overwhelmingly prevails over the target centered continuum. We discuss the relevant structures observed in the coincident DDCS.

Weak values and the quantum phase space

We address the issue of how to properly treat, and in a more general setting, the concept of a weak value of a weak measurement in quantum mechanics. We show that for this purpose, one must take in account the effects of the measuring process on the entire phase space of the measuring system. By using coherent states, we go a step further than Jozsa in a recent paper and we present an example where the result of the measurement is symmetrical in the position and momentum observables and seems to be much better suited for quantum optical implementation.

PROTON-DEUTERON BREAK-UP MEASUREMENTS WITH BINA AT 135 MeV

High-precision measurements of the proton-deuteron elastic and break-up reaction have been performed in the past at KVI and elsewhere with the aim to study three-nucleon force (3NF) effects. In the present work, we explored 3NF effects in the break-up scattering process by performing a measurement of vector analyzing powers and differential cross sections using a 135 MeV polarized-proton beam impinging on a liquid-deuterium target. For this study, we used a new experimental setup, Big Instrument for Nuclear-polarization Analysis, BINA, which covers almost the entire kinematical phase space of the break-up reaction. The results are interpreted with the help of state-of-the-art Faddeev calculations.

THE DYNAMICAL STRUCTURE OF DARK MATTER HALOS WITH UNIVERSAL PROPERTIES

$N$-body simulations have unveiled several apparently universal properties of dark matter halos, including a cusped density profile, a power-law pseudo phase-space density $\rho/\sigma_r^3$, and a linear $\beta-\gamma$ relation between the density slope and the velocity anisotropy. We present a family of self-consistent phase-space distribution functions $F(E,L)$, based on the Dehnen-McLaughlin Jeans models, that incorporate these universal properties very accurately. These distribution functions, derived using a quadratic programming technique, are analytical, positive and smooth over the entire phase space and are able to generate four-parameter velocity anisotropy profiles $\beta(r)$ with arbitrary asymptotic values $\beta_0$ and $\beta_\infty$. We discuss the orbital structure of six radially anisotropic systems in detail and argue that, apart from its use for generating initial conditions for $N$-body studies, our dynamical modeling provides a valuable complementary approach to understand the processes involved in the formation of dark matter halos.

Search forCPviolation in the Dalitz-plot analysis ofD±→K+K−π±

We report on a search for CP asymmetry in the singly Cabibbo-suppressed decay D+ -> K+ K- pi+ using a data sample of 818 pb-1 accumulated with the CLEO-c detector on the psi(3770) resonance. A Dalitz-plot analysis is used to determine the amplitudes of the intermediate states. We find no evidence for CP violation either in specific two-body amplitudes or integrated over the entire phase space. The CP asymmetry in the latter case is measured to be (-0.03+-0.84+-0.29)%.

Multiscale modelling of asphaltene disaggregation

Asphaltene aggregation reduces bitumen upgrading efficiency by increasing bitumen viscosity and coke formation. Our approach to model asphaltene aggregation involves geometry optimisation by using the Harris approximation implemented in DMol3, followed by a solvation calculation by using the three-dimensional molecular theory of solvation (a.k.a. 3D-RISM) we have developed recently [A. Kovalenko, Three-dimensional RISM theory for molecular liquids and solid–liquid interfaces, in Understanding Chemical Reactivity: Molecular Theory of Solvation, F. Hirata ed., Vol. 24, Kluwer Academic Publishers, New York, NY, 2003, pp. 169–275]. From the Harris approximation, we obtain the Hirshfeld and Mulliken asphaltene atomic charges. The 3D-RISM theory allows one to model solvation at given temperature, solvent density and solvent composition. The theory predicts solvation structure and thermodynamic characteristics, such as the potential of mean force (PMF). We investigate the effect of the Hirshfeld and Mulliken charge calculation methods on the PMF values for asphaltene disaggregation in quinoline and 1-methylnaphthalene solvents at 298 and 473 K. Our PMF results predict that asphaltene disaggregation is favoured in quinoline at 473 K, whereas in 1-methylnaphthalene the asphaltene aggregate would remain undisturbed. These results are in agreement with the experiment and correlate with the molecular dynamics (MD) simulation results [T. Takanohashi, S. Sato, and R. Tanaka, Structural relaxation behaviors of three different asphaltenes using MD calculations, Petr. Sci. Technol. 22 (2004), pp. 901–904]. The statistical–mechanical 3D-RISM method probes the entire phase space and yields the solvation structure and thermodynamics at a much lower computational cost than MD, and thus gives access to solvation processes that occur on large time and space scales.