Phase Space Volume Research Articles

Neutron guide geometries for homogeneous phase space volume transformation

We extend geometries for recently developed optical guide systems that perform homogeneous phase space volume transformations on neutron beams. These modules allow rotating beam directions and can simultaneously compress or expand the beam cross-section. Guide systems combining these modules offer the possibility to optimize ballistic guides with and without direct view on the source and beam splitters. All systems are designed for monochromatic beams with a given divergence. The case of multispectral beams with wavelength-dependent divergence distributions is addressed as well.

Energy Transfer and Fluid Flow around a Massive Astrophysical Object

In this work it is presented the modeling and simulation of energy transfer and fluid flow of a stationary spherical arrangement of particles surrounding a gravitational body such as an astrophysical object that carries the curvature of space-time continuum in general relativity, taking into account the thermodynamics of the second law. This model also predicts the drag of space and time around an astrophysical object as it rotates, with results close to the experimental data reported by other authors. To model the energy transfer of the mass and the fluid flow in the space-time, it is used a 4-dimensional system. In order to make measurements of entropy in the arrow of time (past-present), tensors in General Relativity were used to calculate this thermodynamic quantity and with this, the big bang ́s low entropy condition in phase space of coarse graining (Hawking ́s box), according to Weyl curvature hypothesis (WCH) of Roger Penrose. Contribution of this paper is presented by tensors which carry information that has to do with something as non-distortion effect in fluid flow around the astrophysical object and the low entropy condition that is believed to exist in the past, in the big bang; what leads us to search for a new physical-mathematical science to continue. At this point, the Einstein field equations are out of context, which leads us to conclude that it is necessary a mathematical science that allows us to make calculations to rescue lost information due to collapse of matter to a black hole. This math should allow us to clear up physical phenomena (like origin of the universe) and their relationship, with the objective of unifying theories that lead to a physical science without uncertainties, as at the present time. In this regard, we propose a metric in hyperbolic coodinates to build a physical wormhole shaped object where gravitational bodies can be housed that allow us to link the past entropy with the present entropy according to the second law of thermodynamics, as a kind of mathematical space or alternative model to compensate in some way, the link between WCH and the phase space volume of the Hawking's box, and the link between WCH and the quantum-mechanical state-vector reduction, , proposed by Penrose which still have not been determined by any author. Nomenclature

On the problem of singular charge density at the center of pion

We generalize and analyze the expression for the quark density of a pion with allowance for the quantum nature of the impact parameter in a region of small phase space volume. As a result, there is no singularity at the center of a pion.

A quaternionic map for the steady states of the Heisenberg spin-chain

Abstract We show that the steady states of the classical Heisenberg XXX spin-chain in an external magnetic field can be found by iterations of a quaternionic map. A restricted model, e.g., the xy spin-chain is known to have spatially chaotic steady states and the phase space occupied by these chaotic states is known to go through discrete changes as the field strength is varied. The same phenomenon is studied for the xxx spin-chain. It is seen that in this model the phase space volume varies smoothly with the external field.

Physical processes at work in sub-30 fs, PW laser pulse-driven plasma accelerators: Towards GeV electron acceleration experiments at CILEX facility

Optimal regimes and physical processes at work are identified for the first round of laser wakefield acceleration experiments proposed at a future CILEX facility. The Apollon-10P CILEX laser, delivering fully compressed, near-PW-power pulses of sub-25fs duration, is well suited for driving electron density wakes in the blowout regime in cm-length gas targets. Early destruction of the pulse (partly due to energy depletion) prevents electrons from reaching dephasing, limiting the energy gain to about 3GeV. However, the optimal operating regimes, found with reduced and full three-dimensional particle-in-cell simulations, show high energy efficiency, with about 10% of incident pulse energy transferred to 3GeV electron bunches with sub-5% energy spread, half-nC charge, and absolutely no low-energy background. This optimal acceleration occurs in 2cm length plasmas of electron density below 1018cm−3. Due to their high charge and low phase space volume, these multi-GeV bunches are tailor-made for staged acceleration planned in the framework of the CILEX project. The hallmarks of the optimal regime are electron self-injection at the early stage of laser pulse propagation, stable self-guiding of the pulse through the entire acceleration process, and no need for an external plasma channel. With the initial focal spot closely matched for the nonlinear self-guiding, the laser pulse stabilizes transversely within two Rayleigh lengths, preventing subsequent evolution of the accelerating bucket. This dynamics prevents continuous self-injection of background electrons, preserving low phase space volume of the bunch through the plasma. Near the end of propagation, an optical shock builds up in the pulse tail. This neither disrupts pulse propagation nor produces any noticeable low-energy background in the electron spectra, which is in striking contrast with most of existing GeV-scale acceleration experiments.

Dynamically optimized Wang-Landau sampling with adaptive trial moves and modification factors

The density of states of continuous models is known to span many orders of magnitudes at different energies due to the small volume of phase space near the ground state. Consequently, the traditional Wang-Landau sampling which uses the same trial move for all energies faces difficulties sampling the low-entropic states. We developed an adaptive variant of the Wang-Landau algorithm that very effectively samples the density of states of continuous models across the entire energy range. By extending the acceptance ratio method of Bouzida, Kumar, and Swendsen such that the step size of the trial move and acceptance rate are adapted in an energy-dependent fashion, the random walker efficiently adapts its sampling according to the local phase space structure. The Wang-Landau modification factor is also made energy dependent in accordance with the step size, enhancing the accumulation of the density of states. Numerical simulations show that our proposed method performs much better than the traditional Wang-Landau sampling.

All Shook Up: Fluctuations, Maxwell’s Demon and the Thermodynamics of Computation

The most successful exorcism of Maxwell’s demon is Smoluchowski’s 1912 observation that thermal fluctuations would likely disrupt the operation of any molecular-scale demonic machine. A later tradition sought to exorcise Maxwell’s demon by assessing the entropic cost of the demon’s processing of information. This later tradition fails since these same thermal fluctuations invalidate the molecular-scale manipulations upon which the thermodynamics of computation is based. A new argument concerning conservation of phase space volume shows that all Maxwell’s demons must fail.

The Phase Space Elementary Cell in Classical and Generalized Statistics

In the past, the phase-space elementary cell of a non-quantized system was set equal to the third power of the Planck constant; in fact, it is not a necessary assumption. We discuss how the phase space volume, the number of states and the elementary-cell volume of a system of non-interacting N particles, changes when an interaction is switched on and the system becomes or evolves to a system of correlated non-Boltzmann particles and derives the appropriate expressions. Even if we assume that nowadays the volume of the elementary cell is equal to the cube of the Planck constant, h3, at least for quantum systems, we show that there is a correspondence between different values of h in the past, with important and, in principle, measurable cosmological and astrophysical consequences, and systems with an effective smaller (or even larger) phase-space volume described by non-extensive generalized statistics.

Numerical error in modeling of particle-accumulation structures in periodic free-surface flows

The effect of numerical error in modeling of particle-accumulation in periodic free surface flows is evaluated using an analytical flow model for a thermocapillary liquid bridge. Numerical error is shown to lead to particle-accumulation structures very similar in both shape and formation time to those observed experimentally and calculated using numerical simulations where the error is extremely small. This result of numerical error, which has important implications for determining the existence and formation times of particle-accumulation structures through the use of numerical models, is found to arise from the use of integrators that do not preserve phase space volume.

Feedback cooling of an atomic spin ensemble.

We apply entropy removal by measurement and feedback to a cold atomic spin ensemble. Using quantum nondemolition probing by Faraday rotation measurement, and feedback by weak optical pumping, we drive the initially random collective spin variable F toward the origin F=0. We use input-output relations and ensemble quantum noise models to describe this quantum control process and identify an optimal two-round control procedure. We observe 12 dB of spin noise reduction, or a factor-of-63 reduction in phase-space volume. The method offers a nonthermal route to generation of exotic entangled states in ultracold gases, including macroscopic singlet states and strongly correlated states of quantum lattice gases.

Why is Boris algorithm so good?

Due to its excellent long term accuracy, the Boris algorithm is the de facto standard for advancing a charged particle. Despite its popularity, up to now there has been no convincing explanation why the Boris algorithm has this advantageous feature. In this paper, we provide an answer to this question. We show that the Boris algorithm conserves phase space volume, even though it is not symplectic. The global bound on energy error typically associated with symplectic algorithms still holds for the Boris algorithm, making it an effective algorithm for the multi-scale dynamics of plasmas.

Temperature Integration: An efficient procedure for calculation of free energy differences

We propose a method, Temperature Integration, which allows an efficient calculation of free energy differences between two systems of interest, with the same degrees of freedom, which may have rough energy landscapes. The method is based on calculating, for each single system, the difference between the values of lnZ at two temperatures, using a Parallel Tempering procedure. If our two systems of interest have the same phase space volume, they have the same values of lnZ at high-T, and we can obtain the free energy difference between them, using the two single-system calculations described above. If the phase space volume of a system is known, our method can be used to calculate its absolute (versus relative) free energy as well. We apply our method and demonstrate its efficiency on a “toy model” of hard rods on a 1-dimensional ring.

THE DYNAMICS OF MERGING CLUSTERS: A MONTE CARLO SOLUTION APPLIED TO THE BULLET AND MUSKET BALL CLUSTERS

Merging galaxy clusters have become one of the most important probes of dark matter, providing evidence for dark matter over modified gravity and even constraints on the dark matter self-interaction cross-section. To properly constrain the dark matter cross-section it is necessary to understand the dynamics of the merger, as the inferred cross-section is a function of both the velocity of the collision and the observed time since collision. While the best understanding of merging system dynamics comes from N-body simulations, these are computationally intensive and often explore only a limited volume of the merger phase space allowed by observed parameter uncertainty. Simple analytic models exist but the assumptions of these methods invalidate their results near the collision time, plus error propagation of the highly correlated merger parameters is unfeasible. To address these weaknesses I develop a Monte Carlo method to discern the properties of dissociative mergers and propagate the uncertainty of the measured cluster parameters in an accurate and Bayesian manner. I introduce this method, verify it against an existing hydrodynamic N-body simulation, and apply it to two known dissociative mergers: 1ES 0657-558 (Bullet Cluster) and DLSCL J0916.2+2951 (Musket Ball Cluster). I find that this method surpasses existing analytic models - providing accurate (10% level) dynamic parameter and uncertainty estimates throughout the merger history. This coupled with minimal required a priori information (subcluster mass, redshift, and projected separation) and relatively fast computation (~6 CPU hours) makes this method ideal for large samples of dissociative merging clusters.

Beam dynamics for induction accelerators

An induction linac uses pulsed power that is applied directly, without any intervening resonant cavities, to accelerate a charged particle pulse. This approach can accommodate a large multiple-beam focusing lattice capable of transporting a large total beam current with a long pulse duration, which may be compressed while accelerating as well as afterward. The mean accelerating gradient is relatively low (less than about 1.5MV/m), but the potential efficiency of energy transfer can be large up to about 50%. A multiple-beam induction linac is therefore a natural candidate accelerator for a heavy ion fusion (HIF) driver. However, the accelerated beams must meet stringent requirements on occupied phase space volume in order to be focused accurately and with small radius onto the fusion target. Dynamical considerations in the beam injector and linac, as well as in the final compression, final focus, and the fusion chamber, determine the quality of the driver beams as they approach the target. Requirements and tolerances derived from beam dynamics strongly influence the linac configuration and component design.After a summary of dynamical considerations, two major topics are addressed here: transportable current limits, which determine the choice of focal system for the linac, and longitudinal control of the beams, which are potentially destabilized by their interaction with the pulsed power system.

Dynamical fluctuations in baryon–meson ratios

The event-by-event dynamical fluctuations in kaon–proton and proton–pion ratios have been studied as a function of the center-of-mass energies of nucleon–nucleon collisions . Based on the changing phase space volume which apparently is the consequence of the phase transition(s) from hadrons to a quark–gluon plasma at large , the single-particle distribution function f is assumed to be modified. Varying f and the phase space volume are implemented in the grand-canonical ensemble, especially at GeV, so that the hadron resonance gas model, when taking into account the experimental acceptance and the quark phase space occupation factor γ, turns out to be able to reproduce the dynamical fluctuations in and ratios over the entire range of . It seems that the applied thermodynamic statistics could come up with a new modification to the Tsallis statistics. Both non-extensivity and changing the phase space are suggested and utilized in the present work.

Suppression of cardiac alternans by alternating-period-feedback stimulations

Alternans response, comprising a sequence of alternating long and short action potential durations in heart tissue, seen during rapid periodic pacing can lead to conduction block resulting in potentially fatal cardiac failure. A method of pacing with feedback control is proposed to reduce the alternans and therefore the probability of subsequent cardiac failure. The reduction is achieved by feedback control using small perturbations of constant magnitude to the original, alternans-generating pacing period T, viz., using sequences of two alternating periods of T+ΔT and T-ΔT, with ΔT<<T. Such a control scheme for alternans suppression is demonstrated experimentally in isolated whole heart experiments. This alternans suppression scheme is further confirmed and investigated in detail by simulations of ion-channel-based cardiac models both for a single cell and in one-dimensional spatially extended systems. The mechanism of the success of our method can be understood in terms of dynamics in phase space, viz., as the state of activity of the cell being confined within a narrow volume of phase space for the duration of control, resulting in extremely diminished variation in successive action potential durations. Our method is much more robust to noise than previous alternans reduction techniques based on fixed point stabilization and should thus be more efficient in terms of experimental implementation, which has implications for clinical treatment for arrhythmia.

Quantum Hertz entropy increase in a quenched spin chain

The classical Hertz entropy is the logarithm of the volume of phase space bounded by the constant energy surface; its quantum counterpart, the quantum Hertz entropy, is $\hat S = k_B \ln \hat N$, where the quantum operator $\hat N$ specifies the number of states with energy below a given energy eigenstate. It has been recently proved that, when an isolated quantum mechanical system is driven out of equilibrium by an external driving, the change in the expectation of its quantum Hertz entropy cannot be negative, and is null for adiabatic driving. This is in full agreement with the Clausius principle. Here we test the behavior of the expectation of the quantum Hertz entropy in the case when two identical XY spin chains initially at different temperatures are quenched into a single XY chain. We observed no quantum Hertz entropy decrease. This finding further supports the statement that the quantum Hertz entropy is a proper entropy for isolated quantum systems. We further quantify how far the quenched chain is from thermal equilibrium and the temperature of the closest equilibrium.

Tendency to occupy a statistically dominant spatial state of the flow as a driving force for turbulent transition

The transition from laminar to turbulent fluid motion occurring at large Reynolds numbers is generally associated with the instability of the laminar flow. On the other hand, since the turbulent flow characteristically appears in the form of spatially localized structures (e.g., eddies) filling the flow field, a tendency to occupy such a structured state of the flow cannot be ruled out as a driving force for turbulent transition. To examine this possibility, we propose a simple analytical model that treats the flow as a collection of localized spatial structures, each of which consists of elementary cells in which the behavior of the particles (atoms or molecules) is uncorrelated. This allows us to introduce the Reynolds number, associating it with the ratio between the total phase volume for the system and that for the elementary cell. Using the principle of maximum entropy to calculate the most probable size distribution of the localized structures, we show that as the Reynolds number increases, the elementary cells group into the localized structures, which successfully explains turbulent transition and some other general properties of turbulent flows. An important feature of the present model is that a bridge between the spatial-statistical description of the flow and hydrodynamic equations is established. We show that the basic assumptions underlying the model, i.e., that the particles are indistinguishable and elementary volumes of phase space exist in which the state of the particles is uncertain, are involved in the derivation of the Navier-Stokes equation. Taking into account that the model captures essential features of turbulent flows, this suggests that the driving force for the turbulent transition is basically the same as in the present model, i.e., the tendency of the system to occupy a statistically dominant state plays a key role. The instability of the flow at high Reynolds numbers can then be a mechanism to initiate structural rearrangement of the flow to find this state.

Nilpotence in Physics: the case of Tsallis entropy

In an attempt to understand the Tsallis entropy composition property, we construct an embedding of the reals into the set of 3 × 3 upper triangular matrices with real entries. We explore consequences of this embedding and of the geometry of the ambient 3 × 3 Heisenberg group. This approach establishes the polynomial growth of the volume of phase space of systems described by the Tsallis entropy and provides a general framework for understanding Abe's formula in terms of the Pansu derivative between Riemmanian spaces.

上海光源储存环恒流注入束流安全性模拟

For the safety issue for top-up injection, the trajectory of the injection beam was tracked to find out in what kinds of conditions the injection beam would get through the synchrotron light beam pipe and cause radiation hazards. The forward tracking method is used with Accelerator Toolbox (AT) code. We enlarge injection beam phase space volume and reduce the beam line element to simplify the calculation while covering all the possibility. According to this simulation, the interlock criteria are set up for top-up operation.