Phase Space Volume Research Articles

The Magellanic Clouds Are Very Rare in the IllustrisTNG Simulations

The Large and Small Magellanic Clouds (LMC and SMC) form the closest interacting galactic system to the Milky Way, therewith providing a laboratory to test cosmological models in the local Universe. We quantify the likelihood for the Magellanic Clouds (MCs) to be observed within the ΛCDM model using hydrodynamical simulations of the IllustrisTNG project. The orbits of the MCs are constrained by proper motion measurements taken by the Hubble Space Telescope and Gaia. The MCs have a mutual separation of dMCs=24.5kpc and a relative velocity of vMCs=90.8kms−1, implying a specific phase-space density of fMCs,obs≡(dMCs·vMCs)−3=9.10×10−11km−3s3kpc−3. We select analogues to the MCs based on their stellar masses and distances in MW-like halos. None of the selected LMC analogues have a higher total mass and lower Galactocentric distance than the LMC, resulting in >3.75σ tension. We also find that the fMCs distribution in the highest resolution TNG50 simulation is in 3.95σ tension with observations. Thus, a hierarchical clustering of two massive satellites like the MCs in a narrow phase-space volume is unlikely in ΛCDM, presumably because of short merger timescales due to dynamical friction between the overlapping dark matter halos. We show that group infall led by an LMC analogue cannot populate the Galactic disc of satellites (DoS), implying that the DoS and the MCs formed in physically unrelated ways in ΛCDM. Since the 20∘ alignment of the LMC and DoS orbital poles has a likelihood of P=0.030 (2.17σ), adding this χ2 to that of fMCs gives a combined likelihood of P=3.90×10−5 (4.11σ).

Non-unique Hamiltonians for discrete symplectic dynamics.

An outstanding property of any Hamiltonian system is the symplecticity of its flow, namely, the continuous trajectory preserves volume in phase space. Given a symplectic but discrete trajectory generated by a transition matrix applied at a fixed time-increment (τ > 0), it was generally believed that there exists a unique Hamiltonian producing a continuous trajectory that coincides at all discrete times (t = nτ with n integers) as long as τ is small enough. However, it is now exactly demonstrated that, for any given discrete symplectic dynamics of a harmonic oscillator, there exist an infinite number of real-valued Hamiltonians for any small value of τ and an infinite number of complex-valued Hamiltonians for any large value of τ. In addition, when the transition matrix is similar to a Jordan normal form with the supradiagonal element of 1 and the two identical diagonal elements of either 1 or -1, only one solution to the Hamiltonian is found for the case with the diagonal elements of 1, but no solution can be found for the other case.

Transverse emittance reduction in muon beams by ionization cooling

AbstractAccelerated muon beams have been considered for the next-generation studies of high-energy lepton–antilepton collisions and neutrino oscillations. However, high-brightness muon beams have not yet been produced. The main challenge for muon acceleration and storage stems from the large phase-space volume occupied by the beam, derived from the production mechanism of muons through the decay of pions. The phase-space volume of the muon beam can be decreased through ionization cooling. Here we show that ionization cooling leads to a reduction in the transverse emittance of muon beams that traverse lithium hydride or liquid hydrogen absorbers in the Muon Ionization Cooling Experiment. Our results represent a substantial advance towards the realization of muon-based facilities that could operate at the energy and intensity frontiers.

General guide concepts for compact, high-brilliance neutron moderators

The trend in neutron sciences is toward integrating compact, high-brightness moderators into new or upgraded facilities. Transporting neutrons from the source to the sample position with a phase-space distribution tailored to specific requirements is crucial to leverage high source brilliance. We have investigated four guide concepts using Monte Carlo ray tracing simulations: Montel beamline with nested Kirkpatrick–Baez mirrors, curved-tapered beamline with a bender and straight sections, straight-elliptical beamline, and curved-elliptical beamline. The straight-elliptical (curved-elliptical) beamline features two half-ellipse guides connected by a straight (non-straight) guide section. The neutron transport efficiency and phase space homogeneity have been quantitatively compared. Our results show that the straight-elliptical beamline performs best because of few neutron bounces on the guide surface with small reflection angles, minimizing flux loss. The Montel beamline provides the best spatial confinement of neutrons within the desired region; however, there is a high thermal-neutron loss due to large reflection angles. The curved-tapered beamline suffers from significant flux loss due to high bounces, and it shows a non-uniform angular distribution related to broad ranges of bounces and reflection angles. The non-straight guide section of the curved-elliptical beamline increases the phase space inhomogeneity, leading to a spatially non-uniform beam profile. The results apply to general neutron instruments that require transporting thermal and cold neutrons from a compact, high-brilliance moderator to the sample location with a moderate phase-space volume.

Semiclassical perspective on Landau levels and Hall conductivity in an anisotropic cubic Dirac semimetal and the peculiar case of star-shaped classical orbits

We study an anisotropic cubic Dirac semimetal subjected to a constant magnetic field. In the case of an isotropic dispersion in the x−y plane, with parameters vx=vy, it is possible to find exact Landau levels, indexed by the quantum number n, using the typical ladder operator approach. Interestingly, we find that the lowest energy level (the zero-energy state in the case of kz=0) has a degeneracy that is 3 times that of other states. This degeneracy manifests in the Hall conductivity as a step at a zero chemical potential 3/2 the size of other steps. Moreover, as n→∞, we find energies En∝n3/2, which means the nth step as a function of the chemical potential roughly occurs at a value μ∝n3/2. We propose that these exciting features could be used to experimentally identify cubic Dirac semimetals. Subsequently, we analyze the anisotropic case vy=λvx, with λ≠1. First, we consider a perturbative treatment around λ≈1 and find that energies En∝n3/2 still hold as n→∞. To gain further insight into the Landau level structure for a maximum anisotropy, we turn to a semiclassical treatment that reveals interesting star-shaped orbits in phase space that close at infinity. This property is a manifestation of weakly localized states. Despite being infinite in length, these orbits enclose a finite phase space volume and permit finding a simple semiclassical formula for the energy, which has the same form as above. Our findings suggest that both isotropic and anisotropic cubic Dirac semimetals should leave similar experimental imprints. Published by the American Physical Society 2024

On the thermodynamic entropy in the microcanonical ensemble of classical systems

We demonstrate that the surface entropy given by the volume of an energy shell in the phase space can be the thermodynamically consistent entropy in a classical microcanonical ensemble if the thickness of the energy shell is not an arbitrary constant but a non-extensive function satisfying a specific differential equation. A particular form of the energy shell thickness as a possible solution to the differential equation converts the surface entropy into the volume entropy given by the phase-space volume bounded by a constant energy surface. However, such a form bears a problem: The temperature derived accordingly becomes extensive when the density of states is a non-monotonic function of energy. Based on the adiabatic invariance of the degeneracy of a quantum system and the Weyl correspondence, we propose an alternative solution: the energy shell thickness given by the energy level spacing in the quantum counterpart of the classical ensemble considered, which is illustrated by a few simple examples.

Ultralow lattice thermal conductivity in bulk and monolayer TlCuSe: a comparative study from first-principles

Layered TlCuSe was experimentally found to possess ultralow lattice thermal conductivity due to the weak chemical bond and the strong anharmonicity, however, there is an imaginary frequency in the calculated phonon spectrum based on density functional theory (DFT) (Lin et al 2021 Adv. Mater. 33 2104908). Herein, using DFT + U (Coulomb interaction) and phonon Boltzmann transport theory, we demonstrate that the Coulomb interaction can effectively eliminate the imaginary frequency of the phonon spectrum for both bulk and monolayer TlCuSe. The lattice thermal conductivity can be further decreased from bulk (0.43 W m−1K−1 in-plane at 300 K) to monolayer (0.35 W m−1K−1 at 300 K), which comes from the competition between the increased phonon group velocity and the decreased phonon relaxation time. The larger Grüneisen parameters and phase space volume of the monolayer compared to the bulk indicate an enhanced anharmonicity, leading to a low phonon relaxation time and dominating the decreasing lattice thermal conductivity. The present work highlights the indispensability of Coulomb interaction when exploring the phonon transport. The ultralow lattice thermal conductivity of TlCuSe, especially in the form of monolayers, suggests promising thermoelectric applications.

Dimensional measures of generalized entropy

Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond the additive definition pioneered by Boltzmann, Gibbs, and Shannon (applicable to thermodynamic equilibria). For generalized entropies to be applied rigorously to nonequilibrium statistical mechanics, we suggest that there is a need for a physically interpretable (dimensional) framework that can be connected to dynamical processes operating in phase space. In this work, we introduce dimensional measures of entropy that admit arbitrary invertible weight functions (subject to curvature and convergence requirements). These ‘dimensional entropies’ have physical dimensions of phase-space volume and represent the extent of level sets of the distribution function. Dimensional entropies with power-law weight functions (related to Rényi and Tsallis entropies) are particularly robust, as they do not require any internal dimensional parameters due to their scale invariance. We also point out the existence of composite entropy measures that can be constructed from functionals of dimensional entropies. We calculate the response of the dimensional entropies to perturbations, showing that for a structured distribution, perturbations have the largest impact on entropies weighted at a similar phase-space scale. This elucidates the link between dynamics (perturbations) and statistics (entropies). Finally, we derive corresponding generalized maximum-entropy distributions. Dimensional entropies may be useful as a diagnostic (for irreversibility) and for theoretical modeling (if the underlying irreversible processes in phase space are understood) in chaotic and complex systems, such as collisionless systems of particles with long-range interactions.

On the inevitable lightness of vacuum

In this essay, we present a new understanding of the cosmological constant problem, built upon the realization that the vacuum energy density can be expressed in terms of a phase space volume. We introduce a UV-IR regularization which implies a relationship between the vacuum energy and entropy. Combining this insight with the holographic bound on entropy then yields a bound on the cosmological constant consistent with observations. It follows that the universe is large, and the cosmological constant is naturally small, because the universe is filled with a large number of degrees of freedom.

Radial oscillations and dynamical instability analysis for linear-quadratic GUP-modified white dwarfs

A modification to the Heisenberg uncertainty principle is called the generalized uncertainty principle (GUP), which emerged due to the introduction of a minimum measurable length, common among phenomenological approaches to quantum gravity. One approach to GUP is called linear-quadratic GUP (LQGUP) which satisfies both the minimum measurable length and the maximum measurable momentum, resulting to an infinitesimal phase space volume proportional to the first-order momentum (1−αp)−4d3xd3p, where α is the still-unestablished GUP parameter. In this study, we explore the mass–radius relations of white dwarfs whose equation of state has been modified by LQGUP, and provide them with radial perturbations to investigate the dynamical instability arising from the oscillations. We find from the mass–radius relations that the main effect of LQGUP is to worsen the gravitational collapse by decreasing the mass of the relatively massive white dwarfs (including their limiting mass, while increasing their limiting radius). This effect gets more prominent with larger values of α. We then compare the results with available observational data. To further investigate the impact of the GUP parameter, a dynamical instability analysis of the white dwarf was conducted, and we find that instability sets in for all values of α. With increasing α, we also find that the central density at which instability occurs decreases, resulting to a lower maximum mass. This is in contrast to quadratic GUP, where instability only sets in below a critical value of the quadratic GUP parameter.

Vacuum energy density and gravitational entropy

The failure to calculate the vacuum energy is a central problem in theoretical physics. Presumably the problem arises from the insistent use of effective field theory reasoning in a context that is well beyond its intended scope. If one follows this path, then one is led inevitably to statistical or anthropic reasoning for observations. It appears that a more palatable resolution of the vacuum energy problem requires some form of UV/IR feedback. In this paper we take the point of view that such feedback can be thought of as arising by defining a notion of quantum space-time. We reformulate the regularized computation of vacuum energy in such a way that it can be interpreted in terms of a sum over elementary phase space volumes, that we identify with a ground state degeneracy. This observation yields a precise notion of UV/IR feedback, while leaving a scale unfixed. Here we argue that holography can be thought to provide a key piece of information: we show that equating this microscopic ground state degeneracy with macroscopic gravitational entropy yields a prediction for the vacuum energy that can easily be consistent with observations. Essentially, the smallness of the vacuum energy is tied to the large size of the Universe. We discuss how within this scenario notions of effective field theory can go so wrong.

Relative asymptotic oscillations of the out-of-time-ordered correlator as a quantum chaos indicator.

A detailed numerical study reveals that the asymptotic values of the standard-deviation-to-mean ratio of the out-of-time-ordered correlator in energy eigenstates can be successfully used as a measure of the quantum chaoticity of the system. We employ a finite-size fully connected quantum system with two degrees of freedom, namely, the algebraic u(3) model, and demonstrate a clear correspondence between the energy-smoothed relative oscillations of the correlators and the ratio of the chaotic part of the volume of phase space in the classical limit of the system. We also show how the relative oscillations scale with the system size and conjecture that the scaling exponent can also serve as a chaos indicator.

Perspective: Reference-Potential Methods for the Study of Thermodynamic Properties in Chemical Processes: Theory, Applications, and Pitfalls.

In silico investigations of enzymatic reactions and chemical reactions in condensed phases often suffer from formidable computational costs due to a large number of degrees of freedom and enormous important volume in phase space. Usually, accuracy must be compromised to trade for efficiency by lowering the reliability of the Hamiltonians employed or reducing the sampling time. Reference-potential methods (RPMs) offer an alternative approach to reaching high accuracy of simulation without much loss of efficiency. In this Perspective, we summarize the idea of RPMs and showcase some recent applications. Most importantly, the pitfalls of these methods are also discussed, and remedies to these pitfalls are presented.

Sunlight-pumped two-dimensional thermalized photon gas

The Liouville theorem states that the phase-space volume of an ensemble in a closed system remains constant. While gases of material particles can efficiently be cooled by sympathetic or laser cooling techniques, allowing for large phase-space compression upon suitable coupling to the environment, for light both the absence of an internal structure, as well as the nonconservation of photons upon contact with matter imposes fundamental limits for three-dimensional light-harvesting systems, such as fluorescence-based light concentrators. An advantageous physical situation can in principle be expected for dye-solution-filled microcavities with a mirror spacing in the wavelength range, where low-dimensional photon gases with nonvanishing and tunable chemical potential have been experimentally realized. Motivated by the goal to observe phase-space compression of sunlight by cooling the captured radiation to room temperature, in this work we theoretically show that in a lossless, harmonically confined system the phase-space volume scales as ${(\mathrm{\ensuremath{\Delta}}x\mathrm{\ensuremath{\Delta}}p/T)}^{d}=\mathrm{constant}$, where $\mathrm{\ensuremath{\Delta}}x$ and $\mathrm{\ensuremath{\Delta}}p$ denote the position and momentum spread and $d$ the dimensionality of the system ($d=1$ or 2). Experimentally, we realize a corresponding sunlight-pumped dye microcavity and demonstrate thermalization of scattered sunlight to a two-dimensional room temperature photon gas with nonvanishing chemical potential. Prospects of phase-space buildup of light by cooling, as can be feasible in systems with a two- or three-dimensional band gap, range from quantum state preparation in tailored potentials up to technical applications for more efficient collection of diffuse sunlight.

Modelling and dynamic analysis of a novel seven-dimensional Hamilton conservative hyperchaotic systems with wide range of parameter

The study of chaotic attractors has been a hot issue in complex science research in recent years. However, most of the current research has focused on low-dimensional dissipative systems. High-dimensional conservative systems have both conservative and hyperchaotic properties, the phase space is integer dimensional and does not have attractors, and the trajectories expand in multiple directions, thus having higher complexity and spatial ergodicity. In addition, the high dimensional conservative system with wide parameter range not only has better dynamic characteristics, but also has a good application prospect in the field of information security. In this paper, a novel seven-dimensional Hamiltonian conservative hyperchaotic system (7D-HCHCS) is constructed. The dynamical properties of this system are described by analyzing the rate of change of phase space volume, phase trajectory diagram, Poincaré map, Lyapunov exponential spectrum (LEs), bifurcation diagram, equilibrium point, and system complexity. A new pseudo-random number generator (PRNG) is designed on this basis, and the key stream generated by this PRNG passes the NIST test. Besides, the phase diagrams and Poincaré map under a wide range of parameters are compared. The results show that the proposed system satisfies the Hamilton energy conservation and can generate hyperchaotic flow. It also has good pseudorandom characteristics, ergodicity under a large range of control parameters, which also has good prospects in the field of information security.

Physics-Informed Neural Network with Fourier Features for Radiation Transport in Heterogeneous Media

Typical machine learning (ML) methods are difficult to apply to radiation transport due to the large computational cost associated with simulating problems to create training data. Physics-informed Neural Networks (PiNNs) are a ML method that train a neural network with the residual of a governing equation as the loss function. This allows PiNNs to be trained in a low-data regime in the absence of (experimental or synthetic) data. PiNNs also are trained on points sampled within the phase-space volume of the problem, which means they are not required to be evaluated on a mesh, providing a distinct advantage in solving the linear Boltzmann transport equation, which is difficult to discretize. We have applied PiNNs to solve the streaming and interaction terms of the linear Boltzmann transport equation to create an accurate ML model that is wrapped inside a traditional source iteration process. We present an application of Fourier Features to PiNNs that yields good performance on heterogeneous problems. We also introduce a sampling method based on heuristics that improves the performance of PiNN simulations. The results are presented in a suite of one-dimensional radiation transport problems where PiNNs show very good agreement when compared to fine-mesh answers from traditional discretization techniques.

The Hamiltonian for von Zeipel–Lidov–Kozai oscillations

ABSTRACTThe Hamiltonian used in classical analyses of von Zeipel–Lidov–Kozai or ZLK oscillations in hierarchical triple systems is based on the quadrupole potential from a distant body on a fixed orbit, averaged over the orbits of both the inner and the outer bodies (‘double averaging’). This approximation can be misleading, because the corresponding Hamiltonian conserves the component of angular momentum of the inner binary normal to the orbit of the outer binary, thereby restricting the volume of phase space that the system can access. This defect is usually remedied by including the effects of the octopole potential, or by allowing the outer orbit to respond to variations in the inner orbit. However, in a wide variety of astrophysical systems, non-linear perturbations are comparable to or greater than these effects. The long-term effects of non-linear perturbations are described by an additional Hamiltonian, which we call Brown’s Hamiltonian. At least three different forms of Brown’s Hamiltonian are found in the literature; we show that all three are related by a gauge freedom, although one is much simpler than the others. We argue that investigations of ZLK oscillations in triple systems should include Brown’s Hamiltonian.

Microcanonical Thermodynamics of Small Ideal Gas Systems

We consider the thermal, mechanical, and chemical contact of two subsystems composed of ideal gases, both of which are not in the thermodynamic limit. After contact, the combined system is isolated, and the entropy is determined through the use of its standard connection to the phase space density (PSD), where only those microstates at a given energy value are counted. The various intensive properties of these small systems that follow from a derivative of the PSD, such as the temperature, pressure, and chemical potential (evaluated via a backward difference), while equal when the two subsystems are in equilibrium are nevertheless found not to behave in accordance with what is expected from macroscopic thermodynamics. Instead, it is the entropy, defined from its connection to the PSD, that still controls the behavior of these small (nonextensive) systems. We also analyze the contact of these two subsystems utilizing an alternative entropy definition, through its proposed connection to the phase space volume (PSV), where all microstates at or below a given energy value are counted. We show that certain key properties of these small systems obtained with the PSV either do not become equal or do not consistently describe the two subsystems when in contact, suggesting that the PSV should not be used for analyzing the behavior of small isolated systems.

Threefold way to black hole entropy

In this work we propose a correspondence between black hole entropy and a topological quantity defined for projective spaces based on the real, complex, and quaternion numbers. After interpreting Weinstein's integer as the normalized volume of the quantum phase space, whose logarithm gives place to the area law (in the real case) and to logarithmic corrections with $\ensuremath{-}\frac{1}{2}$ and $\ensuremath{-}\frac{3}{2}$ coefficients (in the complex and quaternionic cases, respectively), the exact Bekenstein-Hawking entropy is obtained when certain equally spaced spectrum for the event horizon area is imposed. Even more, the minimal area(s) which emerge from our model, are of the form $4\mathrm{log}k$, $k\ensuremath{\in}{2,4,16}$, in complete agreement with previous works. Finally, the role played by global (complex and quaternionic) phases in different descriptions of black hole entropy is clarified.

Boltzmann’s Entropy During Free Expansion of an Interacting Gas

In this work, we study the evolution of Boltzmann’s entropy in the context of free expansion of a one-dimensional interacting gas inside a box. Our interacting particle model is a gas of hard point particles with alternating masses, a system known to have good ergodicity properties. Boltzmann’s entropy is defined for single microstates and is given by the phase-space volume occupied by microstates with the same value of macrovariables which are coarse-grained physical observables. We demonstrate the idea of typicality in the growth of the Boltzmann’s entropy for two choices of macro-variables—the single particle phase space distribution and the hydrodynamic fields. Due to the presence of interactions, the growth curves for both these entropies are observed to converge to a monotonically increasing limiting curve, on taking the appropriate order of limits, of large system size and small coarse-graining scale. Moreover, we observe that the limiting growth curves for the two choices of entropies are identical as implied by local thermal equilibrium. We also discuss issues related to finite size and finite coarse gaining scale which lead to interesting features such as oscillations in the entropy growth curve. We also discuss shocks observed in the hydrodynamic fields.