Momentum-space Anisotropy Research Articles

Ray–Wave Correspondence in Anisotropic Mesoscopic Billiards

Mesoscopic billiard systems for electrons and light, realized as quantum dots or optical microcavities, have enriched the fields of quantum chaos and nonlinear dynamics not only by enlarging the class of model systems, but also by providing access to their experimental realization. Here, we add yet another system class, two-dimensional billiards with anisotropies. One example is the anisotropic dispersion relation relevant in bilayer graphene known as trigonal warping, and another is the birefringent closed optical disk cavity. We demonstrate that the established concept of ray–wave correspondence also provides useful insight for anisotropic billiard systems. First, we approach the dynamics of the anisotropic disk from the ray-tracing side that takes the anisotropy in momentum space into account, based on the non-spherical index ellipsoid. Second, we use transformation optics to solve the wave problem and find the resonances to be those of the isotropic elliptical cavity. We illustrate ray–wave correspondence and mark differences in the description of optical and electronic anisotropic systems.

Far-from-equilibrium attractors for massive kinetic theory in the relaxation time approximation

In this proceedings contribution, we summarize recent findings concerning the presence of early- and late-time attractors in non-conformal kinetic theory. We study the effects of varying both the initial momentum-space anisotropy and initialization times using an exact solution of the 0+1D boostinvariant Boltzmann equation with a mass- and temperature-dependent relaxation time. Our findings support the existence of a longitudinal pressure attractor, but they do not support the existence of distinct attractors for the bulk viscous and shear pressures. Considering a large set of integral moments, we show that for moments with greater than one power of longitudinal momentum squared, both early- and late-time attractors are present.

Nonlinear inverse bremsstrahlung absorption in magnetized laser-fusion plasma

The nonlinear inverse bremsstrahlung absorption (NLIBA) in magnetized plasma has been investigated within the framework of relativistic kinetic theory. Collisions are described by an improved Krook collision term that accounts for relativistic effects and the Landau microscopic collision form. The non-linearity considered in this paper arises from the anisotropy in electron momentum space in the plasma that is heated by an intense laser pulse. The absorption is explicitly expressed, under reasonable approximations, as a function of the plasma, laser pulse, and magnetic field parameters. Numerical treatment of the model equations shows that absorption increases with laser intensity but decreases with plasma temperature and laser wavelength. It has been shown that the polarization of the laser wave has a significant influence on absorption for high-intense magnetic fields used in magneto-inertial fusion (MIF) experiments. Nonlinear effects clearly reduce absorption for laser intensities comparable to the characteristic intensity, I0=me2c3ε0ωL2/e2, where me is the electron mass, c is the speed of light in vacuum, ɛ0 is the electric permittivity of free space, ωL is the laser wave frequency, and e is the elementary electric charge. Within the intensity I ≪ I0 and laser wavelength in the micro-meter range (λ ∼ μm), relativistic effects appear in the third order of absorption. These findings allow for the optimization of laser pulse parameters to achieve efficient absorption in MIF experiments.

Anisotropic Behavior of S-Wave and P-Wave States of Heavy Quarkonia at Finite Magnetic Field

We studied the effect of momentum space anisotropy on heavy quarkonium states using an extended magnetized effective fugacity quasiparticle model (EQPM). Both the real and imaginary part of the potential has been modified through the dielectric function by including the anisotropic parameter ξ. The real part of the medium-modified potential becomes more attractive in the presence of the anisotropy and constant magnetic field. The binding energy of the 1S, 2S, and 1P quarkonium states including anisotropy effects for both the oblate and the isotropic case were studied. We find that the binding energy of QQ¯ states becomes stronger in the presence of anisotropy. However, the magnetic field is found to reduce the binding energy. The thermal width of the charmonium and bottomonium 1S states has been studied at constant magnetic field eB=0.3 GeV2 for isotropic and prolate cases. The effect of magnetic field on the mass spectra of the 1P state for the oblate case was also examined. The dissociation temperature for the 1S, 2S, and 1P states of charmonium and bottomonium has been determined to be higher for the oblate case with respect to the isotropic case.

Multiple-[formula omitted] instability under fourth-order inplane single-ion anisotropy

Multiple-Q instability under tetragonal single-ion anisotropy is theoretically investigated. By performing the simulated annealing for a spin model with the momentum-resolved interaction and fourth-order inplane single-ion anisotropy on a square lattice, we find that the interplay between the competing exchange interactions in momentum space and single-ion anisotropy leads to various field-induced double-Q states in the ground state. In particular, we show that a double-Q vortex crystal emerges when the interactions at high-harmonic wave vectors are comparable to those at wave vectors that give the dominant contributions. Our results underscore the importance of magnetic anisotropy, which brings about the multiple-Q instability in centrosymmetric magnets.

Far-from-equilibrium attractors for massive kinetic theory in the relaxation time approximation

We investigate whether early and late time attractors for non-conformal kinetic theories exist by computing the time-evolution of a large set of moments of the one-particle distribution function. For this purpose we make use of a previously obtained exact solution of the 0+1D boost-invariant massive Boltzmann equation in relaxation time approximation. We extend prior attractor studies of non-conformal systems by using a realistic mass- and temperature-dependent relaxation time and explicitly computing the effect of varying both the initial momentum-space anisotropy and initialization time on the time evolution of a large set of integral moments. Our findings are consistent with prior studies, which found that there is an attractor for the scaled longitudinal pressure, but not for the shear and bulk viscous corrections separately. We further present evidence that both late- and early-time attractors exist for all moments of the one-particle distribution function that contain greater than one power of the longitudinal momentum squared.

Orthorhombic distortion and rectangular skyrmion crystal in a centrosymmetric tetragonal host

We theoretically investigate the stability of a rectangular skyrmion crystal without fourfold rotational symmetry under an orthorhombic distortion in centrosymmetric tetragonal magnets. The results are obtained by numerically simulated annealing for an effective spin model with competing interactions in momentum space and magnetic anisotropy. By constructing the low-temperature phase diagram while changing the interaction ratio arising from the orthorhombic distortion, we find that the rectangular skyrmion crystal remains stable in an external magnetic field against distortion. We show that the degree of fourfold rotational symmetry tends to recover when the magnetic field is increased. The relevance to the skyrmion-hosting material EuAl4 is also discussed.

Collective modes of gluons in an anisotropic thermomagnetic medium

We study the collective modes of gluons in an anisotropic thermal medium in the presence of a constant background magnetic field using the hard-thermal-loop perturbation theory. The momentum space anisotropy of the medium has been incorporated through the generalized Romatschke-Strickland form of the distribution function, whereas the magnetic modification arising from the quark loop contribution has been taken into account in the lowest Landau level approximation. We consider two special cases: (i) a spheroidal anisotropy with the anisotropy vector orthogonal to the external magnetic field and (ii) an ellipsoidal anisotropy with two mutually orthogonal vectors describing anisotropies along and orthogonal to the field direction. The general structure of the polarization tensor in both cases is equivalent and consists of six independent basis tensors. We find that the introduction of momentum anisotropy ingrains azimuthal angular dependence in the thermomagnetic collective modes. Our study suggests that the presence of a strong background magnetic field can significantly reduce the growth rate of the unstable modes, which may have important implications in the equilibration of magnetized quark-gluon plasma.

Effective Debye screening mass in an anisotropic quark gluon plasma

Due to the rapid longitudinal expansion of the quark gluon plasma created in heavy-ion collisions, large local-rest-frame momentum-space anisotropies are generated during the system's evolution. These momentum-space anisotropies complicate the modeling of heavy-quarkonium dynamics in the quark gluon plasma due to the fact that the resulting interquark potentials are spatially anisotropic, requiring real-time solution of the 3D Schr\"odinger equation. Herein, we introduce a method for reducing anisotropic heavy-quark potentials to isotropic ones by introducing an effective screening mass that depends on the quantum numbers $l$ and $m$ of a given state. We demonstrate that, using the resulting effective Debye screening masses, one can solve a 1D Schr\"odinger equation and reproduce the full 3D results for the energies and binding energies of low-lying heavy-quarkonium bound states to relatively high accuracy. The resulting effective isotropic potential models could provide an efficient method for including momentum-anisotropy effects in open quantum system simulations of heavy-quarkonium dynamics in the quark gluon plasma.

Effect of momentum anisotropy on quark matter in the quark-meson model * *Supported by the National Natural Science Foundation of China (11935007) and the Fundamental Research Funds for the Central Universities (2020CXZZ107)

We investigate the chiral phase structure of quark matter with spheroidal momentum-space anisotropy specified by one anisotropy parameter in the 2+1 flavor quark-meson model. We find that the chiral phase diagram and the location of the critical endpoint (CEP) are significantly affected by the value of . With an increase in , the CEP is shifted to lower temperatures and higher quark chemical potentials. In addition, the temperature of the CEP is more sensitive to the anisotropy parameter than the corresponding quark chemical potential, which is the opposite to that from the finite system volume effect. The effects of the momentum anisotropy on the thermodynamic properties and scalar (pseudoscalar) meson masses are also studied at the vanishing quark chemical potential. The numerical results reveal that an increase in can hinder the restoration of chiral symmetry. We also find that shear viscosity and electrical conductivity decrease as increases. However, the bulk viscosity exhibits a significant non-trivial behavior with in the entire temperature domain of interest.

Nonequilibrium Attractor in High-Temperature QCD Plasmas

We establish the existence of a far-from-equilibrium attractor in weakly coupled gauge theory undergoing one-dimensional Bjorken expansion. We demonstrate that the resulting far-from-equilibrium evolution is insensitive to certain features of the initial condition, including both the initial momentum-space anisotropy and initial occupancy. We find that this insensitivity extends beyond the energy-momentum tensor to the detailed form of the one-particle distribution function. Based on our results, we assess different procedures for reconstructing the full one-particle distribution function from the energy-momentum tensor along the attractor and discuss implications for the freeze-out procedure used in the phenomenological analysis of ultrarelativistic nuclear collisions.

Cross-dimensional relaxation of Li7−Rb87 atomic gas mixtures in a spherical-quadrupole magnetic trap

We measure the interspecies interaction strength between $^7$Li and $^{87}$Rb atoms through cross-dimensional relaxation of two-element gas mixtures trapped in a spherical quadrupole magnetic trap. We record the relaxation of an initial momentum-space anisotropy in a lithium gas when co-trapped with rubidium atoms, with both species in the $|F=1, m_F = -1\rangle$ hyperfine state. Our measurements are calibrated by observing cross-dimensional relaxation of a $^{87}$Rb-only trapped gas. Through Monte Carlo simulations, we compare the observed relaxation to that expected given the theoretically predicted energy-dependent differential cross section for $^7$Li-$^{87}$Rb collisions. The experimentally observed relaxation occurs significantly faster than predicted theoretically, a deviation that appears incompatible with other experimental data characterising the $^7$Li-$^{87}$Rb molecular potential.

Anisotropic hydrodynamics with a scalar collisional kernel

Prior studies of non-equilibrium dynamics using anisotropic hydrodynamics have used the relativistic Anderson-Witting scattering kernel or some variant thereof. In this paper, we make the first study of the impact of using a more realistic scattering kernel. For this purpose, we consider a conformal system undergoing transversally-homogenous and boost-invariant Bjorken expansion and take the collisional kernel to be given by the leading order 2 <-> 2 scattering kernel in scalar lambda phi^4. We consider both classical and quantum statistics in order to assess the impact of Bose enhancement on the dynamics. We also determine the anisotropic non-equilibrium attractor of a system subject to this collisional kernel. We find that, when the near-equilibrium relaxation-times in the Anderson-Witting and scalar collisional kernels are matched, the scalar kernel results in a higher degree of momentum-space anisotropy during the system's evolution, given the same initial conditions. Additionally, we find that taking into account Bose enhancement further increases the dynamically generated momentum-space anisotropy.

Parton self-energies for general momentum-space anisotropy

We introduce an efficient general method for calculating the self-energies, collective modes, and dispersion relations of quarks and gluons in a momentum-anisotropic high-temperature quark-gluon plasma. The method introduced is applicable to the most general classes of deformed anisotropic momentum distributions and the resulting self-energies are expressed in terms of a series of hypergeometric basis functions which are valid in the entire complex phase-velocity plane. Comparing to direct numerical integration of the self-energies, the proposed method is orders of magnitude faster and provides results with similar or better accuracy. To extend previous studies and demonstrate the application of the proposed method, we present numerical results for the parton self-energies and dispersion relations of partonic collective excitations for the case of an ellipsoidal momentum-space anisotropy. Finally, we also present, for the first time, the gluon unstable mode growth rate for the case of an ellipsoidal momentum-space anisotropy.

Dispersion characteristics of anisotropic unmagnetized ultra-relativistic transverse plasma wave with arbitrary electron degeneracy

Thermal momentum space anisotropy is ubiquitous in many astrophysical and laboratory plasma environments. Using Vlasov-Maxwell's model equations, a generalized polarization tensor for a collisionless ultra-relativistic unmagnetized electron plasma is derived. In particular, the tensor is obtained by considering anisotropy in the momentum space. The integral of moments of Fermi-Dirac distribution function in terms of Polylog functions is used for describing the border line plasma systems (TeTFe≈1) comprising arbitrary electron degeneracy, where Te and TFe, are thermal and Fermi temperatures, respectively. Furthermore, the effects of variation in thermal momentum space anisotropy on the electron equilibrium number density and the spectrum of electromagnetic waves are analyzed.

The static hard-loop gluon propagator to all orders in anisotropy

We calculate the (semi-)static hard-loop self-energy and propagator using the Keldysh formalism in a momentum-space anisotropic quark-gluon plasma. The static retarded, advanced, and Feynman (symmetric) self-energies and propagators are calculated to all orders in the momentum-space anisotropy parameter ξ. For the retarded and advanced self-energies/propagators, we present a concise derivation and comparison with previously-obtained results and extend the calculation of the self-energies to next-to-leading order in the gluon energy, ω. For the Feynman self-energy/propagator, we present new results which are accurate to all orders in ξ. We compare our exact results with prior expressions for the Feynman self-energy/propagator which were obtained using Taylor-expansions around an isotropic state. We show that, unlike the Taylor-expanded results, the all-orders expression for the Feynman propagator is free from infrared singularities. Finally, we discuss the application of our results to the calculation of the imaginary-part of the heavy-quark potential in an anisotropic quark-gluon plasma.

Measurement of long-range angular correlations and azimuthal anisotropies in high-multiplicity p+Au collisions at sNN=200 GeV

We present the first measurements of long-range angular correlations and the transverse momentum dependence of elliptic flow $v_2$ in high-multiplicity $p$$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV. A comparison of these results with previous measurements in high-multiplicity $d$$+$Au and $^3{\rm He}$$+$Au collisions demonstrates a relation between $v_2$ and the initial collision eccentricity $\varepsilon_2$, suggesting that the observed momentum-space azimuthal anisotropies in these small systems have a collective origin and reflect the initial geometry. Good agreement is observed between the measured $v_2$ and hydrodynamic calculations for all systems, and an argument disfavoring theoretical explanations based on momentum-space domain correlations is presented. The set of measurements presented here allows us to leverage the distinct intrinsic geometry of each of these systems to distinguish between different theoretical descriptions of the long-range correlations observed in small collision systems.

Phenomenological predictions of 3+1d anisotropic hydrodynamics

We make phenomenological predictions for particle spectra and elliptic flow in heavy-ion collisions using 3+1d anisotropic hydrodynamics (aHydro) including the effects of both shear and bulk viscosities. The dynamical equations necessary are derived by taking moments of the Boltzmann equation allowing for three distinct (diagonal) momentum-space anisotropy parameters. The formulation is based on relaxation-time approximation for the collisional kernel and a lattice-QCD-based equation of state. Evolving the system to late times, we calculate particle production using THERMINATOR 2, modified to account for an ellipsoidal distribution function. We obtain particle spectra for different particle species such as pions, kaons, and protons, and elliptic flow v2 as a function of centrality, transverse momentum, and rapidity. In our model, we have four free parameters, i.e. freeze-out temperature, initial central energy density, initial momentum-space anisotropies, and shear viscosity to entropy density ratio. Using a multidimensional fit to LHC experimental data, we make a preliminary extraction of these parameters. We find reasonable agreement between 3+1d aHydro and available experimental data for η/s ∼ 0:23.

Momentum anisotropy at freeze out

The transition from a hydrodynamical modeling to a particle-based approach is a crucial element of the description of high-energy heavy-ion collisions. Assuming this “freeze out” happens instantaneously at each point of the expanding medium, we show that the local phase-space distribution of the emitted particles is asymmetric in momentum space. This suggests the use of anisotropic hydrodynamics for the last stages of the fluid evolution. We discuss how observables depend on the amount of momentum-space anisotropy at freeze out and how smaller or larger anisotropies allow for different values of the freeze-out temperature.

Centrality and collision event-plane determination in ALICE at the LHC

Investigation of physical phenomena in heavy-ion collisions requires knowledge about collision geometry, which is characterized by the energy distribution in the overlap region of the colliding nuclei and of the collision spectators. Both the event-by-event distributions of produced particles and the spectator nucleons can be used to estimate the collision geometry. Due to the pressure gradients, the spatial anisotropy of initial state geometry is converted during the system evolution to an anisotropy in momentum space. The event-planes of this anisotropy can be estimated via measured azimuthal distributions of particles produced in the collision. We report on the performance of the ALICE experiment at the LHC for the centrality and the event-plane determination for different harmonics using measured distribution of produced particles at central and forward rapidity, and the energy distribution of the spectator neutrons at beam rapidity.