Momentum Anisotropy Research Articles

Spectroscopic signature of moment-dependent electron–phonon coupling in 2H-TaS2

An ARPES study of 2H-TaS2 reveals that its CDW transition is driven by strong electron–phonon coupling along with its momentum anisotropy.

Quark self-energy in an ellipsoidally anisotropic quark-gluon plasma

We calculate the quark self-energy in a quark-gluon plasma that possesses an ellipsoidal momentum-space anisotropy in the local rest frame. By introducing additional transverse momentum anisotropy parameters into the parton distribution functions, we generalize previous results which were obtained for the case of a spheroidal anisotropy. Our results demonstrate that the presence of anisotropies in the transverse directions affects the real and imaginary parts of quark self-energy and, consequently, the self-energy depends on both the polar and azimuthal angles in the local rest frame of the matter. Our results for the quark self-energy set the stage for the calculation of the effects of ellipsoidal momentum-space anisotropy on quark-gluon plasma photon spectra and collective flow.

Power spectrum of flow fluctuations in relativistic heavy-ion collisions

We carry out hydrodynamical simulation of the evolution of fluid in relativistic heavy-ion collisions with random initial fluctuations. The time evolution of power spectrum of momentum anisotropies shows very strong correspondence with the physics of cosmic microwave anisotropies as was earlier predicted by us. In particular, our results demonstrate suppression of superhorizon fluctuations and the correspondence between the location of the first peak in the power spectrum of momentum anisotropies and the length scale of fluctuations and expected freeze-out time-scale (more precisely, the sound horizon size at freeze-out).

Evolution of quasiparticle excitations with enhanced electron correlations in superconductingAFe2As2(A=K, Rb, and Cs)

In the heavily hole-doped iron-based superconductors $A$Fe$_2$As$_2$ ($A=$ K, Rb, and Cs), the electron effective mass increases rapidly with alkali-ion radius. To study how the mass enhancement affects the superconducting state, we measure the London penetration depth $\lambda(T)$ in clean crystals of $A$Fe$_2$As$_2$ down to low temperature $T\sim0.1$ K. In all systems, the superfluid stiffness $\rho_s(T)=\lambda^2(0)/\lambda^2(T)$ can be approximated by a power-law $T$ dependence at low temperatures, indicating the robustness of strong momentum anisotropy in the superconducting gap $\Delta(k)$. The power $\alpha$ increases from $\sim1$ with mass enhancement and approaches an unconventional exponent $\alpha\sim 1.5$ in the heaviest CsFe$_2$As$_2$. This appears to be a hallmark of superconductors near antiferromagnetic quantum critical points, where the quasiparticles excited across the anisotropic $\Delta(k)$ are significantly influenced by the momentum dependence of quantum critical fluctuations.

Testing hydrodynamic descriptions of p+p collisions at $$\sqrt{s}=7$$ TeV

In high-energy collisions of heavy ions, experimental findings of collective flow are customarily associated with the presence of a thermalized medium expanding according to the laws of hydrodynamics. Recently, the ATLAS, CMS, and ALICE experiments found signals of the same type and magnitude in ultrarelativistic proton–proton collisions. In this study, the state-of-the-art hydrodynamic model SONIC is used to simulate the systems created in p+p collisions. By varying the size of the second-order transport coefficients, the range of applicability of hydrodynamics itself to the systems created in p+p collisions is quantified. It is found that hydrodynamics can give quantitatively reliable results for the particle spectra and the elliptic momentum anisotropy coefficient $$v_2$$ . Using a simple geometric model of the proton based on the elastic form factor leads to results of similar type and magnitude to those found in experiment when allowing for a small bulk viscosity coefficient.

Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation

Fluid-dynamical equations of motion can be derived from the Boltzmann equation in terms of an expansion around a single-particle distribution function which is in local thermodynamical equilibrium, i.e., isotropic in momentum space in the rest frame of a fluid element. However, in situations where the single-particle distribution function is highly anisotropic in momentum space, such as the initial stage of heavy-ion collisions at relativistic energies, such an expansion is bound to break down. Nevertheless, one can still derive a fluid-dynamical theory, called anisotropic dissipative fluid dynamics, in terms of an expansion around a single-particle distribution function, $\hat{f}_{0\bf k}$, which incorporates (at least parts of) the momentum anisotropy via a suitable parametrization. We construct such an expansion in terms of polynomials in energy and momentum in the direction of the anisotropy and of irreducible tensors in the two-dimensional momentum subspace orthogonal to both the fluid velocity and the direction of the anisotropy. From the Boltzmann equation we then derive the set of equations of motion for the irreducible moments of the deviation of the single-particle distribution function from $\hat{f}_{0\bf k}$. Truncating this set via the 14-moment approximation, we obtain the equations of motion of anisotropic dissipative fluid dynamics.

Photon and dilepton production from a non-equilibrium quark-gluon plasma

We calculate leading-order medium photon and dilepton yields from a quark-gluon plasma using (3+1)-dimensional anisotropic hydrodynamics. In the case of dileptons, at leading-order it is sufficient to take into account non-equilibrium corrections to the rate through the use of anisotropic distribution functions. In the case of photons, non-equilibrium corrections to the rate are taken into account using a self-consistent modification of the distribution functions and the corresponding anisotropic hard-loop quark self-energies. We present predictions for the high-energy photon and dilepton spectrum and the photon elliptic flow as a function of invariant mass, transverse momentum, shear viscosity, and initial momentum-space anisotropy. Our findings indicate that both high-energy photon and dilepton production are sensitive to the assumed level of initial momentum-space anisotropy of the quark-gluon plasma. In addition, we find that the photon elliptic flow depends on the initial momentum-space anisotropy.

Magnetic-field-induced squeezing effect at energies available at the BNL Relativistic Heavy Ion Collider and at the CERN Large Hadron Collider

In off-central heavy-ion collisions, the quark-gluon plasma (QGP) is exposed to the strongest magnetic fields ever created in the universe. Due to the paramagnetic nature of the QGP at high temperatures, the spatially inhomogeneous magnetic field configuration exerts an anisotropic force density that competes with the pressure gradients resulting from purely geometric effects. In this paper, we simulate (3+1)-dimensional ideal hydrodynamics with external magnetic fields to estimate the effect of this force density on the anisotropic expansion of the QGP in collisions at RHIC and at the LHC. While negligible for quickly decaying magnetic fields, we find that long-lived fields generate a substantial force density that suppresses the momentum anisotropy of the plasma by up to $20\%$ at the LHC energy, and also leaves its imprint on the elliptic flow $v_2$ of charged pions.

Exploring the beam-energy dependence of flow-like signatures in small-systemd+Aucollisions

Recent analyses of small collision systems, namely $p+p$ and $p+$Pb at the LHC and $p+$Au, $d+$Au and $^{3}$He+Au at RHIC, have revealed azimuthal momentum anisotropies commonly associated with collective flow in larger systems. Viscous hydrodynamics and parton cascade calculations have proved successful at describing some flow-like observables in these systems. These two classes of calculations also confirm these observables to be directly related to the initial geometry of the created medium. However, the question of whether equilibrium dynamics is the dominant driver of the signal remains open, given the short lifetime of small systems. In this regime, pre-equilibrium dynamics and late stage hadronic interactions are expected to play a significant role. Hence, a beam energy scan of small systems---that amounts to varying the initial temperature and the lifetime of the medium---can provide valuable information to shed light on these issues. In this paper, we present predictions from viscous hydrodynamics (SONIC), partonic (AMPT) and hadronic (UrQMD) cascade calculations for elliptic $v_2$ and triangular $v_3$ anisotropy coefficients in $d$+Au at $\sqrt{s_{NN}}$ = 7.7, 20, 39, 62.4 and 200 GeV, corresponding to the expected running at RHIC in 2016. We also present predictions for $d$+Pb at $\sqrt{s_{NN}}$ = 5.02 TeV, an interesting system to compare to existing $p+$Pb data taken at the LHC.

Production of photons in relativistic heavy-ion collisions

In this work it is shown that the use of a hydrodynamical model of heavy ion collisions which incorporates recent developments, together with updated photon emission rates greatly improves agreement with both ALICE and PHENIX measurements of direct photons, supporting the idea that thermal photons are the dominant source of direct photon momentum anisotropy. The event-by-event hydrodynamical model uses IP-Glasma initial states and includes, for the first time, both shear and bulk viscosities, along with second order couplings between the two viscosities. The effect of both shear and bulk viscosities on the photon rates is studied, and those transport coefficients are shown to have measurable consequences on the photon momentum anisotropy.

Nematic quantum liquid crystals of bosons in frustrated lattices

The problem of interacting bosons in frustrated lattices is an intricate one due to the absence of a unique minimum in the single-particle dispersion where macroscopic number of bosons can condense. Here we consider a family of tight-binding models with macroscopically degenerate lowest energy band, separated from other bands by a gap. We predict the formation of exotic states that spontaneously break rotational symmetry at relatively low filling. These states belong to three nematic phases: Wigner crystal, supersolid, and superfluid. The Wigner crystal phase is established exactly at low filling. Supersolid and superfluid phases, at larger filling, are obtained by making use of a projection onto the flat band, construction of an appropriate Wannier basis, and subsequent mean-field treatment. The nematic superfluid that we predict is uniform in real space but has an anisotropic momentum distribution, providing a novel scenario for Bose condensation with an additional nematic order. Our findings open up a promising direction of studying microscopic quantum liquid crystalline phases of bosons.

On the chiral imbalance and Weibel instabilities

We study the chiral-imbalance and the Weibel instabilities in presence of the quantum anomaly using the Berry-curvature modified kinetic equation. We argue that in many realistic situations, e.g. relativistic heavy-ion collisions, both the instabilities can occur simultaneously. The Weibel instability depends on the momentum anisotropy parameter $\xi$ and the angle ($\theta_n$) between the propagation vector and the anisotropy direction. It has maximum growth rate at $\theta_n=0$ while $\theta_n=\pi/2$ corresponds to a damping. On the other hand the pure chiral-imbalance instability occurs in an isotropic plasma and depends on difference between the chiral chemical potentials of right and left-handed particles. It is shown that when $\theta_n=0$, only for a very small values of the anisotropic parameter $\xi\sim \xi_c$, growth rates of the both instabilities are comparable. For the cases $\xi_c<\xi\ll1$, $\xi\approx 1$ or $\xi \geq 1$ at $\theta_n=0$, the Weibel modes dominate over the chiral-imbalance instability if $\mu_5/T\leq1$. However, when $\mu_5/T\geq1$, it is possible to have dominance of the chiral-imbalance modes at certain values of $\theta_n$ for an arbitrary $\xi$.

Photon production from a nonequilibrium quark-gluon plasma

We calculate leading-order medium photon yields from a quark-gluon plasma using (3+1)-dimensional anisotropic hydrodynamics. Non-equilibrium corrections to the photon rate are taken into account using a self-consistent modification of the particle distribution functions and the corresponding anisotropic hard-loop fermionic self-energies. We present predictions for the high-energy photon spectrum and photon elliptic flow as a function of transverse momentum, shear viscosity, and initial momentum-space anisotropy. Our findings indicate that high-energy photon production is sensitive to the assumed level of initial momentum-space anisotropy of the quark-gluon plasma. As a result, it may be possible to experimentally constrain the early-time momentum-space anisotropy of the quark-gluon plasma generated in relativistic heavy-ion collisions using high-energy photon yields.

Quarkonium dissociation in an anisotropic QGP

We have studied the properties of quarkonium states in an anisotropic quark-gluon plasma (QGP). We address the effects of non-perturbative confining force and momentum anisotropy on the heavy quark potential at finite temperature, which have been resolved by correcting both perturbative and non-perturbative terms of the Cornell potential through the dielectric function in terms of hard-loop resumed gluon propagator in real-time formalism. We have found that the real-part of the potential becomes stronger and thus makes the quarkonia more bound whereas the (magnitude) imaginary-part too becomes larger and thus contribute more to the thermal width, compared to the medium-contribution of the Coulomb term alone. In addition, the presence of anisotropy makes the real-part of the potential stronger but the imaginary-part is weakened slightly. The potential obtained in anisotropic medium is nonspherical. Therefore, we have used the first-order perturbation theory to estimate the shift in energy eigenvalues due to the small anisotropic correction to the energy eigenvalues from the spherically-symmetric part in isotropic medium and determine their dissociation temperatures. The presence of non-perturbative term in the potential results the quarkonia to dissociate at higher temperatures.

Survival rate of initial azimuthal anisotropy in a multiphase transport model

We investigate the survival rate of an initial momentum anisotropy (${v}_2^{ini}$), not spatial anisotropy, to the final state in a multi-phase transport (AMPT) model in Au+Au collisions at $\sqrt{s_{NN}}$=200~GeV. It is found that both the final-state parton and charged hadron $v_2$ show a linear dependence versus $v_2^{ini}\{\rm PP\}$ with respect to the participant plane (PP). It is found that the slope of this linear dependence (referred to as the survive rate) increases with transverse momentum ($p_T$), reaching~$\sim$100\% at $p_T$$\sim$2.5 GeV/c for both parton and charged hadron. The survival rate decreases with collision centrality and energy, indicating decreasing survival rate with increasing interactions. It is further found that a $v_2^{ini}\{\rm Rnd\}$ with respect to a random direction does not survive in $v_2\{\rm PP\}$ but in the two-particle cumulant $v_2\{2\}$. The dependence of $v_2\{2\}$ on $v_2^{ini}\{\rm Rnd\}$ is quadratic rather than linear.

Using spectator distributions to measure the initial geometry fluctuation

A study of eccentricity (εn) fluctuations and its possible impact on final state momentum anisotropy (υn) for symmetric collisions are presented in the framework of Glauber model. Effect of fluctuations of nucleon's position on the initial geometry has been studied using a new method, where the difference between oppositely moving spectators is taken as a measurement of eccentricity fluctuations. This study shows that higher harmonics (n = 3, 4 and 5) of eccentricity are less sensitive to fluctuations in transverse plane compared to the 2nd harmonic. Position fluctuations in transverse plane will increase ε2 and hence possibly υ2 for the most central nucleus–nucleus collisions. For semi-central and peripheral collisions, the fluctuations have opposite effect, it decreases the eccentricity ε2. The fluctuation of initial geometry can be studied in collider experiments by studying the spectator distribution on the both sides of the beam.

Importance of the Bulk Viscosity of QCD in Ultrarelativistic Heavy-Ion Collisions.

We investigate the consequences of a nonzero bulk viscosity coefficient on the transverse momentum spectra, azimuthal momentum anisotropy, and multiplicity of charged hadrons produced in heavy ion collisions at LHC energies. The agreement between a realistic 3D hybrid simulation and the experimentally measured data considerably improves with the addition of a bulk viscosity coefficient for strongly interacting matter. This paves the way for an eventual quantitative determination of several QCD transport coefficients from the experimental heavy ion and hadron-nucleus collision programs.

The breaks and the hidden components in the power-law spectra of synchrotron radiation of the self-consistent current structures

Widespread use of a broken-power-law description of the spectra of synchrotron emission of various plasma objects requires an analysis of origin and a proper interpretation of spectral components. We show that, for a self-consistent magnetic configuration in a collisionless plasma, these components may be angle-dependent according to an anisotropic particle momentum distribution and may have no counterparts in a particle energy distribution. That has never been studied analytically and is in contrast to a usual model of synchrotron radiation, assuming an external magnetic field and a particle ensemble with isotropic momentum distribution. We demonstrate that for the wide intervals of observation angle the power-law spectra and, in particular, the positions and number of spectral breaks may be essentially different for the cases of the self-consistent and not-self-consistent magnetic fields in current structures responsible for the synchrotron radiation of the ensembles of relativistic particles with the multi-power-law energy distributions.

(3 + 1)-dimensional framework for leading-order nonconformal anisotropic hydrodynamics

In this work I develop a new framework for anisotropic hydrodynamics that generalizes the leading order of the hydrodynamic expansion to the full (3+1)-dimensional anisotropic massive case. Following previous works, my considerations are based on the Boltzmann kinetic equation with the collisional term treated in the relaxation time approximation. The momentum anisotropy is included explicitly in the leading term, allowing for a large difference between the longitudinal and transverse pressures as well as for non trivial transverse dynamics. Energy and momentum conservation is expressed by the first moment of the Boltzmann equation. The system of equations is closed by using the zeroth and second moments of the Boltzmann equation. The close-to-equilibrium matching with second-order viscous hydrodynamics is demonstrated. In particular, I show that the coupling between shear and bulk pressure corrections, recently proved to be important for an accurate description of momentum anisotropy and bulk viscous dynamics, does not vanish in the close-to-equilibrium limit.

Anisotropic stellar structure equations for magnetized strange stars

The fact that a fermion system in an external magnetic field breaks the spherical symmetry suggests that its intrinsic geometry is axisymmetric rather than spherical. In this work we analyze the impact of anisotropic pressures, due to the presence of a magnetic field, in the structure equations of a magnetized quark star. We assume a cylindrical metric and an anisotropic energy momentum tensor for the source. We found that there is a maximum magnetic field that a strange star can sustain, closely related to the violation of the virial relations.