Momentum Distribution Function Research Articles

Thermal Goldstino production with low reheating temperatures

We discuss thermal production of (pseudo) goldstinos, the Goldstone fermions emerging from (multiple) SUSY breaking sectors, when the reheating temperature is well below the superpartner masses. In such a case, the production during matter-dominated era induced by inflaton decay stage is more important than after reheating. Depending on the SUSY breaking scale, goldstinos are produced by freeze-in or freeze-out mechanism via $1\to 2$ decays and inverse decays. We solve the Boltzmann equation for the momentum distribution function of the goldstino.In the freeze-out case, goldstinos maintain chemical equilibrium far after they are kinetically decoupled from the thermal bath, and consequently goldstinos with different momentum decouple at different temperatures. As a result their momentum distribution function shows a peculiar shape and the final yield is smaller than if kinetic equilibrium was assumed. We revisit the cosmological implications in both R-parity-conserving and R-parity-violating supersymmetric scenarios. For the former, thermally produced goldstinos can still be abundant enough to be dark matter at present times even if the reheating temperature is low, of order $1$ GeV. For the latter, if the reheating temperature is low, of order $0.1-1$ GeV, they are safe from the BBN constraints.

KeV sterile neutrino dark matter from singlet scalar decays: basic concepts and subtle features

We perform a detailed and illustrative study of the production of keV sterile neutrino Dark Matter (DM) by decays of singlet scalars in the early Universe. In the current study we focus on providing a clear and general overview of this production mechanism. For the first time we study all regimes possible on the level of momentum distribution functions, which we obtain by solving a system of Boltzmann equations. These quantities contain the full information about the production process, which allows us to not only track the evolution of the DM generation but to also take into account all bounds related to the spectrum, such as constraints from structure formation or from avoiding too much dark radiation. In particular we show that this simple production mechanism can, depending on the regime, lead to strongly non-thermal DM spectra which may even feature more than one peak in the momentum distribution. These cases could have particularly interesting consequences for cosmological structure formation, as their analysis requires more refined tools than the simplistic estimate using the free-streaming horizon. Here we present the mechanism including all concepts and subtleties involved, for now using the assumption that the effective number of relativistic degrees of freedom is constant during DM production, which is applicable in a significant fraction of the parameter space. This allows us to derive analytical results to back up our detailed numerical computations, thus leading to the most comprehensive picture of keV sterile neutrino DM production by singlet scalar decays that exists up to now.

Interaction quantum quenches in the one-dimensional Fermi-Hubbard model with spin imbalance

Using the time-dependent density matrix renormalization group method and exact diagonalization, we study the non-equilibrium dynamics of the one-dimensional Fermi-Hubbard model following a quantum quench or a ramp of the onsite interaction strength. For quenches from the non-interacting to the attractive regime, we investigate the dynamical emergence of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) correlations, which at finite spin polarizations are the dominant two-body correlations in the ground state, and their signatures in the pair quasi-momentum distribution function. We observe that the post-quench double occupancy exhibits a maximum as the interaction strength becomes of the order of the bandwidth. Finally, we study quenches and ramps from attractive to repulsive interactions, which imprint FFLO correlations onto repulsively bound pairs. We show that a quite short ramp time is sufficient to wipe out the characteristic FFLO features in the post-quench pair momentum distribution functions.

Modern studies of the Deuteron: From the lab frame to the light front

We review the recent progress made in studies of deuteron structure at small internucleon distances. This progress is largely facilitated by the new generation of experiments in deuteron electrodisintegration carried out at unprecedentedly high momentum transfer. The theoretical analysis of these data confirms the onset of the high energy eikonal regime in the scattering process which allows one to separate long-range nuclear effects from the effects genuinely related to the short distance structure of the deuteron. Our conclusion is that for the first time the deuteron is probed at relative momenta beyond 300 MeV/c without dominating long-range effects. As a result, at these large nucleon momenta the cross-section is sensitive to the nuclear dynamics at subfermi distances. Due to large internal momenta involved we are dealing with the relativistic bound state that is best described by the light-cone momentum distribution of nucleons in the deuteron. We present the first attempt of extracting the deuteron light-cone momentum distribution function from data and discuss the importance of this quantity for studies of quantum chromodynamics (QCD) structure of the bound nucleon in deep inelastic scattering (DIS) off the deuteron. We conclude the review giving an outlook of the next generation of high energy experiments which will extend our reach to much smaller distances in the deuteron.

Propagation and Generation of Electromagnetic Waves at Proton Gyrofrequencies in a Relativistic Electron–Positron Plasma. I. Low-Frequency Weakly Damped Electromagnetic Waves

We consider the dispersion characteristics of electromagnetic waves in a plasma with strong magnetic field and equal content of relativistic electrons and positrons, whose synchrotron radiation can be the source of optical radiation of a pulsar. It is shown that when a small fraction of nonrelativistic protons with a nonequilibrium distribution function is present in the plasma, an effective instability can develop at frequencies below the first harmonic of the relativistic gyrofrequency of electrons, namely, at the harmonics of the proton gyrofrequency. This instability leads to the excitation of the O- and X-mode electromagnetic waves, which can, in principle, be related with the observed pulsar radiation. In part I of this paper, we study dispersion characteristics of low-frequency electromagnetic waves (with frequencies below the relativistic gyrofrequency of electrons) in an ultrarelativistic electron–positron plasma with an isotropic momentum distribution function of the particles. Instabilities of the O- and X-mode waves and the conditions of escape of the radiation from the region of strong magnetic field into a rarefied isotropic plasma will be considered in paper II. The results can be used in the interpretation of known experimental data on the dynamic pulsar radiation spectra obtained with high temporal and frequency resolution.

Photon emission from a momentum-anisotropic quark-gluon plasma

We compute the photon emission rate from a quark-gluon plasma with an anisotropic particle momentum distribution induced by a non-vanishing local shear pressure tensor. Our calculation includes photon production through Compton scattering and quark-antiquark annihilation at leading order in $\alpha_s$, with all off-equilibrium corrections to leading order in the momentum anisotropy. For fermions we prove that the Kubo-Martin-Schwinger (KMS) relation holds in the hard loop regime for any particle momentum distribution function that is reflection-symmetric. This supports the equivalence, for 2 to 2 scattering processes, of the diagrammatic and kinetic approaches to calculating the photon emission rate. We compare the viscous rates from these two approaches at weak and realistic coupling strengths and provide parameterizations of the equilibrium and viscous photon emission rates for phenomenological studies in relativistic heavy-ion collisions.

Interaction quench in the Holstein model: Thermalization crossover from electron- to phonon-dominated relaxation

We study the relaxation of the Holstein model after a sudden switch-on of the interaction by means of the nonequilibrium dynamical mean field theory, with the self-consistent Migdal approximation as an impurity solver. We show that there exists a qualitative change in the thermalization dynamics as the interaction is varied in the weak-coupling regime. On the weaker interaction side of this crossover, the phonon oscillations are damped more rapidly than the electron thermalization timescale, as determined from the relaxation of the electron momentum distribution function. On the stronger interaction side, the relaxation of the electrons becomes faster than the phonon damping. In this regime, despite long-lived phonon oscillations, a thermalized momentum distribution is realized temporarily. The origin of the thermalization crossover found here is traced back to different behaviors of the electron and phonon self-energies as a function of the electron-phonon coupling. In addition, the importance of the phonon dynamics is demonstrated by comparing the self-consistent Migdal results with those obtained with a simpler Hatree-Fock impurity solver that neglects the phonon self-energy. The latter scheme does not properly describe the evolution and thermalization of isolated electron-phonon systems.

Itinerant-Localized Transitions in Magnetic Phases of the Periodic Anderson Model

To clarify the characteristics of Fermi-surface reconstruction, called Lifshitz transitions, in magnetic phases of f-electron materials, we investigate magnetically ordered states of the periodic Anderson model by applying the variational Monte Carlo method. As variational wavefunctions, we use the Gutzwiller wavefunctions for the paramagnetic, antiferromagnetic, and ferromagnetic states. Around half-filling, we find an antiferromagnetic phase, and far away from half-filling, we find a ferromagnetic phase as the ground state. Inside both magnetic phases, Lifshitz transitions take place. At the Lifshitz transitions, the sizes of the ordered moments change. In order to understand the Lifshitz transitions further, we also analyze the f -electron contribution to the Fermi surface by evaluating the jump in the momentum distribution function at the Fermi momentum. Then, we find that, in the large ordered-moment states, the f -electron contribution to the Fermi surface becomes small. This observation clearly shows that these Lifshitz transitions are itinerant-localized transitions of the f electrons.

Effects of Diagonal Hopping on Stability of Antiferromagnetic State

Intrinsic stability as to phase separation of an antiferromagnetic state is studied for a strongly correlated Hubbard model with frustration (t-t’-U model) near half filling, using a variational Monte Carlo method. In the Hartree-Fock (one-body) part of the many-body trial state, band-renormalization effect, which is necessary for partly recovering the nesting condition, is introduced up to three-step hopping distance. As a result, a doped AF state for ▪ has a low energy but is unstable toward phase separation, which is consistent with previous studies. In contrast, the AF state becomes stable against phase separation for ▪, owing to the contribution of hopping energy in diagonal directions. The doped AF states are metallic for the two values of ▪, but exhibit contrastive behavior in the momentum distribution function in the nodal and antinodal regions.

Correlation functions and momentum distribution of one-dimensional hard-core anyons in optical lattices

We address the problem of calculating the correlation functions in a system of one-dimensional hard-core anyons that can be experimentally realized in optical lattices. Using the summation of form factors we have obtained Fredholm determinant representations for the time-, space-, and temperature-dependent Green's functions which are particularly suited to numerical investigations. In the static case we have also derived the large distance asymptotic behavior of the correlators and computed the momentum distribution function at zero and finite temperature. We present extensive numerical results highlighting the characteristic features of one-dimensional systems with fractional statistics.

Vlasov equation for Schwinger pair production in a time-dependent electric field

Schwinger pair creation in a purely time-dependent electric field can be described through a quantum Vlasov equation describing the time evolution of the single-particle momentum distribution function. This equation exists in two versions, both of which can be derived by a Bogoliubov transformation, but whose equivalence is not obvious. For the spinless case, we show here that the difference between these two evolution equations corresponds to the one between the "in-out" and "in-in" formalisms. We give a simple relation between the asymptotic distribution functions generated by the two Vlasov equations. As examples we discuss the Sauter and single-soliton field cases.

Equations of Motion for the Out-of-Equilibrium Dynamics of Isolated Quantum Systems from the Projection Operator Technique

We present a rigorous framework to obtain evolution equations for the momentum distribution and higher order correlation functions in weakly interacting systems based on the Projection Operator Technique. These equations can be numerically solved in an efficient way. We compare the solution of the equations with known results for 1D models and find an excellent agreement.

Quantum corrections to the momentum distribution in a laser plasma

The evolution of the momentum distribution of particles in a nonrelativistic laser plasma is studied in the context of the kinetic theory of plasma based on the construction of propagators for the plasma particle distribution functions. Damping of plasma waves and induced braking absorption accelerate particles in a plasma. Quantum indeterminacy in energy, which is associated with the interaction of particles with plasma waves and their collisions with one another, also affects their momentum distribution. In the semiclassical approximation, general analytic expressions are obtained for the momentum distribution functions.

Dynamics of correlations in a quasi-two-dimensional dipolar Bose gas following a quantum quench

We study the evolution of correlations in a quasi-2D dipolar gas driven out-of-equilibrium by a sudden ramp of the interaction strength. For sufficiently strong ramps, the momentum distribution, excited fraction and density-density correlation function all display pronounced features that are directly related to the appearance of a roton minimum in the underlying spectrum. Our study suggests that the evolution of correlations following a quench can be used as a probe of roton-like excitations in a dipolar gas. We also find that the build up of density-density correlations following a quench occurs much more slowly in the dipolar gas compared to a non-dipolar gas, owing to the long-range interactions.

Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit

Motivated by recent experiments, we study the relaxation dynamics and thermalization in the one-dimensional Bose-Hubbard model induced by a global interaction quench. Specifically, we start from an initial state that has exactly one boson per site and is the ground state of a system with infinitely strong repulsive interactions at unit filling. Using exact diagonalization and the density matrix renormalization group method, we compute the time dependence of such observables as the multiple occupancy and the momentum distribution function. Typically, the relaxation to stationary values occurs over just a few tunneling times. The stationary values are identical to the so-called diagonal ensemble on the system sizes accessible to our numerical methods and we further observe that the micro-canonical ensemble describes the steady state of many observables reasonably well for small and intermediate interaction strength. The expectation values of observables in the canonical ensemble agree quantitatively with the time averages obtained from the quench at small interaction strengths, and qualitatively provide a good description of steady-state values even in parameter regimes where the micro-canonical ensemble is not applicable due to finite-size effects. We discuss our numerical results in the framework of the eigenstate thermalization hypothesis. Moreover, we also observe that the diagonal and the canonical ensemble are practically identical for our initial conditions already on the level of their respective energy distributions for small interaction strengths. Finally, we discuss implications of our results for the interpretation of a recent sudden expansion experiment [Phys. Rev. Lett. 110, 205301 (2013)], in which the same interaction quench was realized.

Daughters mimic sterile neutrinos (almost!) perfectly

Since only recently, cosmological observations are sensitive to hot dark matter (HDM) admixtures with sub-eV mass, mhdmeff < eV, that are not fully-thermalised, Δ Neff < 1. We argue that their almost automatic interpretation as a sterile neutrino species is neither from theoretical nor practical parsimony principles preferred over HDM formed by decay products (daughters) of an out-of-equilibrium particle decay. While daughters mimic sterile neutrinos in Neff and mhdmeff, there are opportunities to assess this possibility in likelihood analyses. Connecting cosmological parameters and moments of momentum distribution functions, we show that—also in the case of mass-degenerate daughters with indistinguishable main physical effects—the mimicry breaks down when the next moment, the skewness, is considered. Predicted differences of order one in the root-mean-squares of absolute momenta are too small for current sensitivities.

COM(3p) Solution of the 2D Hubbard Model: Momentum-Resolved Quantities

Recently, within the framework of the Composite Operator Method, it has been proposed a three-pole solution for the two-dimensional Hubbard model [Eur. Phys. J. B 87, 45 (2014)], which is still considered one of the best candidate model to microscopically describe high-$T_{c}$ cuprate superconductors. The operatorial basis comprise the two Hubbard operators (complete fermionic local basis) and the electronic operator dressed by the nearest-neighbor spin fluctuations. The effectiveness of the approximate solution has been proved through a positive comparison with different numerical methods for various quantities. In this article, after recollecting the main analytical expressions defining the solution and the behavior of basic local quantities (double occupancy and chemical potential) and of the quasi-particle energy dispersions, we resolve and analyze the momentum components of relevant quantities: filling (i.e. the momentum distribution function), double occupancy and nearest-neighbor spin correlation function. The analysis is extended to COM(2p) solutions that will be used as primary reference. Thanks to this, the role played by the third field, with respect to the two Hubbard ones, in determining the behavior of many relevant quantities and in allowing the extremely good comparison with numerical results is better understood giving a guideline to further improve and, possibly, optimize the application of the COM to the Hubbard model.

Linked-cluster expansion for the Green's function of the infinite-U Hubbard model.

We implement a highly efficient strong-coupling expansion for the Green's function of the Hubbard model. In the limit of extreme correlations, where the onsite interaction is infinite, the evaluation of diagrams simplifies dramatically enabling us to carry out the expansion to the eighth order in powers of the hopping amplitude. We compute the finite-temperature Green's function analytically in the momentum and Matsubara frequency space as a function of the electron density. Employing Padé approximations, we study the equation of state, Kelvin thermopower, momentum distribution function, quasiparticle fraction, and quasiparticle lifetime of the system at temperatures lower than, or of the order of, the hopping amplitude. We also discuss several different approaches for obtaining the spectral functions through analytic continuation of the imaginary frequency Green's function, and show results for the system near half filling. We benchmark our results for the equation of state against those obtained from a numerical linked-cluster expansion carried out to the eleventh order.

Leptonic decays of vector mesons in a power-law potential model of independent quarks

A relativistic power-law potential model of independent quarks is used to study the leptonic decays of neutral vector mesons. Here, the transition probability amplitude for leptonic decay of meson is determined from the momentum distribution function which is found from the assumption of a strong correlation existing between the momenta of quark and antiquark inside the meson. The model parameters are first determined from the application of the model to study the ground state spectra of ρ, ω, ϕ, ψ and ϒ mesons together with the radiative decay widths of mesons. The same model with no adjustable parameters is then used to evaluate the leptonic decay widths and the electromagnetic decay constants for the vector mesons ρ, ω, ϕ, ψ and ϒ. The calculated results are in remarkable agreement with the corresponding experimental values.

Transversity distribution functions in the valon model

By using the valon model, we calculate the Transverse Momentum Distribution functions, TMDs, inside the Nucleon. TMDs indicate the probability to find partons with spin aligned (anti- aligned) to the transversely polarized nucleon. The results are in good agreements with all available experimental data and also global fits.