Kadanoff-Baym Approach Research Articles

In-medium kinetic theory of D mesons and heavy-flavor transport coefficients

We extend the kinetic theory of $D$ mesons to accommodate thermal and off-shell effects due to the medium modification of the heavy-meson spectral functions. From the Kadanoff-Baym approach we derive the off-shell Fokker-Planck equation which encodes the heavy-flavor transport coefficients. We analyze the thermal width (damping rate) of $D$ mesons due to their scattering off light mesons, focusing on new in-medium effects: off-shell corrections, inelastic channels, and the contribution of the Landau cut. We obtain that the latter effect (absent for vacuum scattering amplitudes) brings sizable corrections at moderate temperatures. We discuss how the heavy-flavor transport coefficients, like the drag and diffusion coefficients, are modified in matter. We find that the $D$-meson spatial diffusion coefficient matches smoothly to the latest results of lattice-QCD calculations and Bayesian analyses at higher temperatures.

Many-body effects in third harmonic generation of graphene

The low-energy (intraband) range of the third harmonic generation of graphene in the terahertz regime is governed by the damping terms induced by the interactions. A controlled many-body description of the scattering processes is thus a compelling and desirable requirement. In this paper, using a Kadanoff-Baym approach, we systematically investigate the impact of many-body interaction on the third-harmonic generation (THG) of graphene, taking elastic impurity scattering as a benchmark example. We predict the onset in the mixed inter-intraband regime of novel incoherent features driven by the interaction at four- and five-photon transition frequencies in the third-harmonic optical conductivity with a spectral weight proportional to the scattering rate.We show also that, in spite of the complex many-body physics, the purely intraband term governing the limit $\omega \to 0$ resembles the constraints of the phenomenological model. We ascribe this agreement to the fulfilling of the conservation laws enforced by the conserving approach. The overlap with novel incoherent features and the impact of many-body driven multi-photon vertex couplings limit however severely the validity of phenomenological description.

Real-time Kadanoff-Baym approach to nuclear response functions

Linear density response functions are calculated for symmetric nuclear matter of normal density by time-evolving two-time Green's functions in real time. Of particular interest is the effect of correlations. The system is therefore initially time-evolved with a collision term calculated in a direct Born approximation until fully correlated. An external time-dependent potential is then applied. The ensuing density fluctuations are recorded to calculate the density response. This method was previously used by Kwong and Bonitz for studying plasma oscillations in a correlated electron gas. The energy-weighted sum-rule for the response function is guaranteed by using conserving self-energy insertions as the method then generates the full vertex-functions. These can alternatively be calculated by solving a Bethe -Salpeter equation as done in works by Bozek et al. The (first order) mean field is derived from a momentum-dependent (non-local) interaction while 2nd order self-energies are calculated using a particle-hole two-body effective (or residual) interaction given by a gaussian local potential.We show results of calculations of the response function S(ɷ,q0) for q0 = 0.2, 0.4 and 0.8fm-1. Comparison is made with the nucleons being un-correlated i.e. with only the first order mean field included.We discuss the relation of our work with the Landau quasi-particle theory as applied to nuclear systems by Babu and Brown and followers.

Many-body Green's function theory for electron-phonon interactions: The Kadanoff-Baym approach to spectral properties of the Holstein dimer.

We present a Kadanoff-Baym formalism to study time-dependent phenomena for systems of interacting electrons and phonons in the framework of many-body perturbation theory. The formalism takes correctly into account effects of the initial preparation of an equilibrium state and allows for an explicit time-dependence of both the electronic and phononic degrees of freedom. The method is applied to investigate the charge neutral and non-neutral excitation spectra of a homogeneous, two-site, two-electron Holstein model. This is an extension of a previous study of the ground state properties in the Hartree (H), partially self-consistent Born (Gd) and fully self-consistent Born (GD) approximations published in Säkkinen et al. [J. Chem. Phys. 143, 234101 (2015)]. Here, the homogeneous ground state solution is shown to become unstable for a sufficiently strong interaction while a symmetry-broken ground state solution is shown to be stable in the Hartree approximation. Signatures of this instability are observed for the partially self-consistent Born approximation but are not found for the fully self-consistent Born approximation. By understanding the stability properties, we are able to study the linear response regime by calculating the density-density response function by time-propagation. This amounts to a solution of the Bethe-Salpeter equation with a sophisticated kernel. The results indicate that none of the approximations is able to describe the response function during or beyond the bipolaronic crossover for the parameters investigated. Overall, we provide an extensive discussion on when the approximations are valid and how they fail to describe the studied exact properties of the chosen model system.

Kadanoff–Baym approach to flavour mixing and oscillations in resonant leptogenesis

We describe a loopwise perturbative truncation scheme for quantum transport equations in the Kadanoff–Baym formalism, which does not necessitate the use of the so-called Kadanoff–Baym or quasi-particle ansaetze for dressed propagators. This truncation scheme is used to study flavour effects in the context of Resonant Leptogenesis (RL), showing explicitly that, in the weakly-resonant regime, there exist two distinct and pertinent flavour effects in the heavy-neutrino sector: (i) the resonant mixing and (ii) the oscillations between different heavy-neutrino flavours. Moreover, we illustrate that Kadanoff–Baym and quasi-particle ansaetze, whilst appropriate for the flavour-singlet dressed charged-lepton and Higgs propagators of the RL scenario, should not be applied to the dressed heavy-neutrino propagators. The use of these approximations for the latter is shown to capture only flavour oscillations, whilst discarding the separate phenomenon of flavour mixing.

Fate of the excitonic insulator in the presence of phonons

The influence of phonons on the formation of the excitonic insulator has hardly been analyzed so far. Recent experiments on $\rm Ta_2NiSe_5$, 1$T$-$\rm TiSe_2$, and $\rm TmSe_{0.45}Te_{0.55}$, being candidates for realizing the excitonic-insulator state, suggest, however, that the underlying lattice plays a significant role. Employing the Kadanoff-Baym approach we address this issue theoretically. We show that owing to the electron-phonon coupling a static lattice distortion may arise at the excitonic instability. Most importantly such a distortion will destroy the acoustic phase mode being present if the electron-hole pairing and condensation is exclusively driven by the Coulomb interaction. The absence of off-diagonal long-range order, when lattice degrees of freedom are involved, challenges that excitons in these materials form a superfluid condensate of Bose particles or Cooper pairs composed of electrons and holes.

Kadanoff-Baym approach to the thermal resonant leptogenesis

Using the non-equilibrium Green function method (Kadanoff-Baym equations) in the expanding universe, we investigate evolution of the lepton number asymmetry when the right-handed (RH) neutrinos have almost degenerate masses $|M_i^2-M_j^2| \ll M_i^2$. The resonantly enhanced $CP$-violating parameter $\varepsilon_i$ associated with the decay of the RH neutrino $N_i$ is obtained. It is proportional to an enhancement factor $(M_i^2-M_j^2) M_i \Gamma_j/ ((M_i^2-M_j^2)^2 +R_{ij}^2)$ with the regulator $R_{ij}=M_i \Gamma_i+M_j \Gamma_j$. The result is consistent with the previous result obtained by Garny et al., in a constant background with an out-of-equilibrium initial state. We discuss the origin of such a regulator, and why it is not like $R_{ij}=M_i \Gamma_i-M_j \Gamma_j$.

Soft gravitational effects in Kadanoff-Baym approach

In de Sitter space, the gravitational fluctuation at the super-horizon scale may make physical quantities time dependent by breaking the de Sitter symmetry. We adopt the Kadanoff-Baym approach to evaluate soft gravitational effects in a matter system at the sub-horizon scale. This investigation proves that only the local terms contribute to the de Sitter symmetry breaking at the one-loop level. The IR singularities in the non-local terms cancel after summing over degenerate states between real and virtual processes. The corresponding IR cut-off is given by the energy resolution like QED. Since the energy resolution is physical and independent of cosmic evolution, the non-local contributions do not induce the de Sitter symmetry breaking. We can confirm that soft gravitational effects preserve the effective Lorentz invariance.

Kadanoff-Baym Approach to Thermalization of Quantum Fields

Numerical results of nonequilibrium field theory are shown for O(N) sealer model in 2+1 dimensions with longitudinal expansion. We adopt Next-to-Leading Order of 1/N expansion of self energy with background classical fields to cover all of time evolution of instability. We show differences between quantum dynamics and classical statistical approximation in strongly coupled regimes. As a result we show that we can achieve Boltzmann tail of the final distribution function only in quantum dynamics.

Leptogenesis from first principles in the resonant regime

The lepton asymmetry generated by the out-of-equilibrium decays of heavy Majorana neutrinos with a quasi-degenerate mass spectrum is resonantly enhanced. In this work, we study this scenario within a first-principle approach. The quantum field theoretical treatment is applicable for mass splittings of the order of the width of the Majorana neutrinos, for which the enhancement is maximally large. The non-equilibrium evolution of the mixing Majorana neutrino fields is described by a formal analytical solution of the Kadanoff–Baym equations, that is obtained by neglecting the back-reaction. Based on this solution, we derive approximate analytical expressions for the generated asymmetry and compare them to the Boltzmann result. We find that the resonant enhancement obtained from the Kadanoff–Baym approach is smaller compared to the Boltzmann approach, due to additional contributions that describe coherent transitions between the Majorana neutrino species. We also discuss corrections to the masses and widths of the degenerate pair of Majorana neutrinos that are relevant for very small mass splitting, and compare the approximate analytical result for the lepton asymmetry with numerical results.

The Kadanoff–Baym approach to double excitations in finite systems

We benchmark many-body perturbation theory by studying neutral, as well as non-neutral, excitations of finite lattice systems. The neutral excitation spectra are obtained by time-propagating the Kadanoff–Baym equations in the Hartree–Fock and the second Born approximations. Our method is equivalent to solving the Bethe–Salpeter equation with a high-level kernel while respecting self-consistency, which guarantees the fulfillment of a frequency sum rule. As a result, we find that a time-local method, such as Hartree–Fock, can give incomplete spectra, while already the second Born approximation, which is the simplest time-non-local approximation, reproduces well most of the additional excitations, which are characterized as double excitations.

Kadanoff-Baym Approach to Thermalization of Gluonic Matter

Kadanoff-Baym Approach to Thermalization of Gluonic Matter

Kadanoff-Baym Approach to Entropy Production in O(N) Theory with Next-to-Leading Order Self-Energy

Abstract We investigate entropy production in the O(N) scalar theory using the Kadanoff-Baym equation. We show that one of the candidate expressions of the kinetic entropy satisfies the H-theorem in the first order of the gradient expansion with the next-to-leading-order self-energy of the 1/N expansion in the symmetric phase, and that entropy production occurs as the Green's function evolves with nonzero collision term contributions. Entropy production stops at local thermal equilibrium where the collision term contribution vanishes and the maximal entropy state is realized. We numerically examine these features of entropy production in thermalization processes in 1+1 dimensions for a couple of homogeneous cases, where the thermalization can proceed only with the off-shell effects. We find that the entropy production rate γ is larger for smaller N and is found to follow γ ∝ (1/N)ν where δ ≳ 2 at strong coupling measured in the unit of bare mass (m), ⋋= 40 m2.

Kadanoff-Baym Approach to Entropy Production inO(N) Theory with Next-to-Leading Order Self-Energy

Left in a dry. atmosphere for a while, gels become glasslike dehydrated substances. We investigated the dehydration process of some gels by adopting simultaneous time-resolved measuring method of weight and other properties. The feature during the dehydration process was different depending on the properties of the network and solvent in gel. Besides, in the DTA measurements of the dehydrated egg white gel, we observed an endothermic peak of which the intensity and peak position increased with elevating heating rate, similar to the glass transition in the non-crystalline polymers.

Kadanoff-Baym approach to time-dependent quantum transport in AC and DC fields

We have developed a method based on the embedded Kadanoff-Baym equations to study the time evolution of open and inhomogeneous systems. The equation of motion for the Green's function on the Keldysh contour is solved using different conserving many-body approximations for the self-energy. Our formulation incorporates basic conservation laws, such as particle conservation, and includes both initial correlations and initial embedding effects, without restrictions on the time-dependence of the external driving field. We present results for the time-dependent density, current and dipole moment for a correlated tight binding chain connected to one-dimensional non-interacting leads exposed to DC and AC biases of various forms. We find that the self-consistent 2B and GW approximations are in extremely good agreement with each other at all times, for the long-range interactions that we consider. In the DC case we show that the oscillations in the transients can be understood from interchain and lead-chain transitions in the system and find that the dominant frequency corresponds to the HOMO-LUMO transition of the central wire. For AC biases with odd inversion symmetry odd harmonics to high harmonic order in the driving frequency are observed in the dipole moment, whereas for asymmetric applied bias also even harmonics have considerable intensity. In both cases we find that the HOMO-LUMO transition strongly mixes with the harmonics leading to harmonic peaks with enhanced intensity at the HOMO-LUMO transition energy.

Entropy production in 2D [formula omitted] theory in the Kadanoff–Baym approach

We study non-equilibrium quantum dynamics of the single-component scalar field theory in 1 + 1 space–time dimensions on the basis of the Kadanoff–Baym equation including the next-to-leading-order (NLO) skeleton diagrams. As an extension of the non-relativistic case, we derive relativistic kinetic entropy at the first order in the gradient expansion of the Kadanoff–Baym equations. The derived entropy satisfies the H-theorem. Next we perform numerical simulations in spatially homogeneous configurations to investigate thermalization properties of the system by evaluating the system entropy. We find that at later times the kinetic entropy increases approaching the equilibrium value, although the limited time interval in the early stage invalidates the use of it.

Kadanoff-Baym approach to quantum transport through interacting nanoscale systems: From the transient to the steady-state regime

We propose a time-dependent many-body approach to study the short-time dynamics of correlated electrons in quantum transport through nanoscale systems contacted to metallic leads. This approach is based on the time-propagation of the Kadanoff-Baym equations for the nonequilibrium many-body Green's function of open and interacting systems out of equilibrium. An important feature of the method is that it takes full account of electronic correlations and embedding effects in the presence of time-dependent external fields, while at the same time satisfying the charge conservation law. The method further extends the Meir-Wingreen formula to the time domain for initially correlated states. We study the electron dynamics of a correlated quantum wire attached to two-dimensional leads exposed to a sudden switch-on of a bias voltage using conserving many-body approximations at Hartree-Fock, second Born and GW level. We obtain detailed results for the transient currents, dipole moments, spectral functions, charging times, and the many-body screening of the quantum wire as well as for the time-dependent density pattern in the leads, and we show how the time-dependence of these observables provides a wealth of information on the level structure of the quantum wire out of equilibrium. For moderate interaction strenghts the 2B and GW results are in excellent agreement at all times. We find that many-body effects beyond the Hartree-Fock approximation have a large effect on the qualitative behavior of the system and lead to a bias dependent gap closing and quasiparticle broadening, shortening of the transient times and washing out of the step features in the current-voltage curves.

Real-time kadanoff-baym approach to plasma oscillations in a correlated electron Gas

A nonequilibrium Green's functions approach to the collective response of correlated Coulomb systems at finite temperatures is presented. It is shown that solving Kadanoff-Baym-type equations of motion for the two-time correlation functions including the external perturbing field allows one to compute the plasmon spectrum with collision effects in a systematic and consistent way. The scheme has a "built-in" sum-rule preservation and is simpler to implement numerically than the equivalent equilibrium approach based on the Bethe-Salpeter equation.