Quantum Kinetic Equation Research Articles

Conductivity Tensor in Cylindrical Quantum Wire with Parabolic Potential for the Case of Electron-Acoustic Phonon Scattering

Conductivity tensor is an important concept in materials, this work studies conductivity tensors in cylindrical quantum wires with parabolic potential in the presence of two external fields, a linearly polarized electromagnetic wave, and a laser field. This work is also only considered for the case of electron-acoustic phonon scattering. Research results are obtained by using quantum kinetic equations for the carrier system in a quantum wire. The conductivity tensor is calculated by solving the quantum kinetic equation of the system, which is a function of the external field frequency, the external field amplitude, the temperature of the helium, and parameters specific to the quantum wire. Results will also be examined and plotted for quantum wire GaAs / GaAsAl.

Boltzmann and Poincaré Entropy, Boltzmann Extremals, and Hamilton–Jacobi Method for Non-Hamiltonian Situation

In this paper, we prove the H-theorem for generalized chemical kinetics equations. We consider the following important physical examples of such a generalization: discrete models of quantum kinetic equations (Uehling–Uhlenbeck equations) and a quantum Markov process (quantum random walk). We prove that time means coincide with Boltzmann extremals for all such equations and for the Liouville equation as well. This gives us an approach to select the action–angle variables in the Hamilton–Jacobi method for the non-Hamiltonian situation. We propose a simple derivation of the Hamilton–Jacobi equation from the Liouville equations in the finite-dimensional case.

Quantum Kinetic Equation for Fermionic Fluids and Chiral Kinetic Theory

We first review how one can establish the quantum kinetic equation for fluids of spin-1/2 particles. Then we present the construction of the semiclassical relativistic chiral kinetic equation of the fluid in the presence of the external electromagnetic fields. We derive the resulting nonrelativistic chiral kinetic theory. We calculated the particle number current density and showed that chiral effects are correctly generated. Moreover, it satisfies the anomalous continuity equation.

One-dimensional cylindrical quantum wire: The theoretical study of photo-stimulated Ettingshausen effect

Based on the quantum kinetic equation (QKE) for electron, we have theoretically studied the theory of photo-stimulated Ettingshausen effect in a one-dimensional cylindrical quantum wire (CQW). The strong electromagnetic wave (EMW) [Formula: see text] plays a role as photo-stimulation source. We obtain the analytic expressions for the kinetic tensors [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and the Ettingshausen coefficient (EC) in the CQW with the dependence on the amplitude and the energy of EMW, the CQW radius, the magnetic field and the temperature for two cases: optical phonon and acoustic phonon. The results are numerically evaluated and graphed for GaAs/AlGaAs CQW model. It is shown that we observe the cyclotron resonance and magneto-phonon resonance effect while surveying EC in terms of magnetic field (with and without EMW) and EMW energy, considered the electron-optical phonon scattering. In case of electron-acoustic phonon scattering, the oscillation of EC is obtained with the transition between low Landau levels (LLs). We also clarify the impact of quantum size effect (QSE) on EC by surveying the influence of EC on the radius of CQW.

Resistivity Minimum in Beryllium Films

In the analysis of the resistivity of metals, the classical Boltzmann transport equation fails in the condition that the thermal phonon wavelength is larger than the electron mean free path (called the non‐Boltzmann transport regime), and a quantum kinetic equation must be solved. In such a case, the interference between electron−phonon and electron−impurity scattering (electron−phonon−impurity interference effect) should be considered. Herein, the electrical transport properties of Be films grown via direct current magnetron sputtering are studied. Due to the high Debye temperatures and high impurity/defect concentrations of the Be films, the thermal phonon wavelength is larger than the electron mean free path, indicating the non‐Boltzmann transport. The significant resistivity correction from the electron−phonon−impurity interference effect should be observed in the Be films. In the temperature dependence of the resistivity of the Be films, a resistivity minimum near 90 K is observed. After subtracting the contributions of electron−electron and electron−phonon interactions, the electron−phonon−impurity interference‐contributed resistivity is obtained, which increases with temperature like . The signature of the resistivity contribution from electron−phonon−impurity interference effect is observed in the non‐Boltzmann transport regime.

Neutrino Transport with the Monte Carlo Method. II. Quantum Kinetic Equations

Abstract Neutrinos have a unique quantum feature as flavor conversions. Recent studies suggested that collective neutrino oscillations play important roles in high-energy astrophysical phenomena. The quantum kinetic equation (QKE) is capable of describing the neutrino flavor conversion, transport, and matter collision self-consistently. However, we have experienced many technical difficulties in their numerical implementation. In this paper, we present a new QKE solver based on a Monte Carlo (MC) approach. This is an upgraded version of our classical MC neutrino transport solver; in essence, a flavor degree of freedom including mixing state is added into each MC particle. This extension requires updating numerical treatments of collision terms, in particular for scattering processes. We deal with the technical problem by generating a new MC particle at each scattering event. To reduce statistical noise inherent in MC methods, we develop the effective mean free path method. This suppresses a sudden change of flavor state due to collisions without increasing the number of MC particles. We present a suite of code tests to validate these new modules with comparison to the results reported in previous studies. Our QKE-MC solver is developed with fundamentally different philosophy and design from other deterministic and mesh methods, suggesting that it will be complementary to others and potentially provide new insights into physical processes of neutrino dynamics.

Quantum-mechanical model of dielectric losses in nanometer layers of solid dielectrics with hydrogen bonds at ultra-low temperatures

Upon based the finite difference methods construct the solutions for Liouville quantum kinetic equation linearized by the external field, in complex with the stationary Schrodinger equation and the Poisson operator equation, for an ensemble of non-interacting hydrogen ions (protons) migrating in the field of a crystal lattice perturbed by a variable polarizing field. The influence of the phonon subsystem is not taken into account. The equilibrium (non-balanced) proton density matrix is calculated using quantum Boltzmann statistics. The temperature spectra of dielectric losses tangent angle for hydrogen bonded crystals (HBC) in a wide temperature range (50–550 K) are calculated. At the theoretical level detected the effects of nano-crystalline states (1–10 nm) during the polarization of HBC in the region of ultra-low temperatures (4–25 K).

Indirect momentum excitation of graphene using high transversal modes of light in hyperbolic media.

Electrons in indirect semiconductors can optically transit between the valance and conduction band edges only when the momentum conservation is satisfied with help of a third quasi-particle, such as a phonon. In this report, we theoretically demonstrate that indirect interband transition of graphene electrons can be optically enabled only by light with highly enhanced transversal modes, which can be generated by scattering of point dipole radiation with periodic metal slits fabricated in a natural hyperbolic material. The light-matter interaction for graphene electrons is reformulated by using indirect transition matrix elements, and interband polarizations of graphene are obtained by solving quantum kinetic equations of motion in the semi-classical regime. The interband optical current density of graphene as a function of the polarization angle of the incident field shows clear hexagonal response to the high transversal modes of light, which results from the low dependence on dephasing rate and dominance of the indirect polarizations over the direct interband contributions.

Generalization of the Gross–Pitaevskii equation for multi-particle cases

A new method is proposed to obtain Gross–Pitaevskii equation by the chain of Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) quantum kinetic equations. In that sense, we investigate the dynamics of a quantum system including infinite number of identical particles which interact via a (special) pair potential on the form of Dirac delta-function.

Quantum kinetic equation for fluids of spin-1/2 fermions

Fluid of spin-1/2 fermions is represented by a complex scalar field and a four-vector field coupled both to the scalar and the Dirac fields. We present the underlying action and show that the resulting equations of motion are identical to the (hydrodynamic) Euler equations in the presence of Coriolis force. As a consequence of the gauge invariances of this action we established the quantum kinetic equation which takes account of noninertial properties of the fluid in the presence of electromagnetic fields. The equations of the field components of Wigner function in Clifford algebra basis are employed to construct new semiclassical covariant kinetic equations of the vector and axial-vector field components for massless as well as massive fermions. Nonrelativistic limit of the chiral kinetic equation is studied and shown that it generates a novel three-dimensional transport theory which does not depend on spatial variables explicitly and possesses a Coriolis force term. We demonstrated that the three-dimensional chiral transport equations are consistent with the chiral anomaly. For massive fermions the three-dimensional kinetic transport theory generated by the new covariant kinetic equations is established in small mass limit. It possesses the Coriolis force and the massless limit can be obtained directly.

Saturable absorption and nonlinear refraction in free-standing carbon nanotube film: Theory and experiment

The nonlinear absorption and refraction of free-standing films made of single-walled carbon nanotubes (SWNTs) have been investigated experimentally and theoretically. By solving the quantum kinetic equations that take into account both the intra- and interband transitions, we obtain the analytical expression for the SWNT nonlinear conductivity. The nonlinear absorption coefficient and saturation intensity of the film comprising randomly orientated SWNTs have been calculated in a broad spectral range spanning over M11, S11, and S22 absorption bands. The effects of the laser pulse duration and dynamic Burstein−Moss shift on the saturation intensity have been revealed. We demonstrate in the experiment that, under irradiation with femtosecond laser pulses, the absorption modulation depth of SWNT film at resonance wavelength 1375 nm is as high as 30%. The observed saturation intensity minimum is red-shifted with respect to the absorption maximum due to the dynamic Burstein−Moss shift. The saturation intensity within the S22 band is 26−fold lower than that out of the band at 795 nm. The closed-aperture z-scan measurements reveal the negative nonlinear refractive index n2 = −3.1 × 10−12 cm2/W at 795 nm.

The influence of Fermi surface anisotropy and the charge carrier surface scattering kinetics on the electrical conductivity of a thin metal film in the view of the quantum size effect

The electrical conductivity of a thin metal film in an alternating electric field is calculated considering the quantum size effect. The Fermi surface of the metal has the shape of an ellipsoid of rotation, the main axis of which is parallel to the plane of the film. The quantum kinetic equation obtained from the von Neumann equation (the Liouville quantum equation) is solved. The Soffer model is used as the boundary conditions for the distribution function. The dependence of the electrical conductivity on the film thickness is analyzed. A comparison is made with experimental data on the electrical conductivity of bismuth thin films.

Theory of spin–charge-coupled transport in proximitized graphene: an SO(5) algebraic approach

Establishing the conditions under which orbital, spin and lattice-pseudospin degrees of freedom are mutually coupled in realistic nonequilibrium conditions is a major goal in the emergent field of graphene spintronics. Here, we use linear-response theory to obtain a unified microscopic description of spin dynamics and coupled spin–charge transport in graphene with an interface-induced Bychkov–Rashba effect. Our method makes use of an SO(5) extension of the familiar inverse-diffuson approach to obtain a quantum kinetic equation for the single-particle density matrix that treats spin and pseudospin on equal footing and is valid for arbitrary external perturbations. As an application of the formalism, we derive a complete set of drift–diffusion equations for proximitized graphene with scalar impurities in the presence of electric and spin-injection fields which vary slowly in space and time. Our approach is amenable to a wide variety of generalizations, including the study of coupled spin–charge dynamics in layered materials with strong spin–valley coupling and spin–orbit torques in van der Waals heterostructures.

Shear-Induced Spin Polarization in Heavy-Ion Collisions.

We study the spin polarization generated by the hydrodynamic gradients. In addition to the widely studied thermal vorticity effects, we identify an undiscovered contribution from the fluid shear. This shear-induced polarization (SIP) can be viewed as the fluid analog of strain-induced polarization observed in elastic and nematic materials. We obtain the explicit expression for SIP using the quantum kinetic equation and linear response theory. Based on a realistic hydrodynamic model, we compute the differential spin polarization along both the beam direction z[over ^] and the out-plane direction y[over ^] in noncentral heavy-ion collisions at sqrt[s_{NN}]=200 GeV, including both SIP and thermal vorticity effects. We find that SIP contribution always shows the same azimuthal angle dependence as experimental data and competes with thermal vorticity effects. In the scenario that Λ inherits and memorizes the spin polarization of a strange quark, SIP wins the competition, and the resulting azimuthal angle dependent spin polarization P_{y} and P_{z} agree qualitatively with the experimental data.

Reconciling resonant leptogenesis and baryogenesis via neutrino oscillations

Right-handed neutrinos offer an elegant solution to two well established phenomena beyond the Standard Model (SM) - masses and oscillations of neutrinos, as well as the baryon asymmetry of the Universe. It is also a minimalistic solution since it requires only singlet Majorana fermions to be added to the SM particle content. If these fermions are nearly degenerate, the mass scale of right-handed neutrinos can be very low and accessible by the present and planned experiments. There are at least two well studied mechanisms of the low-scale leptogenesis: baryogenesis via oscillations and resonant leptogenesis. These two mechanisms were often considered separate, but they can in fact be understood as two different regimes of one and the same mechanism, described by a unique set of quantum kinetic equations. In this work we show, using a unified description based on quantum kinetic equations, that the parameter space of these two regimes of low-scale leptogenesis significantly overlap. We present a comprehensive study of the parameter space of the low-scale leptogenesis with the mass scale ranging from $0.1$ GeV to $\sim 10^6$ GeV. The unified perspective of this work reveals the synergy between intensity and energy frontiers in the quest for heavy Majorana neutrinos.

Flavour mixing transport theory and resonant leptogenesis

We derive non-equilibrium quantum transport equations for flavour-mixing fermions. We develop the formalism mostly in the context of resonant leptogenesis with two mixing Majorana fermions and one lepton flavour, but our master equations are valid more generally in homogeneous and isotropic systems. We give a hierarchy of quantum kinetic equations, valid at different approximations, that can accommodate helicity and arbitrary mass differences. In the mass-degenerate limit the equations take the familiar form of density matrix equations. We also derive the semiclassical Boltzmann limit of our equations, including the CP-violating source, whose regulator corresponds to the flavour coherence damping rate. Boltzmann equations are accurate and insensitive to the particular form of the regulator in the weakly resonant case ∆m » Γ, but for ∆m ≲ Γ they are qualitatively correct at best, and their accuracy crucially depends on the form of the CP-violating source.

Magnetoelectric effects in superconductors due to spin-orbit scattering: Nonlinear σ -model description

We suggest a generalization of nonlinear $\sigma$-model for diffusive superconducting systems to account for magnetoelectric effects due to spin-orbit scattering. In the leading orders of spin-orbit strength and gradient expansion it includes two additional terms responsible for the spin-Hall effect and the spin-current swapping. First, assuming a delta-correlated disorder we derive the new terms from the Keldysh path integral representation of the generating functional. Then we argue phenomenologically that they exhaust all invariants allowed in the effective action to the leading order in the spin-orbit coupling (SOC). Finally, the results are confirmed by a direct derivation of the saddle-point (Usadel) equation from the quantum kinetic equations in the presence of randomly distributed impurities with SOC. At this point we correct a recent derivation of the Usadel equation that includes magneto-electric effects and does not resort to the Born approximation.

Magnonic thermal transport using the quantum Boltzmann equation

We present a formula for thermal transport in the bulk of Bose systems based on the quantum Boltzmann equation (QBE). First, starting from the quantum kinetic equation and using the Born approximation for impurity scattering, we derive the QBE of Bose systems and provide a formula for thermal transport subjected to a temperature gradient. Next, we apply the formula to magnons. Assuming a relaxation time approximation and focusing on the linear response regime, we show that the longitudinal thermal conductivity of the QBE exhibits the different behavior from the conventional. The thermal conductivity of the QBE reduces to the Drude-type in the limit of the quasiparticle approximation, while not in the absence of the approximation. Finally, applying the quasiparticle approximation to the QBE, we find that the correction to the conventional Boltzmann equation is integrated as the self-energy into the spectral function of the QBE, and this enhances the thermal conductivity. Thus we shed light on the thermal transport property of the QBE beyond the conventional.

Quantum kinetic equation for the Wigner function and reduction to the Boltzmann transport equation under discrete impurities.

We derive a quantum kinetic equation under discrete impurities for the Wigner function from the quantum Liouville equation. To attain this goal, the electrostatic Coulomb potential is separated into the long- and short-range parts, and the self-consistent coupling with Poisson's equation is explicitly taken into account within the analytical framework. It is shown that the collision integral associated with impurity scattering as well as the usual drift term is derived on an equal footing. As a result, we find that the conventional treatment of impurity scattering under the Wigner function scheme is inconsistent in the sense that the collision integral is introduced in an ad hoc way and, thus, the short-range part of the impurity potential is double-counted. The Boltzmann transport equation (BTE) is then derived without imposing the assumption of random impurity configurations over the substrate. The derived BTE would be applicable to describe the discrete nature of impurities such as potential fluctuations.

Sterile Neutrinos as Dark Matter: Alternative Production Mechanisms in the Early Universe

We study various production mechanisms of sterile neutrinos in the early universe beyond and within the standard model. We obtain the quantum kinetic equations for production and the distribution function of sterile-like neutrinos at freeze-out, from which we obtain free streaming lengths, equations of state and coarse grained phase space densities. In a simple extension beyond the standard model, in which neutrinos are Yukawa coupled to a Higgs-like scalar, we derive and solve the quantum kinetic equation for sterile production and analyze the freeze-out conditions and clustering properties of this dark matter constituent. We argue that in the mass basis, standard model processes that produce active neutrinos also yield sterile-like neutrinos, leading to various possible production channels. Hence, the final distribution function of sterile-like neutrinos is a result of the various kinematically allowed production processes in the early universe. As an explicit example, we consider production of light sterile neutrinos from pion decay after the QCD phase transition, obtaining the quantum kinetic equation and the distribution function at freeze-out. A sterile-like neutrino with a mass in the keV range produced by this process is a suitable warm dark matter candidate with a free-streaming length of the order of few kpc consistent with cores in dwarf galaxies.