Quantum Kinetic Equation Research Articles

Kinetic theory of vacuum pair production in uniform electric fields revisited

We investigate the phenomenon of electron-positron pair production from vacuum in the presence of a uniform time-dependent electric field of arbitrary polarization. Taking into account the interaction with the external classical background in a nonperturbative manner, we quantize the electron-positron field and derive a system of ten quantum kinetic equations (QKEs) showing that the previously-used QKEs are incorrect once the external field rotates in space. We employ then the Wigner-function formalism of the field quantization and establish a direct connection between the Dirac-Heisenberg-Wigner (DHW) approach to investigating the vacuum pair-production process and the QKEs. We provide a self-contained description of the two theoretical frameworks rigorously proving their equivalence and present an exact one-to-one correspondence between the kinetic functions involved within the two techniques. Special focus is placed on the analysis of the spin effects in the final particle distributions. Published by the American Physical Society 2024

Radio-electric Effect in Semi-parabolic Plus Semi-inverse Squared QuantumWells

Radioelectric field in semi-parabolicplus semi-inverse squared quantum wells has been studied in the presence of a linearly polarized electromagnetic wave. By using quantum kinetic equations for electrons in the case of electrons – optical phonons scattering, the analytical expression for the Radioelectricfield was obtained as a function of the frequency, the amplitude of the linearly polarized electromagnetic field and temperature. Numerical results of specific GaAs/GaAlAs semi-parabolicplus semi-inverse squared quantum wells were also achieved. The results showed that when temperature increases, the Radioelectric field increases nonlinearly.

Tight-binding implementation of the quantum kinetic equation for graphene

Tight-binding implementation of the quantum kinetic equation for graphene

Lorentz-violating extension of Wigner function formalism and chiral kinetic theory

The quantum kinetic equation for the gauge-invariant Wigner function, constructed from spinor fields that obey the Dirac equation modified by CPT and Lorentz symmetry-violating terms, is presented. The equations for the components of the Wigner function in the Clifford algebra basis are accomplished. Focusing on the massless case, an extended semiclassical chiral kinetic theory in the presence of external electromagnetic fields is developed. We calculate the chiral currents and establish the anomalous magnetic and separation effects in a Lorentz-violating background. The chiral anomaly within the context of extended quantum electrodynamics is elucidated. Finally, we derive the semiclassical Lorentz-violating extended chiral transport equation. Published by the American Physical Society 2024

Case study of the validity of truncation schemes of kinetic equations of motion: Few magnetic impurities in a semiconductor quantum ring

We carry out a study on the validity and limitations of truncation schemes customarily employed to treat the quantum kinetic equations of motion of complex interacting systems. Our system of choice is a semiconductor quantum ring with one electron interacting with few magnetic impurities via a Kondo-like Hamiltonian. This system is an interesting prototype which displays the necessary complexity when suitably scaled (large number of magnetic impurities) but can also be solved exactly when few impurities are present. The complexity in this system comes from the indirect electron-mediated impurity–impurity interaction and is reflected in the Heisenberg equations of motion, which form an infinite hierarchy. For the cases of two and three magnetic impurities, we solve for the quantum dynamics of our system both exactly and following a truncation scheme developed for diluted magnetic semiconductors in the bulk. We find an excellent agreement between the two approaches when physical observables like the impurities’ spin angular momentum are computed for times that well exceed the time window of validity of perturbation theory. On the other hand, we find that within time ranges of physical interest, the truncation scheme introduces negative populations which represents a serious methodological drawback.

Pair production in rotating electric fields via quantum kinetic equations: Resolving helicity states

We investigate the phenomenon of electron-positron pair production from vacuum in the presence of a strong electric field of circular polarization. By means of a nonperturbative approach based on the quantum kinetic equations (QKEs), we numerically calculate helicity-resolved momentum distributions of the particles produced and analyze the corresponding helicity asymmetry. It is demonstrated that the external rotating field tends to generate left-handed and right-handed particles traveling in opposite directions. Generic symmetry properties of the momentum spectra are examined analytically by means of the QKEs and also confirmed and illustrated by direct numerical computations. The helicity signatures revealed in our study are expected to provide a firmer basis for possible experimental investigations of the fundamental phenomenon of vacuum pair production in strong fields. Published by the American Physical Society 2024

Quantum kinetic equation and thermal conductivity tensor for bosons

Quantum kinetic equation and thermal conductivity tensor for bosons

Derivation of dirac exchange interaction potential from quantum plasma kinetic theory

The Dirac exchange interaction is derived from recent quantum kinetic theory for collisionless plasmas. For this purpose, the kinetic equation is written in the semiclassical and long wavelength approximations. The validity of the model for real systems is worked out, in terms of temperature and density parameters. Within the region of applicability, the correlation potential energy is shown to be always smaller than the exchange contribution. From the moments of the quantum kinetic equations, macroscopic, hydrodynamic equations are found, for an electron-ion plasma. The Dirac exchange term is explicitly derived, in the case of a completely degenerate electron gas. These results show, within quantum kinetic theory for charged particle systems, a new view of the Dirac exchange interaction frequently used in density functional theory parametrization. Finally, a simpler form of the quantum plasma exchange kinetic theory is also found.

The Impact of a Strong Electromagnetic Wave on the Quantum Hall Effect in Cylindrical Quantum Wires

The impact of strong electromagnetic waves Hall effect is studied theoretically in a Cylindrical Quantum Wire (CQW) with infinitely high potential inside the wire and elsewhere subjected to a dc electric field , a magnetic field and a laser radiation . By using the quantum kinetic equation method for electrons interacting with Acoustic Phonon (AP) at low temperatures, we obtain analytical expressions for the conductivity tensor and the Hall Coefficient (HC), which are different from in comparison to those obtained for a rectangular quantum wire (RQW) or two-dimensional (2D) electron systems. Numerical calculations are also applied for GaAs/GaAsAl CQW to show the nonlinear dependence of the HC on the electromagnetic wave (EMW) frequency, and the radius, the length characteristic parameters of CQW. Wave function and energy spectrum in a CQW are dissiminar to those in Quantum Wires (QWs). Therefore, all numerical results are different from those in the case of QWs. The most important result is that the HC reaches saturation as the radius, the length of CQW or the EMW frequency increases.

Chaos in inhomogeneous neutrino fast flavor instability

In dense neutrino gases, the neutrino-neutrino coherent forward scattering gives rise to a complex flavor oscillation phenomenon not fully incorporated in simulations of neutron star mergers (NSM) and core collapse supernovae (CCSNe). Moreover, it has been proposed to be chaotic, potentially limiting our ability to predict neutrino flavor transformations in simulations. To address this issue, we explore how small flavor perturbations evolve in the nonlinear regime of the neutrino quantum kinetic equation within a narrow centimeter-scale region inside a NSM and a toy neutrino distribution. Our findings reveal that paths in the flavor state space of solutions with similar initial conditions diverge exponentially, exhibiting chaos. This inherent chaos makes the microscopic scales of neutrino flavor transformations unpredictable. However, the domain-averaged neutrino density matrix remains relatively stable, with chaos minimally affecting it. This particular property suggests that domain-averaged quantities remain reliable despite the exponential amplification of errors. Published by the American Physical Society 2024

Once-in-a-lifetime encounter models for neutrino media: From coherent oscillations to flavor equilibration

Collective neutrino oscillations are typically studied using the lowest-order quantum kinetic equation, also known as the mean-field approximation. However, some recent quantum many-body simulations suggest that quantum entanglement among neutrinos may be important and may result in flavor equilibration of the neutrino gas. In this work, we develop new quantum models for neutrino gases in which any pair of neutrinos can interact at most once in their lifetimes. A key parameter of our models is γ=μΔz, where μ is the neutrino coupling strength, which is proportional to the neutrino density, and Δz is the duration over which a pair of neutrinos can interact each time. Our models reduce to the mean-field approach in the limit γ→0 and achieve flavor equilibration in time t≫(γμ)−1. These models demonstrate the emergence of coherent flavor oscillations from the particle perspective and may help elucidate the role of quantum entanglement in collective neutrino oscillations. Published by the American Physical Society 2024

Photon quantum kinetic equations and collective modes in an axion background

We develop a quantum kinetic theory for photons in the presence of an axion background and in the collisioness limit. In deriving the classical regime of our quantum kinetic equations, we observe that they capture well-known features of axion electrodynamics. By projecting the Wigner function onto a polarization basis, relating the Wigner matrix function with the Stokes parameters, we establish the dispersion relations and transport equations for each polarization space component. Additionally, we investigate how the axion background affects the dispersion relations of photon collective modes within an electron-positron plasma at equilibrium temperature T. While the plasmon remains unaffected, we find that the axion background breaks the degeneracy of transverse collective modes at order egaγT(∂a), where e represents the electron charge, gaγ denotes the photon-axion coupling, and ∂a represents the scale associated with variations in the axion field. Published by the American Physical Society 2024

Symmetry breaking due to multi-angle matter-neutrino resonance in neutron star merger remnants

Neutron star merger remnants are unique sites for exploring neutrino flavor conversion in dense media. Because of the natural excess of ν̅e over νe , the neutrino-neutrino potential can cancel the matter potential, giving rise to matter-neutrino resonant flavor conversion. Under the assumption of two (anti)neutrino flavors and spatial homogeneity, we solve the neutrino quantum kinetic equations to investigate the occurrence of the matter-neutrino resonance within a multi-angle framework. We find that isotropy is broken spontaneously, regardless of the mass ordering. Relying on a hydrodynamical simulation of a binary neutron star merger remnant with a black hole of 3 M ⊙ and an accretion torus of 0.3 M ⊙, we find that complete flavor conversion caused by the matter-neutrino resonance is unlikely, although the matter and neutrino potentials cancel at various locations above the disk. Importantly, the matter-neutrino resonant flavor conversion crucially depends on the shape of the neutrino angular distributions. Our findings suggest that an accurate modeling of the neutrino angular distributions is necessary to understand flavor conversion physics in merger remnants, its implications on the disk physics and synthesis of the elements heavier than iron.

Photostimulated Nernst effect in two-dimensional compositional semiconductor superlattices under the influence of confined phonons

The photostimulated Nernst effect in compositional semiconductor superlattices under the influence of a confined acoustic phonon is studied by using the quantum kinetic equation. The case of the confined electron-confined acoustic phonon scattering process is examined in detail. The obtained analytical results reveal that the Nernst coefficient (NC) depends on the external field such as magnetic field B, the frequency Ω, and the amplitude E 0 of the electromagnetic wave in a complicated way but also like a function of the temperature of the system and the period of the superlattice. It also depends on the quantum number m-describing the confined acoustic phonon. The theoretical results are depicted and discussed for GaAs/AlxGa 1 − xAs compositional semiconductors superlattices. The results indicate that the Shubnikov-De hass oscillations have appeared. The confined phonons make the magnitude of the Nernst coefficient higher and more obvious than the case of a bulk phonon. In addition, the magneto-photon resonance condition is also proved. Besides, the Nernst coefficient decreases significantly as the temperature increases. The oscillations Nernst coefficient in a magnetic field are consistent with the previous experimental.

Numerical modeling of non-equilibrium neutrino radiation field by solving quantum kinetic equation

Numerical modeling of neutrino quantum kinetics is a new frontier in the study of core-collapse supernova (CCSN) and binary neutron star merger (BNSM). The noticeable feature in the quantum kinetics is neutrino flavor conversion driven by neutrino self-interactions. Although there remain many unresolved issues in their non-linear properties of flavor conversions, rapid progress has been made in the last few years. In this article, we introduce the current status for the study of collective neutrino oscillations, which are representative characteristics in self-induced flavor conversions, and then we show our recent results: global quantum kinetic simulations in CCSN and BNSM environments.

Influence of confined acoustic phonons on the acousto-electric field in doped semiconductor superlattices

By using a quantum kinetic equation for electrons, the expression of the acoustoelectric field under the influence of confined acoustic phonons in doped semiconductor superlattices (DSSL) is obtained. From these expressions, the acousto-electric field depends on temperature, acoustic wave frequency, Fermi energy level, doped concentration, and quantum number m characterizing the phonons confinement. The results are numerically calculated for the GaAs:Be/GaAs:Si DSSL and show that the appearance of phonons confinement makes the acousto-electric field value become different than the cases of unconfined phonons.

Theoretical Study of the Nernst Effect in Compositional Superlattices in the Presence of Strong Electromagnetic Wave

The Nernst effect has been theoretically studied in compositional superlattice in the presence of a strong electromagnetic wave. Using the quantum kinetic equation for electrons with two cases electrons-acoustic phonons scattering and electrons-optical phonons scattering, we obtained the analytic expression of the Nernst coefficient and kinetic tensors as a function of the magnetic field, temperature, frequency, and amplitude of the electromagnetic wave and parameters of the compositional superlattice. The dependence of the Nernst coefficient on the magnetic field and temperature is achieved by numerical calculations for AlGa/AlGaAs material. The result indicates that in the case of electron-acoustic phonon scattering, the Shubnikov-de Hass oscillation appears. Whereas, in the case of electrons-optical phonons scattering, the peak of magneto-photon-phonon resonance appears. In both cases, when temperature increases, the Nernst coefficient decreases rapidly, and for electrons-optical phonons scattering, the resonance peak has a movement.

The Solution of the Hierarchy of Quantum Kinetic Equations for Correlation Matrices with Delta function Potential

The Solution of the Hierarchy of Quantum Kinetic Equations for Correlation Matrices with Delta function Potential

О генерации электрического разряда в диэлектрике потоком фотонов

The development of an electric discharge during photon scattering in a dielectric material is considered. A preliminary mathematical model of the discharge process is presented. The model is based on a quantum kinetic equation for quasi-free charge carriers produced by bulk radiation effects and impact ionization. Equations are obtained for the concentration, drift current density, and gas temperature of quasi-free electrons. A test example is considered, confirming that the model does not contradict the known conditions for the formation of an electric discharge.

Coulomb Blockade in a Nonthermalized Quantum Dot.

We investigate nonequilibrium transport properties of a quantum dot in the Coulomb blockade regime under the condition of negligible inelastic scattering during the dwelling time of the electrons in the dot. Using the quantum kinetic equation we show that the absence of thermalization leads to a double step in the distribution function of electrons on the dot, provided that it is symmetrically coupled to the leads. This drastically changes nonlinear transport through the dot resulting in an additional (compared to the thermalized case) jump in the conductance at voltages close to the charging energy, which could serve as an experimental manifestation of the absence of thermalization.