14 Aug 2009-Physical Review B (American Physical Society)-Vol. 80, Iss: 7, pp 073301-1-073301-4
Abstract: We demonstrate the existence of a breather mode in the self-consistent electron dynamics of a semiconductor quantum well. A nonperturbative variational method based on quantum hydrodynamics is used to determine the salient features of the electron breather mode. Numerical simulations of the time-dependent Wigner-Poisson or Hartree equations are shown to be in excellent agreement with our analytical results. For asymmetric quantum wells, a signature of the breather mode is observed in the dipole response, which can be detected by standard optical means.
Abstract: Quantum plasmas are an important topic in astrophysics and high pressure laboratory physics for more than 50 years. In addition, many condensed matter systems, including the electron gas in metals, metallic nanoparticles, or electron-hole systems in semiconductors and heterostructures, exhibit—to some extent—plasmalike behavior. Among the key theoretical approaches that have been applied to these systems are quantum kinetic theory, Green function theory, quantum Monte Carlo, semiclassical and quantum molecular dynamics, and more recently, density functional theory simulations. These activities are in close contact with the experiments and have firmly established themselves in the fields of plasma physics, astrophysics, and condensed matter physics. About two decades ago, a second branch of quantum plasma theory emerged that is based on a quantum fluid description and has attracted a substantial number of researchers. The focus of these studies has been on collective oscillations and linear and nonlinear waves in quantum plasmas. Even though these papers pretend to address the same physical systems as the more traditional papers mentioned above, the former appear to form a rather closed community that is largely isolated from the rest of the field. The quantum hydrodynamics (QHD) results have—with a few exceptions—not found application in astrophysics or in experiments in condensed matter physics. Moreover, these results practically did not have any impact on the former quantum plasma theory community. One reason is the unknown accuracy of the QHD for dense plasmas. In this paper, we present a novel derivation, starting from reduced density operators that clearly point to the deficiencies of QHD, and we outline possible improvements. It is also to be noted that some of the QHD results have attracted negative attention being criticized as unphysical. Examples include the prediction of “novel attractive forces” between protons in an equilibrium quantum plasma, the notion of “spinning quantum plasmas,” or the new field of “quantum dusty plasmas.” In the present article, we discuss the latter system in some detail because it is a particularly disturbing case of formal theoretical investigations that are detached from physical reality despite bold and unproven claims of importance for, e.g., dense astrophysical plasmas or microelectronics. We stress that these deficiencies are not a problem of QHD itself, which is a powerful and efficient method, but rather are due to ignorance of its properties and limitations. We analyze the common flaws of these works and come up with suggestions to improve the situation of QHD applications to quantum plasmas.
Cites background from "Breather mode in the many-electron ..."
...Moreover, in addition to the monopole mode that is due to the pair interaction between particles and that exists in classical systems as well, a quantum system supports a second purely quantum monopole mode that arises from the quantum kinetic energy (Bohm potential) [198, 201]....
Abstract: We present new solutions to the nonautonomous nonlinear Schrodinger equation that may be realized through convenient manipulation of Bose–Einstein condensates. The procedure is based on the modulation of breathers through an analytical study of the one-dimensional Gross–Pitaevskii equation, which is known to offer a good theoretical model to describe quasi-one-dimensional cigar-shaped condensates. Using a specific ansatz , we transform the nonautonomous nonlinear equation into an autonomous one, which engenders composed states corresponding to solutions localized in space, with an oscillating behavior in time. Numerical simulations confirm stability of the modulated breathers against random perturbation on the input profile of the solutions.
Abstract: We studied the surface plasmon waves in a quantum plasma half-space by considering the effects of exchange and correlation for the electrons. We used a quantum hydrodynamic approach, including the full set of Maxwell equations and considering two new quantities (measuring the exchange and correlation effects) in addition to the Fermi electron temperature and the quantum Bohm potential, to derive the dispersion relation for the surface plasmon waves. It was found that the exchange-correlation effects significantly modified the behavior of surface plasmon waves. We showed that the frequency of surface plasmon wave was down-shifted by the exchange-correlation effects. On the other hand, the quantum effects (including of the exchange-correlation effects and the quantum Bohm potential) was seen to cause an increase in the phase speed of surface plasmon waves. Our results can help to understand the propagation properties of surface waves in intense laser produced solid density plasmas and metallic plasmas.
Abstract: We derive a four-component Vlasov equation for a system composed of spin-1/2 fermions (typically electrons). The orbital part of the motion is classical, whereas the spin degrees of freedom are treated in a completely quantum-mechanical way. The corresponding hydrodynamic equations are derived by taking velocity moments of the phase-space distribution function. This hydrodynamic model is closed using a maximum entropy principle in the case of three or four constraints on the fluid moments, both for Maxwell-Boltzmann and Fermi-Dirac statistics.
Abstract: A self-consistent relativistic two-fluid model is proposed for one-dimensional electron-ion plasma dynamics. A multiple scales perturbation technique is employed, leading to an evolution equation for the wave envelope, in the form of a nonlinear Schrodinger type equation (NLSE). The inclusion of relativistic effects is shown to introduce density-dependent factors, not present in the non-relativistic case—in the conditions for modulational instability. The role of relativistic effects on the linear dispersion laws and on envelope soliton solutions of the NLSE is discussed.