Quantum Hydrodynamics

  title={Quantum Hydrodynamics},
  author={Shabbir Ahmad Khan and Michael Bonitz},
Quantum plasma physics is a rapidly evolving research field with a very inter-disciplinary scope of potential applications, ranging from nano-scale science in condensed matter to the vast scales of astrophysical objects. The theoretical description of quantum plasmas relies on various approaches, microscopic or macroscopic, some of which have obvious relation to classical plasma models. The appropriate model should, in principle, incorporate the quantum mechanical effects such as diffraction… 

Quantum hydrodynamics for plasmas—Quo vadis?

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,

Fluid descriptions of quantum plasmas

Quantum fluid (or hydrodynamic) models provide an attractive alternative for the modeling and simulation of the electron dynamics in nano-scale objects. Compared to more standard approaches, such as

Modeling quantum fluid dynamics at nonzero temperatures

This work introduces a framework based on a nonlinear classical-field equation that is mathematically identical to the Landau model and provides a mechanism for severing and coalescence of vortex lines, so that the questions related to the behavior of quantized vortices can be addressed self-consistently.

Towards quantum turbulence in cold atomic fermionic superfluids

Fermionic superfluids provide a new realization of quantum turbulence, accessible to both experiment and theory, yet relevant to phenomena from both cold atoms to nuclear astrophysics. In particular,

Generalized hydrodynamics revisited

During the past decade a number of attempts to formulate a continuum description of complex states of matter have been proposed to circumvent more cumbersome many-body and simulation methods.

Numerical Studies of Quantum Turbulence

We review numerical studies of quantum turbulence. Quantum turbulence is currently one of the most important problems in low temperature physics and is actively studied for superfluid helium and

Time in quantum mechanics: A fresh look on quantum hydrodynamics and quantum trajectories

Quantum hydrodynamics is a formulation of quantum mechanics based on the probability density and flux (current) density of a quantum system. It can be used to define trajectories which allow for a

A Critique of Recent Semi‐Classical Spin‐Half Quantum Plasma Theories

Certain recent semi‐classical theories of spin‐half quantum plasmas are examined with regard to their internal consistency, physical applicability and relevance to fusion, astrophysical and condensed

Mathematical Models and Numerical Methods for Bose-Einstein Condensation

The achievement of Bose-Einstein condensation (BEC) in ultracold vapors of alkali atoms has given enormous impulse to the theoretical and experimental study of dilute atomic gases in condensed

Interactions and scattering of quantum vortices in a polariton fluid

A polariton system is used to experimentally investigate the behavior and scattering of vortices in a two-component superfluid, revealing the role of nonlinearity, as well as of density and phase gradients, in driving their rotational dynamics.



Quantum collision theory with phase-space distributions

Quantum-mechanical phase-space distributions, introduced by Wigner in 1932, provide an intuitive alternative to the usual wave-function approach to problems in scattering and reaction theory. The aim

Introduction to Quantum Plasma Simulations

This chapter contains a brief introduction to the field of quantum simulations. Beginning with a numerical treatment of single-particle problems by exact numerical solution of the time-dependent

On description of a collisionless quantum plasma

A plasma is regarded as quantum if its macroscopic properties are significantly affected by the quantum nature of its constituent particles. A proper description is necessary to comprehend when

The Quantum Hydrodynamic Model for Semiconductor Devices

The full three-dimensional quantum hydrodynamic (QHD) model is derived for the first time by a moment expansion of the Wigner–Boltzmann equation.

Quantum and classical dynamics of Langmuir wave packets.

  • F. HaasP. Shukla
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2009
The quantum Zakharov system in three spatial dimensions and an associated Lagrangian description, as well as its basic conservation laws, are derived and the variational method is shown to preserve the essential conservation laws of the quantum modified vector NLS equation.

Colloquium : nonlinear collective interactions in quantum plasmas with degenerate electron fluids

The current understanding of some important nonlinear collective processes in quantum plasmas with degenerate electrons is presented. After reviewing the basic properties of quantum plasmas, model

Quantum ion-acoustic waves

The one-dimensional two-species quantum hydrodynamic model is considered in the limit of small mass ratio of the charge carriers. Closure is obtained by adopting an equation of state pertaining to a

Kinetic Theory for Quantum Plasmas

Quantum plasmas have been studied theoretically for more than four decades. Important early applications include the electron gas in metals and the electron-hole plasma in semiconductors and

Theory and simulation of strong correlations in quantum Coulomb systems

Strong correlations in quantum Coulomb systems (QCS) are attracting increasing interest in many fields ranging from dense plasmas and semiconductors to metal clusters and ultracold trapped ions.

Quantum mechanics as a statistical theory

  • J. E. Moyal
  • Physics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1949
An attempt is made to interpret quantum mechanics as a statistical theory, or more exactly as a form of non-deterministic statistical dynamics. The paper falls into three parts. In the first, the