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Produktbeschreibung In recent years there has been a huge increase in the research and development of nanoscale science and technology. Central to the understanding of the properties of nanoscale structures is the modeling of electronic conduction through these systems. This graduate textbook provides an in-depth description of the transport phenomena relevant to systems of nanoscale dimensions. The micro-canonical picture of transport-- 8. Hydrodynamics of the electron liquid-- Appendices-- References-- Index. Central to the understanding of the properties of nanoscale structures is the modeling of electronic conduction through these systems.

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This graduate textbook provides an in-depth description of the transport phenomena relevant to systems of nanoscale dimensions. In this textbook the different theoretical approaches are critically discussed, with emphasis on their basic assumptions and approximations.

The book also covers information content in the measurement of currents, the role of initial conditions in establishing a steady state, and the modern use of density-functional theory. Topics are introduced by simple physical arguments, with particular attention to the non-equilibrium statistical nature of electrical conduction, and followed by a detailed formal derivation. This textbook is ideal for graduate students in physics, chemistry, and electrical engineering. Subject Electron transport. Electric conductivity. Nanoelectromechanical systems.

## Nanoscale Electrical Transport in Self-Organized Molecular Assemblies (NETSOMA)

Electron transport. Nanostrukturiertes Material Transportprozess. Bibliographic information. Skip to main content. You're using an out-of-date version of Internet Explorer. By using our site, you agree to our collection of information through the use of cookies. To learn more, view our Privacy Policy. Log In Sign Up.

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Hydrodynamic approach to transport and turbulence in nanoscale conductors Journal of Physics: Condensed Matter, Roberto D'Agosta. Massimiliano Di Ventra. Hydrodynamic approach to transport and turbulence in nanoscale conductors. Bg, Mb, Jn, Nm Abstract. The description of electron-electron interactions in transport problems is both analytically and numerically difficult.

Here we show that a much simpler description of electron transport in the presence of interactions can be achieved in nanoscale systems. In particular, we show that the electron flow in nanoscale conductors can be described by Navier-Stokes type of equations with an effective electron viscosity, i. By using this hydrodynamic approach we derive the conditions for the transition from laminar to turbulent flow in nanoscale systems and discuss possible experimental tests of our predictions. Introduction The electron liquid is both viscous and compressible; properties which suggest an intriguing analogy with a classical liquid [1].

In the classical case one can derive time-dependent equations, called Navier-Stokes equations, for the velocity field of the fluid as a function of its density, visco-elastic coefficients, pressure and the geometric confinement [1]. These equations are centrefold in hydrodynamics and describe both laminar and turbulent regimes. Unfortunately, the derivation of these equations in the quantum case is generally not possible.

In this paper we show that transport in nanoscale conductors satisfies the conditions to derive quantum Navier-Stokes equations. In this regime, we show that one can truncate the infinite hierarchy of equations of motion for the electron stress tensor to second order and thus derive quantum hydrodynamic equations.

## Approach to Steady-State Transport in Nanoscale Conductors | Nano Letters

We then predict the conditions for the transition from laminar to turbulent flow in quantum point contacts QPCs and suggest specific experiments to verify our predictions. It is well known that the TDSE can be equivalently written as two coupled equations of motion for the single-particle density, n r, t , and velocity field, v r, t , as obtained from the Heisenberg equation of motion for the corresponding operators [2, 3].

In order to solve 3 one proceeds by calculating an equation of motion for G2 , which can be derived from the Heisenberg equation of motion of the particle creation and destruction operators. However, this equation of motion contains the three-particle density matrix.

## Electrical transport in nanoscale systems /

In turn, the equation of motion for the three-particle density matrix contains the four-particle density matrix and so forth, thus generating an infinite hierarchy of nested equations, making the problem practically unsolvable [2, 3]. Quantum Navier-Stokes equations We show here that in the case of electrical transport in nanoscale systems we can instead close this set of equations.

We proceed as follows. First, let us derive the dependence of the stress tensor Pi,j on the rate at which the system reaches a quasi-steady state. The collisional integral contains two terms, one elastic and the other inelastic.

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In what follows, it is important to realize that both terms can drive the system toward a local equilibrium configuration.