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    Electrical Transport in Nanoscale Systems

    ISBN-10: 0521896347
    ISBN-13: 9780521896344
    Author(s): Massimiliano Di Ventra
    Description: 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  More...
    List price: $109.99
    Buy it from: $24.20
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    List Price: $109.99
    Publisher: Cambridge University Press
    Binding: Hardcover
    Pages: 496
    Size: 6.85" wide x 9.72" long x 1.06" tall
    Weight: 2.640
    Language: English

    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. 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.

    Massimiliano Di Ventra is Professor of Physics at the University of California, San Diego. He has published over 70 papers in refereed journals, co-edited the textbook Introduction to Nanoscale Science and Technology (Springer, 2004), and has delivered more than 100 invited talks worldwide on the subject of this book.

    A primer on electron transport
    Nanoscale systems
    Generating currents
    Finite versus infinite systems
    Electron sources
    Intrinsic nature of the transport problem
    Measuring currents
    Microscopic states
    The current operator
    The measurement process
    Complete measurement and pure states
    The statistical operator and macro-states
    Pure and mixed states
    Quantum correlations
    Time evolution of the statistical operator
    Random or partially specified Hamiltonians
    Open quantum systems
    Equilibrium statistical operators
    Current measurement and statistical operator truncation
    One current, different viewpoints
    Summary and open questions
    Exercises
    Drude model, Kubo formalism and Boltzmann equation
    Drude model
    Resistance, coherent and incoherent transport
    Relaxation vs. dephasing
    Mean-free path
    The meaning of momentum relaxation time
    Kubo formalism
    The current-current response function
    The use of Density-Functional Theory in the Kubo approach
    The fluctuation-dissipation theorem
    Ohmic vs. ballistic regimes
    Chemical, electrochemical and electrostatic potentials
    Drift-diffusion equations
    Diffusion coefficient of an ideal electron gas in the non-degenerate limit
    Generalization to spin-dependent transport
    Distribution functions
    Boltzmann equation
    Approach to local equilibrium
    Entropy, loss of information, and macroscopic irreversibility
    The classical statistical entropy
    Quantum statistical entropy
    Information content of the N- and one-particle statistical operators
    Entropy of open quantum systems
    Loss of information in the Kubo formalism
    Loss of information with stochastic Hamiltonians
    Entropy associated with the measurement of currents
    Summary and open questions
    Exercises
    Landauer approach
    Formulation of the problem
    Local resistivity dipoles and the "field response"
    Conduction from transmission
    Scattering boundary conditions
    Transmission and reflection probabilities
    Total current
    Two-probe conductance
    The Lippmann-Schwinger equation
    Time-dependent Lippmann-Schwinger equation
    Time-independent Lippmann-Schwinger equation
    Green's functions and self-energy
    Relation to scattering theory
    The S matrix
    Relation between the total Green's function and the S matrix
    The transfer matrix
    Coherent scattering of two resistors in series
    Incoherent scattering of two resistors in series
    Relation between the conductance and the transfer matrix
    Localization, ohmic and ballistic regimes
    Four-probe conductance in the non-invasive limit
    Single-channel case
    Geometrical "dilution"
    Multi-channel case
    Multi-probe conductance in the invasive limit
    Floating probes and dephasing
    Generalization to spin-dependent transport
    Spin-dependent transmission functions
    Multi-probe conductance in the presence of a magnetic field
    Local resistivity spin dipoles and dynamical effects
    The use of Density-Functional Theory in the Landauer approach
    Summary and open questions
    Exercises
    Non-equilibrium Green's function formalism
    Formulation of the problem
    Contour ordering
    Equilibrium Green's functions
    Time-ordered Green's functions
    Dyson's equation for interacting particles
    More Green's functions
    The spectral function
    Contour-ordered Green's functions
    Equations of motion for non-equilibrium Green's functions
    Application to steady-state transport
    Coulomb blockade
    Quantum kinetic equations
    Summary and open questions
    Exercises
    Noise
    The moments of the current
    Shot noise
    The classical (Poisson) limit
    Quantum theory of shot noise
    Counting statistics
    Thermal noise
    Summary and open questions
    Exercises
    Electron-ion interaction
    The many-body electron-ion Hamiltonian
    The adiabatic approximation for a current-carrying system
    The phonon subsystem
    Electron-phonon coupling in the presence of current
    Inelastic current
    Inelastic current from standard perturbation theory
    Inelastic current from the NEGF
    Local ionic heating
    Lattice heat conduction
    Thermopower
    Current-induced forces
    Elastic vs. inelastic contribution to electro-migration
    One force, different definitions
    Local resistivity dipoles and the force sign
    Forces at equilibrium
    Forces out of equilibrium
    Are current-induced forces conservative?
    Local ionic heating vs. current-induced forces
    Summary and open questions
    Exercises
    The micro-canonical picture of transport
    Formulation of the problem
    Transport from a finite-system point of view
    Initial conditions and dynamics
    Electrical current theorems within dynamical DFTs
    Closed and finite quantum systems in a pure state
    Closed quantum systems in a pure state with arbitrary boundary conditions
    Current in open quantum systems
    Closure of the BBGKY hierarchy
    Functional approximations and loss of information
    Transient dynamics
    Properties of quasi-steady states
    Variational definition of quasi-steady states
    Dependence of quasi-steady states on initial conditions
    A non-equilibrium entropy principle
    Approach to steady state in nanoscale systems
    Definition of conductance in the micro-canonical picture
    Summary and open questions
    Hydrodynamics of the electron liquid
    The Madelung equations for a single particle
    Hydrodynamic form of the Schrodinger equation
    Quantum Navier-Stokes equations
    Conductance quantization from hydrodynamics
    Viscosity from Time-Dependent Current Density-Functional Theory
    Functional approximation, loss of information, and dissipative dynamics
    Effect of viscosity on resistance
    Turbulent transport
    Local electron heating
    Electron heat conduction
    Hydrodynamics of heat transfer
    Effect of local electron heating on ionic heating
    Summary and open questions
    Exercises
    Appendices
    A primer on second quantization
    The quantum BBGKY hierarchy
    The Lindblad equation
    The Lindblad theorem
    Derivation of the Lindblad equation
    Steady-state solutions
    Ground-state Density-Functional Theory
    The Hohenberg-Kohn theorem
    The Kohn-Sham equations
    Generalization to grand-canonical equilibrium
    The local density approximation and beyond
    Time-Dependent DFT
    The Runge-Gross theorem
    The time-dependent Kohn-Sham equations
    The adiabatic local density approximation
    Time-Dependent Current DFT
    The current density as the main variable
    The exchange-correlation electric field
    Approximate formulas for the viscosity
    Stochastic Time-Dependent Current DFT
    The stochastic Schrodinger equation
    Derivation of the quantum master equation
    The theorem of Stochastic TD-CDFT
    Inelastic corrections to current and shot noise
    Hydrodynamic form of the Schrodinger equation
    Equation of motion for the stress tensor
    Cut-off of the viscosity divergence
    Bernoulli's equation
    References
    Index

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