Quantum master equation approach to quantum transport through mesoscopic systems

Abstract

For quantum transport through mesoscopic system, a quantum master equation approach is developed in terms of compact expressions for the transport current and the reduced density matrix of the system. The present work is an extension of Gurvitz's approach for quantum transport and quantum measurement, namely, to finite temperature and arbitrary bias voltage. Our derivation starts from a second-order cummulant expansion of the tunneling Hamiltonian, then follows conditional average over the electrode reservoir states. As a consequence, in the usual weak tunneling regime, the established formalism is applicable for a wide range of transport problems. The validity of the formalism and its convenience in application are well illustrated by a number of examples.

8 pages, 1 figure; with considerable extension of the previous version submitted in September 2004; to appear in Phys. Rev. B

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• Probing the existence and dynamics of Majorana fermion via transport through a quantum dot
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• Switching the current through molecular wires
• Local Temperatures Out of Equilibrium
• Geometrical effects and signal delay in time-dependent transport at the nanoscale
• Time-dependent transport via the generalized master equation through a finite quantum wire with an embedded subsystem
• Nonequilibrium perturbation theory in Liouville-Fock space for inelastic electron transport
• Non-Markovian finite-temperature two-time correlation functions of system operators: beyond the quantum regression theorem
• Quantum master equation scheme of time-dependent density functional theory to time-dependent transport in nano-electronic devices
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• Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. I. Formalism
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• Noise spectrum of a quantum dot-resonator lasing circuit
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• Non-renewal statistics in quantum transport through the eyes of first-passage and waiting time distributions
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• Non-Markovian dynamics of a nanomechanical resonator measured by a quantum point contact
• Quantum measurement characteristics of double-dot single electron transistor
• Effect of finite Coulomb interaction on full counting statistics of electronic transport through single-molecule magnet
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• Transport Signatures of a Majorana Qubit and Read-out-induced Dephasing
• Current-induced forces in nanosystems: A hierarchical equations of motion approach
• Real-time counting of single electron tunneling through a T-shaped double quantum dot system
• Master equation approach for transport through Majorana zero modes
• A new quantum machine learning algorithm: split hidden quantum Markov model inspired by quantum conditional master equation
• Reduced dynamics with renormalization in solid-state charge qubit measurement
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• Manipulating quantum coherence of charge states in interacting double-dot Aharonov-Bohm interferometers
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• Quantum trajectory analysis for electrical detection of single-electron spin resonance
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• Lindblad theory for incoherently-driven electron transport in molecular nanojunctions
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