Path integral approach to quantum Brownian motion

Caldeira, A. O.; Leggett, Anthony J.

doi:10.1016/0378-4371(83)90013-4

Cited by 2,667 publications

(3,089 citation statements)

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“…We wish to investigate dissipative dynamics in a more quantum mechanically rigorous manner. With this aim, we employ a model based on the Caldeira-Leggett (or Brownian) Hamiltonian, 1,2) H ¼p…”

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confidence: 99%

An Approach to Quantum Transport Based on Reduced Hierarchy Equations of Motion: Application to a Resonant Tunneling Diode

Sakurai

Tanimura

2013

J. Phys. Soc. Jpn.

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The quantum dissipative dynamics of a tunneling process through double barrier structures is investigated on the basis of a rigorous treatment for the first time. We employ a Caldeira-Leggett Hamiltonian with an effective potential calculated self-consistently, accounting for the electron distribution. With this Hamiltonian, we use the reduced hierarchy equations of motion in the Wigner space representation to study the effects of non-Markovian thermal fluctuations and dissipation at finite temperature in a rigorous manner. Hysteresis, double plateau-like behavior, and self-excited current oscillation are observed in a negative differential resistance (NDR) region of the current-voltage curve. We find that while most of the current oscillations decay in time in the NDR region, there is a steady oscillation characterized by a tornado-like rotation in the Wigner space in the upper plateau of the NDR region.KEYWORDS: quantum transport, Caldeira-Leggett, dissipative dynamics, resonant tunneling, non-MarkovianThe Caldeira-Leggett (or Brownian) Hamiltonian has been applied to the investigation of quantum dissipative dynamics in several fundamental contexts, including quantum tunneling, 1-3) chemical reactions, 4) SQUID rings, 5) nonlinear optical response, 6) and quantum ratchets. 7) Because a complete model of quantum dissipative dynamics must treat phenomena that can only be described in real time, a great deal of effort has been dedicated to the problem of numerically integrating equations of motion derived from the Hamiltonian that describe real-time behavior. [8][9][10] Although such equations are analogous to the classical kinetic equations, which have proved to be useful in the study of classical transport phenomena, they are difficult to derive in a quantum mechanical framework without approximations and/or assumptions.In this paper, we demonstrate that the reduced hierarchy equations of motion (HEOM) in the Wigner space representation provide a powerful method to study quantum dissipative dynamics in systems subject to non-Markovian and non-perturbative thermal fluctuations and dissipation at finite temperature. [11][12][13][14][15] As an example, we employ a model describing the thermal effects in resonant tunneling diodes (RTDs). 16,17) Although the validity of the Caldeira-Leggett Hamiltonian for describing electron transport phenomena has not yet been investigated thoroughly, because it has a firm quantum mechanical foundation, and because we feel that it is necessary to investigate the validity of the previous theoretical results in a fully quantum mechanical treatment, we believe that the present study will be helpful in constructing a general understanding of electron transport phenomena.Due to quantum effects, an RTD system exhibits novel negative differential resistance (NDR) in its current-voltage (I-V ) relation. 18) Moreover, current oscillations, 19) plateaulike behavior and hysteresis of the I-V curve have been observed in the NDR region. 20) Theoretically, Frensley found NDR in the I-V curve in...

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confidence: 99%

An Approach to Quantum Transport Based on Reduced Hierarchy Equations of Motion: Application to a Resonant Tunneling Diode

Sakurai

Tanimura

2013

J. Phys. Soc. Jpn.

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“…An alternative approach is not to use one of the more formal relaxation theories, 87,88,[97][98][99][100][101] but to incorporate the system-environment coupling in a phenomenological way. In this case the density operator r s of the system is propagated with the von Neumann equation, eqn (10), with additional relaxation terms.…”

Section: This Journal Is C the Owner Societies 2010mentioning

confidence: 99%

Single molecule charge transport: from a quantum mechanical to a classical description

Kocherzhenko

Grozema

Siebbeles

2011

Phys. Chem. Chem. Phys.

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This paper explores charge transport at the single molecule level. The conductive properties of both small organic molecules and conjugated polymers (molecular wires) are considered. In particular, the reasons for the transition from fully coherent to incoherent charge transport and the approaches that can be taken to describe this transition are addressed in some detail. The effects of molecular orbital symmetry, quantum interference, static disorder and molecular vibrations on charge transport are discussed. All of these effects must be taken into account (and may be used in a functional way) in the design of molecular electronic devices. An overview of the theoretical models employed when studying charge transport in small organic molecules and molecular wires is presented.

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“…The master equation (56) is often referred to as the Caldeira-Leggett master equation [23,24]. It consists of three parts: a von Neumann part which describes the free motion without the coupling to the environment, a diffusive part and a dissipative part.…”

Section: B Master Equationmentioning

confidence: 99%