Towards an understanding of escape rate and state dependent diffusion for a quantum dissipative system

2014

New J. Phys.

The quantum dissipative dynamics of a tunneling process through double barrier structures is investigated on the basis of non-perturbative and non-Markovian treatment. 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 non-Markovian and nonperturbative thermal effects at finite temperature in a rigorous manner. We study current variation in time and the current-voltage (I -V ) relation of the resonant tunneling diode for several widths of the contact region, which consists of doped GaAs. Hysteresis and both single and double plateau-like behavior are observed in the negative differential resistance (NDR) region. While all of the current oscillations decay in time in the NDR region in the case of a strong system-bath coupling, there exist self-excited high-frequency current oscillations in some parts of the plateau in the NDR region in the case of weak coupling. We find that the effective potential in the oscillating case possesses a basin-like form on the emitter side (emitter basin) and that the current oscillation results from tunneling between the emitter basin and the quantum well in the barriers.

Section: Introductionmentioning

confidence: 99%

Self-excited current oscillations in a resonant tunneling diode described by a model based on the Caldeira–Leggett Hamiltonian

Sakurai

2014

New J. Phys.

“…2. Similarly, the quantum Fokker-Planck equation can be derived from the Caldeira-Leggett Hamiltonian under a Markovian approximation, [51,52,53,54,55] but in order for this to be possible, the heat bath must be at a sufficiently high temperature, in which case quantum tunneling processes play a minor role. The quantum master equation expressed in terms of Floquet states provides a more rigorous treatment of quantum dissipative dynamics than the methods mentioned above, [46] but it can only be applied to systems possessing weak interactions.…”

Section: Introductionmentioning

confidence: 99%

Quantum Suppression of Ratchet Rectification in a Brownian System Driven by a Biharmonic Force

Kato

2013

J. Phys. Chem. B

We rigorously investigate the quantum dissipative dynamics of a ratchet system described by a periodic potential model based on the Caldeira-Leggett Hamiltonian with a biharmonic force. In this model, we use the reduced hierarchy equations of motion in the Wigner space representation. These equations represent a generalization of the Gaussian-Markovian quantum Fokker-Planck equation introduced by Tanimura and Wolynes (1991), which was formulated to study non-Markovian and nonperturbative thermal effects at finite temperature. This formalism allows us to treat both the classical limit and the tunneling regimes, and it is helpful for identifying purely quantum mechanical effects through the time evolution of the Wigner distribution. We carried out extensive calculations of the classical and quantum currents for various temperatures, coupling strengths, and barrier heights. Our results reveal that at low temperature, while the quantum current is larger than the classical current in the case of a high barrier, the opposite is true in the case of a low barrier. We find that this behavior results from the fact that the tunneling enhances the current in the case of a high barrier, while it suppresses the current in the case of a low barrier. This is because the effect of the ratchet potential is weak in the case of a low barrier due to the large dispersion of the distribution introduced by tunneling. This causes the spatiotemporal asymmetry, which is necessary for ratchet current, to be weak, and as a result, the net current is suppressed.

“…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).…”

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confidence: 99%

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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

2013

J. Phys. Soc. Jpn.

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...