Microscopic derivation of rate equations for quantum transport

Gurvitz, S. A.; Prager, Ya. S.

doi:10.1103/physrevb.53.15932

Cited by 391 publications

(584 citation statements)

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“…(8) are a generalization of the previously derived Bloch-type rate-equations for quantum transport in mesoscopic systems [5,12]. They have a clear physical interpretation.…”

mentioning

confidence: 88%

“…(3) are converted to the Bloch-type equations for the reduced density-matrix σ (n) ij (t). Such a technique has been derived in [5,12]. In this paper we generalize it by converting Eqs.…”

mentioning

confidence: 99%

“…Performing the same procedure with all other equations (3), we reduce them to the following system of equations for the amplitudes b(E) [5,12] …”

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confidence: 99%

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Effect of the Measurement on the Decay Rate of a Quantum System

Elattari

Gurvitz

Statistical and Dynamical Aspects of Mesoscopic Systems

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We investigated the electron tunneling out of a quantum dot in the presence of a continuous monitoring by a detector. It is shown that the Schrödinger equation for the whole system can be reduced to new Bloch-type rate equations describing the time-development of the detector and the measured system at once. Using these equations we find that the continuous measurement of the unstable system does not affect its exponential decay, exp(−Γt), contrary to expectations based on the Quantum Zeno effect . However, the width of the energy distribution of the tunneling electron is no more Γ, but increases due to the decoherence, generated by the detector. It was suggested that an unstable quantum system slows down its decay rate under frequent or continuous observations [1]. This phenomenon, known as the quantum Zeno effect, is believed to be related to the projection postulate in the theory of quantum measurements [2]. Indeed, in the standard example of two-level systems, the probability of a quantum transition from an initially occupied unstable state is Q(∆t) = a(∆t) 2 . If we assume that ∆t is the measurement time, which consists in projecting the system onto the initial state, then after N successive measurements the probability of finding the unstable system in its initial state, at time t = N ∆t, is P (t) = [1 − a(∆t) 2 ] (t/∆t) . It follows from this result that P (t) → 1 for ∆t → 0, i.e. suppression of quantum transition. PACSOriginally quantum Zeno effect has been considered as a slowing down of the decay rate [1] of quantum systems in which a discrete initial state is coupled to a continuum of final states. This coupling leads to an irreversible exponential decay from the discrete state to the continuum of states. This situation is very often encountered in physics, as for instance, the α-decay of a nucleus, the spontaneous emission of a photon by an excited atom, the photoelectric effect, and so on. But from the theoretical and experimental point of view, the effort has been mainly concentrated on quantum transitions between isolated levels [3] characterized by an oscillatory behavior between the different states. In this latter case the slowing down of the transition rate has, indeed, been found. However, this was attributed to the decoherence generated by the detector without an explicit involvement of the projection postulate [4,5]. On the other hand, the slowing down of the exponential decay rate still remains a controversial issue, despite the fact that it is extensively studied [6][7][8][9] and further investigations are clearly desirable.In this letter we focus our attention on the quantum Zeno effect in exponentially decaying systems, using a microscopic description which includes the measurement devices. The latter is an essential point missed in many studies. This work is motivated by the distinct difference between continuum energy levels and discrete levels, stated above, as well as by the theoretical and experimental importance of the subject. We also propose an experimental set up which is with...

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“…(8) are a generalization of the previously derived Bloch-type rate-equations for quantum transport in mesoscopic systems [5,12]. They have a clear physical interpretation.…”

mentioning

confidence: 88%

“…(3) are converted to the Bloch-type equations for the reduced density-matrix σ (n) ij (t). Such a technique has been derived in [5,12]. In this paper we generalize it by converting Eqs.…”

mentioning

confidence: 99%

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Effect of the Measurement on the Decay Rate of a Quantum System

Elattari

Gurvitz

Statistical and Dynamical Aspects of Mesoscopic Systems

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“…In quantum systems, one of the theoretical frameworks widely used for open systems is the quantum master equation (QME) [1], an equation of motion for the density matrix of the system. In fact, the QME is used in various fields of physics: e.g., quantum optics [1,2], nuclear magnetic resonance [3], electron transfer in chemical physics and biophysics [4,5], heat transport [6,7,8,9,10,11,12,13,14], electronic transport in mesoscopic conductors [15,16,17,18,19], spin transport [20], and nonequilibrium thermodynamics and statistical physics [21,22,23,24,25]. Therefore, the QME is a reliable approach to investigating NESS in various systems (c.f.…”

Section: Introductionmentioning

confidence: 99%

A Perturbative Method for Nonequilibrium Steady State of Open Quantum Systems

Yuge

Sugita

2015

J. Phys. Soc. Jpn.

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We develop a method of calculating the nonequilibrium steady state (NESS) of an open quantum system that is weakly coupled to reservoirs in different equilibrium states. We describe the system using a Redfield-type quantum master equation (QME). We decompose the Redfield QME into a Lindblad-type QME and the remaining part R. Regarding the steady state of the Lindblad QME as the unperturbed solution, we perform a perturbative calculation with respect to R to obtain the NESS of the Redfield QME. The NESS thus determined is exact up to the first order in the system-reservoir coupling strength (pump/loss rate), which is the same as the order of validity of the QME. An advantage of the proposed method in numerical computation is its applicability to systems larger than those in methods of directly solving the original Redfield QME. We apply the method to a noninteracting fermion system to obtain an analytical expression of the NESS density matrix. We also numerically demonstrate the method in a nonequilibrium quantum spin chain.

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“…As a second step, we use the large bias assumption [25] and a straightforward calculation yields a chain differential equations for the density matrix elements defined in eq. (21) …”

Section: The Modelmentioning

confidence: 99%

Double detected spin-dependent quantum dot

Bernád

2012

Physica B: Condensed Matter

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We study the dynamics of a spin-dependent quantum dot system, where an unsharp and a sharp detection scenario is introduced. The back-action of the unsharp detection related to the magnetization, proposed in terms of the continuous quantum measurement theory, is observed via the von Neumann measurement (sharp detection) of the electric charge current. The behavior of the average electron charge current is studied as a function of the unsharp detection strength γ, and features of measurement back-action are discussed. The achieved equations reproduce the quantum Zeno effect. Considering magnetic leads, we demonstrate that the measurement process may freeze the system in its initial state. We show that the continuous observation may enhance the transition between spin states, in contradiction with rapidly repeated projective observations, when it slows down. Experimental issue, such as the accuracy of the electric current measurement, is analyzed.

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Microscopic derivation of rate equations for quantum transport

Cited by 391 publications

References 20 publications

Effect of the Measurement on the Decay Rate of a Quantum System

Effect of the Measurement on the Decay Rate of a Quantum System

A Perturbative Method for Nonequilibrium Steady State of Open Quantum Systems

Double detected spin-dependent quantum dot

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