Effective Dynamics of Disordered Quantum Systems

Kropf, Chahan M.; Gneiting, Clemens; Buchleitner, Andreas

doi:10.1103/physrevx.6.031023

Cited by 48 publications

(155 citation statements)

References 71 publications

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“…[363] It should be pointed out that master equation models with memory effects do not necessarily require convolution integrals, [78] and that memory kernel master equations can even usually be cast into a time-local form. [79,83,366] Thus, a promising approach toward a more generalized treatment of dissipation is to start with the Lindblad equation in the form Equation (4), and to generalize the matrix D i j mn given in Equation (6) for an arbitrary set of Lindblad operators. As already mentioned in Section 2, time dependent Lindblad operatorsL k (t), corresponding to time-varying dissipation rates in Equations (8) and (11), are unproblematic.…”

Section: Discussionmentioning

confidence: 99%

“…As already mentioned in Section 2, time dependent Lindblad operatorsL k (t), corresponding to time-varying dissipation rates in Equations (8) and (11), are unproblematic. [78,79] Any further generalization of D i j mn comes at the price of potentially unphysical results. One example is the occurrence of temporarily negative rates in Equations (8) or (11), which indeed introduces memory effects into the Lindblad equation.…”

Section: Discussionmentioning

confidence: 99%

“…[82] This also does not affect the physical validity of Equation (3), since conservation of trace and complete positivity are further guaranteed. [78,79] Moreover, Equation (3) with time dependent operatorsĤ and L k is still time-local and also Markovian. [83]…”

Section: Lindblad Equationmentioning

confidence: 99%

“…Equation (82b) does not yet have the desired form since it contains an x derivative and the longitudinal field component in the term ∂ x H z . With Equations (76b), (79), and (81), we obtain…”

Section: Transverse Electric Modementioning

confidence: 99%

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Optoelectronic Device Simulations Based on Macroscopic Maxwell–Bloch Equations

Jirauschek

Riesch

Tzenov

2019

Advcd Theory and Sims

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Due to their intuitiveness, flexibility, and relative numerical efficiency, the macroscopic Maxwell-Bloch (MB) equations are a widely used semiclassical and semi-phenomenological model to describe optical propagation and coherent light-matter interaction in media consisting of discrete-level quantum systems. This review focuses on the application of this model to advanced optoelectronic devices, such as quantum cascade and quantum dot lasers. The Bloch equations are here treated as a density matrix model for driven quantum systems with two or multiple discrete energy levels, where dissipation is included by Lindblad terms. Furthermore, the 1D MB equations for semiconductor waveguide structures and optical fibers are rigorously derived. Special analytical solutions and suitable numerical methods are presented. Due to the importance of the MB equations in computational electrodynamics, an emphasis is placed on the comparison of different numerical schemes, both with and without the rotating wave approximation. The implementation of additional effects which can become relevant in semiconductor structures, such as spatial hole burning, inhomogeneous broadening, and local-field corrections, is discussed. Finally, links to microscopic models and suitable extensions of the Lindblad formalism are briefly addressed. of a lower bandgap material than the adjacent layers, which restricts the free electron motion in that layer to the in-plane directions and gives rise to quantized energy states in growth direction. As a consequence of the further restriction of the energy spectrum and the even stronger carrier localization, additional improvement can be expected from 2D or 3D confinement, resulting in quantum wire/dash and quantum dot (QD) structures, respectively. Indeed, QD [1][2][3] and quantum dash [4] lasers and laser amplifiers have been shown to exhibit excellent characteristics. In Figure 1, the formation of quantized states in quantum wells, wires, and dots is schematically illustrated. The term quantum dash refers to an elongated nanostructure, that is, some kind of short quantum wire. By contrast, the term nanowire does not necessarily indicate strong quantum confinement. For example, in nanowire lasers, the nanowire geometry typically serves as a single-mode optical waveguide resonator, while the active region is based on a heterostructure or quantum well, as in a conventional laser diode. [5,6] Semiconductor optoelectronic devices usually rely on electron-hole recombination, that is, optical transitions between conduction and valence band states. The associated resonance wavelength is largely determined by the semiconductor bandgap, which establishes a lower bound on the transition energy. Thus, the coverage of a certain spectral region depends on the existence of suitable semiconductor materials, which for example restricts the availability of practical optoelectronic sources and detectors in the mid-infrared and terahertz regions. An alternative concept is based on intersubband devices, which employ so-called i...

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Lindblad Equationmentioning

confidence: 99%

Section: Transverse Electric Modementioning

confidence: 99%

See 2 more Smart Citations

Optoelectronic Device Simulations Based on Macroscopic Maxwell–Bloch Equations

Jirauschek

Riesch

Tzenov

2019

Advcd Theory and Sims

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“…t is completely positive and hence, due to Proposition 2, the tensor product Λ t ⊗ Λ t is positive. Using the Pauli matrix algebra, one reduces the product S µ S ν to the action of single S λ and finds [17].…”

Section: Proposition 1 the Corresponding Map λ T Ismentioning

confidence: 99%

Tensor power of dynamical maps and positive versus completely positive divisibility

2017

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The are several non-equivalent notions of Markovian quantum evolution. In this paper we show that the one based on the so-called CP-divisibility of the corresponding dynamical map enjoys the following stability property: the dynamical map Λt is CP-divisible iff the second tensor power Λt ⊗ Λt is CP-divisible as well. Moreover, the P-divisibility of the map Λt ⊗ Λt is equivalent to the CP-divisibility of the map Λt. Interestingly, the latter property is no longer true if we replace the P-divisibility of Λt ⊗ Λt by simple positivity and the CPdivisibility of Λt by complete positivity. That is, unlike when Λt has a time-independent generator, positivity of Λt ⊗ Λt does not imply complete positivity of Λt.

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Absence of operator growth for average equal-time observables in charge-conserved sectors of the Sachdev-Ye-Kitaev model

Paviglianiti

Bandyopadhyay

Uhrich

et al. 2023

J. High Energ. Phys.

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Quantum scrambling plays an important role in understanding thermalization in closed quantum systems. By this effect, quantum information spreads throughout the system and becomes hidden in the form of non-local correlations. Alternatively, it can be described in terms of the increase in complexity and spatial support of operators in the Heisenberg picture, a phenomenon known as operator growth. In this work, we study the disordered fully-connected Sachdev-Ye-Kitaev (SYK) model, and we demonstrate that scrambling is absent for disorder-averaged expectation values of observables. In detail, we adopt a formalism typical of open quantum systems to show that, on average and within charge-conserved sectors, operators evolve in a relatively simple way which is governed by their operator size. This feature only affects single-time correlation functions, and in particular it does not hold for out-of-time-order correlators, which are well-known to show scrambling behavior. Making use of these findings, we develop a cumulant expansion approach to approximate the evolution of equal-time observables. We employ this scheme to obtain analytic results that apply to arbitrary system size, and we benchmark its effectiveness by exact numerics. Our findings shed light on the structure of the dynamics of observables in the SYK model, and provide an approximate numerical description that overcomes the limitation to small systems of standard methods.

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Effective Dynamics of Disordered Quantum Systems

Cited by 48 publications

References 71 publications

Optoelectronic Device Simulations Based on Macroscopic Maxwell–Bloch Equations

Optoelectronic Device Simulations Based on Macroscopic Maxwell–Bloch Equations

Tensor power of dynamical maps and positive versus completely positive divisibility

Absence of operator growth for average equal-time observables in charge-conserved sectors of the Sachdev-Ye-Kitaev model

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