在開放性量子系統中，系統和外在環境之間的交互作用可以用許多理論模型的方法來描述。透過對環境的自由度取跡（trace out），我們可因此得知約化（reduced）系統的動力學並研究外加環境的對其產生的效應。

在本論文中，我們利用多種互補的理論方法來探討開放性量子系統。在這些例子中，我們分析在微擾範疇(perturbative regime)和非微擾範疇裡系統與環境的交互作用。除此之外，我們也探討系統與環境之間的關聯性如何影響可觀測量，並建立這些關聯性與可測量特徵之間的定量關係。

在論文的第一個部分，我們考慮的模型是一個含有雜訊通道的馬克斯威爾惡魔熱引擎。透過計算該引擎的平均取功量，我們觀察到時間關聯性可以增強它的表現。為了降低通道雜訊的影響，我們採用了量子疊加通道方法—由多個量子通道和一個可以決定系統路徑的額外控制系統所組成。為此我們提出了一個熱引擎包含了兩個馬克斯威爾惡魔，並在雲端量子電腦上執行對應的量子電路，結果與雜訊模擬相符，證實了量子通道疊加可以有效抑制雜訊的影響。

在論文的第二個部分，我們探討記憶效應對等待時間分布（waiting time distribution）的影響。我們考慮由一個量子點與兩個費米環境耦合的單一雜質安德森模型。這兩個費米環境中，其中一個可以展現非馬可夫效應，另一個則只能展示馬可夫效應。為了捕捉非馬可夫環境產生的非微擾效應，我們使用了融合玻恩-馬可夫主方程式和分層運動方程式(HEOM)的混合方法計算等待時間分布的數值並做傅立葉分析。除此之外，我們套用了偽費米子(pseudofermion)方法以更深入理解其背後的物理圖像及其機制。從我們的分析中，記憶效應如: 非馬可夫效應和近藤效應會在等待時間分布裡產生短時間的震盪。除此之外，調變能讓記憶效應增強之參數的同時，我們發現也能增強震盪行為。這顯示等待時間分布可以當作探測記憶效應的潛在工具。

In open quantum systems, system–environment interactions can be modeled using various theoretical frameworks. By tracing out the environmental degrees of freedom, one can obtain the dynamics of the reduced system and investigate the effects by the external bath.

In this thesis, we explore open quantum systems using complementary theoretical approaches. Among these cases, we analyze the system-bath interactions ranging from the perturbative to the nonperturbative regime. Furthermore, we investigate how system–environment correlations influence observable quantities and establish quantitative links between these correlations and measurable signatures.

In the first part, we consider a Maxwell's demon heat engine under a noisy channel. By calculating the average extracted work, we show that temporal quantum correlations can enhance engine performance. To reduce the noise influenced by the quantum channel, we utilize the superposition of quantum channels, which is composed of multiple quantum channels placed in parallel with an additional control system deciding the path for the system. We further introduce the heat engine assisted by two Maxwell's demons and implement the corresponding quantum circuits on cloud quantum computers. The results agree with noise simulations, confirming that the noise effects are suppressed due to the superposed quantum channels.

In the second part, we investigate the influence of the memory effects on waiting time distribution (WTD). We consider the single impurity Anderson model, which consists of a quantum dot coupled to two fermionic baths, one of which is Markovian and the other is non-Markovian. To capture the nonperturbative effects from the non-Markovian bath, we apply the hybrid approach combining the Born-Markov master equation with the hierarchical equations of motion (HEOM) to compute the WTD numerically and perform Fourier analysis. Furthermore, we employ a toy model using the pseudofermion method to gain deeper physical insight. From our analysis, the memory effects, e.g., the non-Markovian effect and the Kondo resonance, lead to short-time oscillations in the waiting time distribution. In addition, enhancing the memory effects by tuning the relevant parameters strengthens these oscillatory features. This indicates that the WTD can serve as a probe of memory effects.

[1] Chan, F.-J. et al. Maxwell's two-demon engine under pure dephasing noise. Phys. Rev. A 106, 052201 (2022).
[2] Chan, F.-J., Kuo, P.-C., Lambert, N., Cirio, M. & Chen, Y.-N. Revealing non-Markovian Kondo transport with waiting time distributions. Phys. Rev. Res. 7, 033270 (2025).
[3] Breuer, H.-P. & Petruccione, F. The Theory of Open Quantum Systems (Oxford University Press on Demand, New York, 2002).
[4] Weiss, U. Quantum Dissipative Systems. G - Reference, Information and Interdisciplinary Subjects Series (World Scientific, 2012).
[5] Rivas, Á. & Huelga, S. F. Open Quantum Systems (Springer, Berlin, 2012).
[6] de Vega, I. & Alonso, D. Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017).
[7] Kraus, K., Böhm, A., Dollard, J. D. & Wootters, W. H. (eds.) States, Effects, and Operations Fundamental Notions of Quantum Theory (Springer Berlin, Heidelberg, 1983).
[8] Tanimura, Y. & Kubo, R. Time Evolution of a Quantum System in Contact with a Nearly Gaussian-Markoffian Noise Bath. J. Phys. Soc. Jpn. 58, 101-114 (1989).
[9] Tanimura, Y. Numerically “exact” approach to open quantum dynamics: The hierarchical equations of motion (heom). The Journal of Chemical Physics 153 (2020).
[10] Cirio, M. et al. Pseudofermion method for the exact description of fermionic environments: From single-molecule electronics to the Kondo resonance. Phys. Rev. Res. 5, 033011 (2023).
[11] Scully, M. O., Chapin, K. R., Dorfman, K. E., Kim, M. B. & Svidzinsky, A. Quantum heat engine power can be increased by noise-induced coherence. Proc. Natl. Acad. Sci. U.S.A. 108, 15097–15100 (2011).
[12] Rahav, S., Harbola, U. & Mukamel, S. Heat fluctuations and coherences in a quantum heat engine. Phys. Rev. A 86, 043843 (2012).
[13] Brunner, N. et al. Entanglement enhances cooling in microscopic quantum refrigerators. Phys. Rev. E 89, 032115 (2014).
[14] Mitchison, M. T., Woods, M. P., Prior, J. & Huber, M. Coherence-assisted single-shot cooling by quantum absorption refrigerators. New J. Phys. 17, 115013 (2015).
[15] Chen, S.-L. et al. Quantifying Non-Markovianity with Temporal Steering. Phys. Rev. Lett. 116, 020503 (2016).
[16] Brandner, K., Bauer, M. & Seifert, U. Universal Coherence-Induced Power Losses of Quantum Heat Engines in Linear Response. Phys. Rev. Lett. 119, 170602 (2017).
[17] Manzano, G., Plastina, F. & Zambrini, R. Optimal Work Extraction and Thermodynamics of Quantum Measurements and Correlations. Phys. Rev. Lett. 121, 120602 (2018).
[18] Woods, M. P., Ng, N. H. Y. & Wehner, S. The maximum efficiency of nano heat engines depends on more than temperature. Quantum 3, 177 (2019).
[19] Niedenzu, W., Huber, M. & Boukobza, E. Concepts of work in autonomous quantum heat engines. Quantum 3, 195 (2019).
[20] Horne, N. V. et al. Single-atom energy-conversion device with a quantum load. npj Quantum Inf. 6 (2020).
[21] Gluza, M. et al. Quantum field thermal machines. PRX Quantum 2, 030310 (2021).
[22] Son, J., Talkner, P. & Thingna, J. Monitoring Quantum Otto Engines. PRX Quantum 2, 040328 (2021).
[23] Lu, Y. et al. Steady-State Heat Transport and Work With a Single Artificial Atom Coupled to a Waveguide: Emission Without External Driving. PRX Quantum 3, 020305 (2022).
[24] Funo, K., Watanabe, Y. & Ueda, M. Thermodynamic work gain from entanglement. Phys. Rev. A 88, 052319 (2013).
[25] Skrzypczyk, P., Short, A. J. & Popescu, S. Work extraction and thermodynamics for individual quantum systems. Nat. Commun. 5 (2014).
[26] Alhambra, A. M., Masanes, L., Oppenheim, J. & Perry, C. Fluctuating work: From quantum thermodynamical identities to a second law equality. Phys. Rev. X 6, 041017 (2016).
[27] Elouard, C., Herrera-Martí, D., Huard, B. & Auffèves, A. Extracting Work from Quantum Measurement in Maxwell's Demon Engines. Phys. Rev. Lett. 118, 260603 (2017).
[28] Morris, B., Lami, L. & Adesso, G. Assisted Work Distillation. Phys. Rev. Lett. 122, 130601 (2019).
[29] Allahverdyan, A. E. Nonequilibrium quantum fluctuations of work. Phys. Rev. E 90, 032137 (2014).
[30] Talkner, P. & Hänggi, P. Aspects of quantum work. Phys. Rev. E 93, 022131 (2016).
[31] Lostaglio, M., Alhambra, Á. M. & Perry, C. Elementary thermal operations. Quantum 2, 52 (2018).
[32] Schrödinger, E. Discussion of probability relations between separated systems. Math. Proc. Camb. Philos. Soc. 31, 555–563 (1935).
[33] Wiseman, H. M., Jones, S. J. & Doherty, A. C. Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox. Phys. Rev. Lett. 98, 140402 (2007).
[34] Cavalcanti, D. & Skrzypczyk, P. Quantum steering: a review with focus on semidefinite programming. Rep. Prog. Phys. 80, 024001 (2016).
[35] Uola, R., Costa, A. C. S., Nguyen, H. C. & Gühne, O. Quantum steering. Rev. Mod. Phys. 92, 015001 (2020).
[36] Xiang, Y., Cheng, S., Gong, Q., Ficek, Z. & He, Q. Quantum steering: Practical challenges and future directions. PRX Quantum 3, 030102 (2022).
[37] Beyer, K., Luoma, K. & Strunz, W. T. Steering Heat Engines: A Truly Quantum Maxwell Demon. Phys. Rev. Lett. 123, 250606 (2019).
[38] Ji, W. et al. Spin Quantum Heat Engine Quantified by Quantum Steering. Phys. Rev. Lett. 128, 090602 (2022).
[39] Knott, C. G. Life and Scientific Work of Peter Guthrie Tait (Cambridge University Press, 1911).
[40] Leggett, A. J. & Garg, A. Quantum Mechanics versus Macroscopic Realism: Is the Flux There when Nobody Looks? Phys. Rev. Lett. 54, 857 (1985).
[41] Joarder, K., Saha, D., Home, D. & Sinha, U. Loophole-free interferometric test of macrorealism using heralded single photons. PRX Quantum 3, 010307 (2022).
[42] Ku, H.-Y., Hsieh, C.-Y., Chen, S.-L., Chen, Y.-N. & Budroni, C. Complete classification of steerability under local filters and its relation with measurement incompatibility. Nat. Commun. 13, 4973 (2022).
[43] Vieira, L. B. & Budroni, C. Temporal correlations in the simplest measurement sequences. Quantum 6, 623 (2022).
[44] Maity, A. G., Mal, S., Jebarathinam, C. & Majumdar, A. S. Self-testing of binary Pauli measurements requiring neither entanglement nor any dimensional restriction. Phys. Rev. A 103, 062604 (2021).
[45] Chen, Y.-N. et al. Temporal steering inequality. Phys. Rev. A 89, 032112 (2014).
[46] Li, C.-M., Chen, Y.-N., Lambert, N., Chiu, C.-Y. & Nori, F. Certifying single-system steering for quantum-information processing. Phys. Rev. A 92, 062310 (2015).
[47] Ku, H.-Y., Chen, S.-L., Lambert, N., Chen, Y.-N. & Nori, F. Hierarchy in temporal quantum correlations. Phys. Rev. A 98, 022104 (2018).
[48] Lin, J.-D. et al. Quantum steering as a witness of quantum scrambling. Phys. Rev. A 104, 022614 (2021).
[49] Guérin, P. A., Feix, A., Araújo, M. & Brukner, Č. Exponential Communication Complexity Advantage from Quantum Superposition of the Direction of Communication. Phys. Rev. Lett. 117, 100502 (2016).
[50] Chiribella, G. & Kristjánsson, H. Quantum Shannon theory with superpositions of trajectories. Proc. R. Soc. A 475, 20180903 (2019).
[51] Abbott, A. A., Wechs, J., Horsman, D., Mhalla, M. & Branciard, C. Communication through coherent control of quantum channels. Quantum 4, 333 (2020).
[52] Kristjánsson, H., Chiribella, G., Salek, S., Ebler, D. & Wilson, M. Resource theories of communication. New J. Phys. 22, 073014 (2020).
[53] Ban, M. Two-qubit correlation in two independent environments with indefiniteness. Phys. Lett. A. 385, 126936 (2021).
[54] Rubino, G. et al. Experimental quantum communication enhancement by superposing trajectories. Phys. Rev. Res. 3, 013093 (2021).
[55] Lin, J.-D. et al. Space-time dual quantum zeno effect: Interferometric engineering of open quantum system dynamics. Phys. Rev. Res. 4, 033143 (2022).
[56] Lee, K.-Y. et al. Steering-enhanced quantum metrology using superpositions of quantum channels. arXiv:2206.03760 (2022).
[57] IBM Quantum Services. https://quantum-computing.ibm.com/services?services=systems&system. [May. 2022].
[58] Berke, C., Varvelis, E., Trebst, S., Altland, A. & DiVincenzo, D. P. Transmon platform for quantum computing challenged by chaotic fluctuations. Nat. Commun. 13 (2022).
[59] Strikis, A., Qin, D., Chen, Y., Benjamin, S. C. & Li, Y. Learning-based quantum error mitigation. PRX Quantum 2, 040330 (2021).
[60] Branciard, C., Cavalcanti, E. G., Walborn, S. P., Scarani, V. & Wiseman, H. M. One-sided device-independent quantum key distribution: Security, feasibility, and the connection with steering. Phys. Rev. A 85, 010301(R) (2012).
[61] Yadin, B., Fadel, M. & Gessner, M. Metrological complementarity reveals the Einstein-Podolsky-Rosen paradox. Nat. Commun. 12, 2410 (2021).
[62] Zhao, Y.-Y. et al. Experimental demonstration of measurement-device-independent measure of quantum steering. npj Quantum Inf. 6, 77 (2020).
[63] Slussarenko, S. et al. Quantum steering with vector vortex photon states with the detection loophole closed. npj Quantum Inf. 8 (2022).
[64] Sagnol, G. & Stahlberg, M. PICOS: A Python interface to conic optimization solvers. J. Open Source Softw. 7, 3915 (2022).
[65] Stinespring, W. F. Positive functions on C∗-algebras. Proc. Amer. Math. Soc. 6, 211–216 (1955).
[66] Wilde, M. M. Preface to the Second Edition (Cambridge University Press, 2017), 2 edn.
[67] Gallego, R. & Aolita, L. Resource theory of steering. Phys. Rev. X 5, 041008 (2015).
[68] Nery, R. V. et al. Distillation of Quantum Steering. Phys. Rev. Lett. 124, 120402 (2020).
[69] Gupta, S., Das, D. & Majumdar, A. S. Distillation of genuine tripartite Einstein-Podolsky-Rosen steering. Phys. Rev. A 104, 022409 (2021).
[70] Ku, H.-Y. et al. Experimental test of non-macrorealistic cat states in the cloud. npj Quantum Inf. 6, 98 (2020).
[71] Huang, Y.-T., Lin, J.-D., Ku, H.-Y. & Chen, Y.-N. Benchmarking quantum state transfer on quantum devices. Phys. Rev. Res. 3, 023038 (2021).
[72] Magesan, E., Gambetta, J. M. & Emerson, J. Scalable and Robust Randomized Benchmarking of Quantum Processes. Phys. Rev. Lett. 106, 180504 (2011).
[73] Magesan, E., Gambetta, J. M. & Emerson, J. Characterizing quantum gates via randomized benchmarking. Phys. Rev. A 85, 042311 (2012).
[74] Urbanek, M. et al. Mitigating Depolarizing Noise on Quantum Computers with Noise-Estimation Circuits. Phys. Rev. Lett. 127, 270502 (2021).
[75] Figueroa-Romero, P., Modi, K., Harris, R. J., Stace, T. M. & Hsieh, M.-H. Randomized Benchmarking for Non-Markovian noise. PRX Quantum 2, 040351 (2021).
[76] Davies, E. Quantum Theory of Open Systems (Academic Press, London, 1976).
[77] Carmichael, H. An Open Systems Approach to Quantum Optics (Springer, Berlin, 1991).
[78] Breuer, H.-P. & Petruccione, F. The Theory of Open Quantum Systems (Oxford University Press, New York, 2007).
[79] Liu, B.-H. et al. Experimental control of the transition from Markovian to non-Markovian dynamics of open quantum systems. Nat. Phys. 7, 931–934 (2011).
[80] Zhang, W.-M., Lo, P.-Y., Xiong, H.-N., Tu, M. W.-Y. & Nori, F. General Non-Markovian Dynamics of Open Quantum Systems. Phys. Rev. Lett. 109, 170402 (2012).
[81] Xiong, H.-N., Lo, P.-Y., Zhang, W.-M., Feng, D. H. & Nori, F. Non-Markovian Complexity in the Quantum-to-Classical Transition. Sci. Rep. 5, 13353 (2015).
[82] Breuer, H.-P., Laine, E.-M., Piilo, J. & Vacchini, B. Colloquium: Non-Markovian dynamics in open quantum systems. Rev. Mod. Phys. 88, 021002 (2016).
[83] Wolf, M. M., Eisert, J., Cubitt, T. S. & Cirac, J. I. Assessing Non-Markovian Quantum Dynamics. Phys. Rev. Lett. 101, 150402 (2008).
[84] Breuer, H.-P., Laine, E.-M. & Piilo, J. Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems. Phys. Rev. Lett. 103, 210401 (2009).
[85] Laine, E.-M., Piilo, J. & Breuer, H.-P. Measure for the non-Markovianity of quantum processes. Phys. Rev. A 81, 062115 (2010).
[86] Liu, F., Zhou, X. & Zhou, Z.-W. Memory effect and non-Markovian dynamics in an open quantum system. Phys. Rev. A 99, 052119 (2019).
[87] Braggio, A., König, J. & Fazio, R. Full Counting Statistics in Strongly Interacting Systems: Non-Markovian Effects. Phys. Rev. Lett. 96, 026805 (2006).
[88] Flindt, C., Novotný, T., Braggio, A., Sassetti, M. & Jauho, A.-P. Counting Statistics of Non-Markovian Quantum Stochastic Processes. Phys. Rev. Lett. 100, 150601 (2008).
[89] Schaller, G., Kießlich, G. & Brandes, T. Transport statistics of interacting double dot systems: Coherent and non-Markovian effects. Phys. Rev. B 80, 245107 (2009).
[90] Moreira, S. V. et al. Enhancing quantum transport efficiency by tuning non-Markovian dephasing. Phys. Rev. A 101, 012123 (2020).
[91] Bellomo, B., Lo Franco, R. & Compagno, G. Non-Markovian Effects on the Dynamics of Entanglement. Phys. Rev. Lett. 99, 160502 (2007).
[92] Rivas, Á., Huelga, S. F. & Plenio, M. B. Entanglement and Non-Markovianity of quantum evolutions. Phys. Rev. Lett. 105, 050403 (2010).
[93] Cialdi, S., Brivio, D., Tesio, E. & Paris, M. G. A. Programmable entanglement oscillations in a non-Markovian channel. Phys. Rev. A 83, 042308 (2011).
[94] Huelga, S. F., Rivas, Á. & Plenio, M. B. Non-Markovianity-Assisted Steady State Entanglement. Phys. Rev. Lett. 108, 160402 (2012).
[95] Xu, J.-S. et al. Experimental recovery of quantum correlations in absence of system-environment back-action. Nat. Commun. 4, 2851 (2013).
[96] Orieux, A. et al. Experimental on-demand recovery of entanglement by local operations within non-Markovian dynamics. Sci Rep 5, 8575 (2015).
[97] Kouwenhoven, L. & Glazman, L. Revival of the Kondo effect. Phys. World 14, 33-38 (January 2001).
[98] Tu, N. H. et al. Electrical control of a Kondo spin screening cloud. 2404.11955.
[99] Cho, S. Y. & McKenzie, R. H. Quantum entanglement in the two-impurity Kondo model. Phys. Rev. A 73, 012109 (2006).
[100] Amico, L., Fazio, R., Osterloh, A. & Vedral, V. Entanglement in many-body systems. Rev. Mod. Phys. 80, 517–576 (2008).
[101] Affleck, I., Laflorencie, N. & Sørensen, E. S. Entanglement entropy in quantum impurity systems and systems with boundaries. J. Phys. A: Math. Theor. 42, 504009 (2009).
[102] Lee, S.-S. B., Park, J. & Sim, H.-S. Macroscopic Quantum Entanglement of a Kondo Cloud at Finite Temperature. Phys. Rev. Lett. 114, 057203 (2015).
[103] Wagner, C., Chowdhury, T., Pixley, J. H. & Ingersent, K. Long-Range Entanglement near a Kondo-Destruction Quantum Critical Point. Phys. Rev. Lett. 121, 147602 (2018).
[104] Kim, D., Shim, J. & Sim, H.-S. Universal Thermal Entanglement of Multichannel Kondo Effects. Phys. Rev. Lett. 127, 226801 (2021).
[105] Kuo, P.-C. et al. Kondo QED: The Kondo effect and photon trapping in a two-impurity Anderson model ultrastrongly coupled to light. Phys. Rev. Res. 5, 043177 (2023).
[106] Cohen, G. & Rabani, E. Memory effects in nonequilibrium quantum impurity models. Phys. Rev. B 84, 075150 (2011).
[107] Bruch, V., Pletyukhov, M., Schoeller, H. & Kennes, D. M. Floquet renormalization group approach to the periodically driven Kondo model. Phys. Rev. B 106, 115440 (2022).
[108] Cao, L. et al. Simulating Non-Markovian Open Quantum Dynamics with Neural Quantum States (2024). 2404.11093v2.
[109] Vanhoecke, M. & Schirò, M. Kondo-zeno crossover in the dynamics of a monitored quantum dot. Nat. Commun. 16, 6155 (2025).
[110] Sprinzak, D., Ji, Y., Heiblum, M., Mahalu, D. & Shtrikman, H. Charge Distribution in a Kondo-Correlated Quantum Dot. Phys. Rev. Lett. 88, 176805 (2002).
[111] Avinun-Kalish, M., Heiblum, M., Silva, A., Mahalu, D. & Umansky, V. Controlled Dephasing of a Quantum Dot in the Kondo Regime. Phys. Rev. Lett. 92, 156801 (2004).
[112] Pustilnik, M. & Glazman, L. Kondo effect in quantum dots. J. Phys. Condens. Matter 16, R513 (2004).
[113] Keller, A. J. et al. Emergent SU(4) Kondo physics in a spin–charge-entangled double quantum dot. Nat. Phys. 10, 145–150 (2014).
[114] Le Hur, K. Quantum dots and the Kondo effect. Nature 526, 203–204 (2015).
[115] Shang, R.-N. et al. Direct observation of the orbital spin Kondo effect in gallium arsenide quantum dots. Phys. Rev. B 97, 085307 (2018).
[116] Brandes, T. Waiting times and noise in single particle transport. Ann. Phys (Berlin) 520, 477–496 (2008).
[117] Welack, S., Esposito, M., Harbola, U. & Mukamel, S. Interference effects in the counting statistics of electron transfers through a double quantum dot. Phys. Rev. B 77, 195315 (2008).
[118] Welack, S., Mukamel, S. & Yan, Y. Waiting time distributions of electron transfers through quantum dot Aharonov-Bohm interferometers. Europhys. Lett. 85, 57008 (2009).
[119] Welack, S. & Yan, Y. Non-Markovian theory for the waiting time distributions of single electron transfers. J. Chem. Phys. 131, 114111 (2009).
[120] Thomas, K. H. & Flindt, C. Electron waiting times in non-Markovian quantum transport. Phys. Rev. B 87, 121405(R) (2013).
[121] Tang, G.-M., Xu, F. & Wang, J. Waiting time distribution of quantum electronic transport in the transient regime. Phys. Rev. B 89, 205310 (2014).
[122] Sothmann, B. Electronic waiting-time distribution of a quantum-dot spin valve. Phys. Rev. B 90, 155315 (2014).
[123] Talbo, V., Mateos, J., Retailleau, S., Dollfus, P. & González, T. Timedependent shot noise in multi-level quantum dot-based single-electron devices. Semicond. Sci. Technol. 30, 055002 (2015).
[124] Rudge, S. L. & Kosov, D. S. Distribution of residence times as a marker to distinguish different pathways for quantum transport. Phys. Rev. E 94, 042134 (2016).
[125] Rudge, S. L. & Kosov, D. S. Distribution of tunnelling times for quantum electron transport. J. Chem. Phys. 144, 124105 (2016).
[126] Ptaszyński, K. Nonrenewal statistics in transport through quantum dots. Phys. Rev. B 95, 045306 (2017).
[127] Rudge, S. L. & Kosov, D. S. Distribution of waiting times between electron cotunneling events. Phys. Rev. B 98, 245402 (2018).
[128] Stegmann, P., König, J. & Weiss, S. Coherent dynamics in stochastic systems revealed by full counting statistics. Phys. Rev. B 98, 035409 (2018).
[129] Kleinherbers, E., Stegmann, P. & König, J. Revealing attractive electron–electron interaction in a quantum dot by full counting statistics. New J. Phys. 20, 073023 (2018).
[130] Tang, G., Xu, F., Mi, S. & Wang, J. Spin-resolved electron waiting times in a quantum-dot spin valve. Phys. Rev. B 97, 165407 (2018).
[131] Rudge, S. L. & Kosov, D. S. Nonrenewal statistics in quantum transport from the perspective of first-passage and waiting time distributions. Phys. Rev. B 99, 115426 (2019).
[132] Kleinherbers, E., Stegmann, P. & König, J. Synchronized coherent charge oscillations in coupled double quantum dots. Phys. Rev. B 104, 165304 (2021).
[133] Stegmann, P., Sothmann, B., König, J. & Flindt, C. Electron Waiting Times in a Strongly Interacting Quantum Dot: Interaction Effects and Higher-Order Tunneling Processes. Phys. Rev. Lett. 127, 096803 (2021).
[134] Fu, W., Ke, S.-S., Guo, Y., Zhang, H.-W. & Lü, H.-F. Waiting time distribution and current correlations via a Majorana single-charge transistor. Phys. Rev. B 106, 075404 (2022).
[135] Gorman, S. K. et al. Tunneling statistics for analysis of spin-readout fidelity. Phys. Rev. Appl. 8, 034019 (2017).
[136] Jenei, M. et al. Waiting time distributions in a two-level fluctuator coupled to a superconducting charge detector. Phys. Rev. Res. 1, 033163 (2019).
[137] Brange, F. et al. Controlled emission time statistics of a dynamic single-electron transistor. Sci. Adv. 7, eabe0793 (2021).
[138] Ranni, A., Brange, F., Mannila, E. T., Flindt, C. & Maisi, V. F. Real-time observation of Cooper pair splitting showing strong non-local correlations. Nat. Commun. 12, 6358 (2021).
[139] Bayer, J. C. et al. Real-time Detection and Control of Correlated Charge Tunneling in a Quantum Dot. Phys. Rev. Lett. 134, 046303 (2025).
[140] Hu, J., Xu, R.-X. & Yan, Y. Communication: Padé spectrum decomposition of Fermi function and Bose function. J. Chem. Phys. 133, 101106 (2010).
[141] Huang, Y.-T. et al. An efficient Julia framework for hierarchical equations of motion in open quantum systems. Commun. Phys 6, 313 (2023).
[142] Li, Z. H. et al. Hierarchical Liouville-Space Approach for Accurate and Universal Characterization of Quantum Impurity Systems. Phys. Rev. Lett. 109, 266403 (2012).
[143] Lambert, N. et al. QuTiP-BoFiN: A bosonic and fermionic numerical hierarchical-equations-of-motion library with applications in light-harvesting, quantum control, and single-molecule electronics. Phys. Rev. Res. 5, 013181 (2023).
[144] Lin, J.-D. et al. Non-Markovian quantum exceptional points. Nat. Commun. 16, 1289 (2025).
[145] Beaudoin, F., Gambetta, J. M. & Blais, A. Dissipation and ultrastrong coupling in circuit QED. Phys. Rev. A 84, 043832 (2011).
[146] Rajabi, L., Pöltl, C. & Governale, M. Waiting Time Distributions for the Transport through a Quantum-Dot Tunnel Coupled to One Normal and One Superconducting Lead. Phys. Rev. Lett. 111, 067002 (2013).
[147] Wrzésniewski, K. & Weymann, I. Current cross-correlations and waiting time distributions in Andreev transport through Cooper pair splitters based on a triple quantum dot system. Phys. Rev. B 101, 155409 (2020).
[148] Roch, N., Florens, S., Costi, T. A., Wernsdorfer, W. & Balestro, F. Observation of the Underscreened Kondo effect in a Molecular Transistor. Phys. Rev. Lett. 103, 197202 (2009).
[149] Cirio, M., Kuo, P. C., Chen, Y. N., Nori, F. & Lambert, N. Canonical derivation of the fermionic influence superoperator. Phys. Rev. B 105, 035121 (2022).
[150] Costi, T. A. Kondo Effect in a Magnetic Field and the Magnetoresistivity of Kondo Alloys. Phys. Rev. Lett. 85, 1504–1507 (2000).
[151] Liang, W., Shores, M. P., Bockrath, M., Long, J. R. & Park, H. Kondo resonance in a single-molecule transistor. Nature 417, 725 (2002).
[152] Zhang, Y.-h. et al. Temperature and magnetic field dependence of a Kondo system in the weak coupling regime. Nat. Commun. 4, 2110 (2013).
[153] Nagaoka, K., Jamneala, T., Grobis, M. & Crommie, M. F. Temperature Dependence of a Single Kondo Impurity. Phys. Rev. Lett. 88, 077205 (2002).
[154] Cheng, Y. et al. Time-dependent transport through quantum-impurity systems with Kondo resonance. New J. Phys. 17, 033009 (2015).
[155] Shiono, H. et al. Temperature dependence of the Kondo resonance peak in photoemission spectra of YbCdCu4. AIP Conf. Proc. 2054, 040013 (2019).
[156] Schäfer, S. Anderson impurity model with a narrow-band host: From orbital physics to the Kondo effect. Phys. Rev. B 83, 195110 (2011).
[157] Allub, R. & Proetto, C. R. Hybrid quantum dot–superconducting systems: Josephson current and Kondo effect in the narrow-band limit. Phys. Rev. B 91, 045442 (2015).
[158] Shen, S. et al. Inducing and tuning Kondo screening in a narrow-electronic-band system. Nat. Commun. 13, 2156 (2022).
[159] Kourris, C. & Vojta, M. Kondo screening and coherence in kagome localmoment metals: Energy scales of heavy fermions in the presence of flat bands. Phys. Rev. B 108, 235106 (2023).
[160] Tran, M.-T. & Nguyen, T. T. Molecular Kondo effect in flat-band lattices. Phys. Rev. B 97, 155125 (2018).
[161] Allub, R. & Proetto, C. R. Anderson model out of equilibrium: Zero-bandwidth limit. Phys. Rev. B 62, 10923 (2000).
[162] Brange, F., Menczel, P. & Flindt, C. Photon counting statistics of a microwave cavity. Phys. Rev. B 99, 085418 (2019).
[163] Kleinherbers, E., Schünemann, A. & König, J. Full counting statistics in a Majorana single-charge transistor. Phys. Rev. B 107, 195407 (2023).
[164] Schinabeck, C. & Thoss, M. Hierarchical quantum master equation approach to current fluctuations in nonequilibrium charge transport through nanosystems. Phys. Rev. B 101, 075422 (2020).
[165] Gurvitz, S. A. Rate equations for quantum transport in multidot systems. Phys. Rev. B 57, 6602–6611 (1998).