To convincingly demonstrate the functioning of cMPS to- mographic tools applied to **quantum** **transport** experiments, we presented a simple example that consists of electrons tun- nelling through a single-level **quantum** dot. Making use of ex- perimental data, we showed that we could successfully recon- struct the distribution of waiting times from the measurement of the two-point correlation function only. This work consti- tutes therefore a significant step towards accessing the wait- ing time distribution in the **quantum** regime experimentally, a challenge present for several years now. Importantly, the ap- plication of our reconstruction procedure goes beyond the in- terest in waiting time distributions: It also provides an access to higher-order correlation functions, which are key quantities to better understand interacting **quantum** systems.

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Here, we carry out numerically exact calculations of infinite one-dimensional disordered systems over the entire regime of dephasing within the HSR model. In section 2.1 **quantum** master equations are derived for the time evolution of the density matrix in the limiting regimes of weak and strong dephasing. These results allow for analytical estimates of the diffusion constant and provide an intuitive physical description of the underlying dynamics. For large dephasing, it is well known that any coherences created during the evolution are quickly destroyed and the diffusion proceeds by way of classical hopping between sites [ 34 , 35 ]. In the opposite regime of weak dephasing, the exact eigenstates of the system are accurately approximated by those of the disordered system Hamiltonian, and coherent **quantum** **transport** proceeds via hopping through the eigenstates. This is the regime of phonon-assisted hopping discussed in the early studies of the conductivity of disordered solids [ 36 ]. These analytical arguments coupled with the exact numerical calculations lead to several interesting features in the exciton dynamics:

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1 Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 2 Centre for **Quantum** Technologies, National University of Singapore, 117543 Singapore
(Received 23 December 2014; accepted 7 April 2015; published online 24 April 2015)
**Quantum** **transport** in disordered systems is studied using a polaron-based master equation. The polaron approach is capable of bridging the results from the coherent band-like **transport** regime governed by the Redfield equation to incoherent hopping **transport** in the classical regime. A non-monotonic dependence of the di ffusion coefficient is observed both as a function of temperature and system-phonon coupling strength. In the band-like **transport** regime, the di ffusion coefficient is shown to be linearly proportional to the system-phonon coupling strength and vanishes at zero coupling due to Anderson localization. In the opposite classical hopping regime, we correctly recover the dynamics described by the Fermi’s Golden Rule and establish that the scaling of the di ffusion coe fficient depends on the phonon bath relaxation time. In both the hopping and band-like **transport** regimes, it is demonstrated that at low temperature, the zero-point fluctuations of the bath lead to non-zero **transport** rates and hence a finite di ffusion constant. Application to rubrene and other organic semiconductor materials shows a good agreement with experimental mobility data. C 2015 AIP

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To accurately determine **quantum** **transport** properties of gated DBWs or, in fact, any semiconductor nanostructures, ﬁ rst-principles methods face three main challenges. First, density functional theory (DFT) at local density approximation (LDA) or generalized gradient approximation (GGA) levels can not correctly determine band gaps, 29 making the calculated results questionable at these levels of theory. Second, experimentally it is shown 1 , 21 that a DB interacts with its surroundings up to a distance of ∼16 Å, which demands systems with large number of atoms for ﬁrst-principles calculations. Third, experimental systems contain randomly distributed impurity dopant atoms, which in principle requires one to obtain disorder conﬁguration average of any calculated quantity. To the best of our knowledge, these theoretical challenges have not been overcome before. In our work, we meet these challenges by using a state-of-the-art ﬁrst-principles approach where DFT is carried out within the nonequilibrium Green’s function (NEGF) formalism. Our NEGF-DFT method Received: October 1, 2016

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In many cases, another intrinsic limitation came from the ﬁnite bulk-carrier conductivity, often dominating the conduc- tance in 3D TI ﬁlms. An elegant way to overcome this issue and to evidence the existence of TSS was found by studying **quantum** coherent **transport** in 3D TI NWs and revealing their contribution to well-de ﬁned Aharonov–Bohm oscillations of the magnetoresistance, by applying a magnetic ﬁeld along the axis of the nanostructure. [5] Aharonov –Bohm oscillations are directly related to the **quantum** con ﬁnement of surface Dirac fermions in the NW cross section, thus leading to a ﬂux-tunable quantized band structure that strongly differs from that of bulk carriers, and **quantum** **transport** measurements indeed became a powerful tool to investigate the speci ﬁc physics of TSS in 3D TI **quantum** wires. In such nanostructures, all surface modes lose their topological protection, but for one mode that becomes gapless if half of a ﬂux **quantum** is applied. [4] Therefore, in a NW geom- etry, all modes are partially re ﬂected at the interface between

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2 Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA 共Received 14 June 2010; published 23 November 2010兲
We present an efficient and accurate computational approach to study phase-coherent **quantum** **transport** in molecular and nanoscale electronics. We formulate a Green’s-function method in the recently developed ab initio nonorthogonal quasiatomic orbital basis set within the Landauer-Büttiker formalism. These quasiatomic orbitals are efficiently and robustly transformed from Kohn-Sham eigenwave functions subject to the maximal atomic-orbital similarity measure. With this minimal basis set, we can easily calculate electrical conductance using Green’s-function method while keeping accuracy at the level of plane-wave density-functional theory. Our approach is validated in three studies of two-terminal electronic devices, in which projected density of states and conductance eigenchannel are employed to help understand microscopic mechanism of **quantum** **transport**. We first apply our approach to a seven-carbon atomic chain sandwiched between two finite cross- sectioned Al 共001兲 surfaces. The emergence of gaps in the conductance curve originates from the selection rule with vanishing overlap between symmetry-incompatible conductance eigenchannels in leads and conductor. In the second application, a 共4,4兲 single-wall carbon nanotube with a substitutional silicon impurity is investi- gated. The complete suppression of transmission at 0.6 eV in one of the two conductance eigenchannels is attributed to the Fano antiresonance when the localized silicon impurity state couples with the continuum states of carbon nanotube. Finally, a benzene-1,4-dithiolate molecule attached to two Au 共111兲 surfaces is considered. Combining fragment molecular orbital analysis and conductance eigenchannel analysis, we demonstrate that conductance peaks near the Fermi level result from resonant tunneling through molecular orbitals of benzene- 1,4-dithiolate molecule. In general, our conductance curves agree very well with previous results obtained using localized basis sets while slight difference is observed near the Fermi level and conductance edges. DOI: 10.1103/PhysRevB.82.195442 PACS number 共s兲: 73.63.⫺b, 71.15.Ap, 73.22.⫺f

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agation along **quantum** Hall edge states 3–5 and terahertz
measurements in carbon nanotubes 6 . While the mathe-
matical framework for describing **quantum** **transport** in the time domain has been around since the 90s 7,8 , the corresponding non-equilibrium Green’s function formal- ism (NEGF) is rather cumbersome and can only be solved in rather simple situations, even with the help of numer- ics. In Ref. 9 we developed an alternative formulation of the theory which is much easier to solve numerically, in addition to being more physically transparent. The approach of Ref. 9 (to which we refer for further refer- ences) was recently used in a variety of situations includ- ing electronic interferometers 10,11 , **quantum** Hall effect 12 ,

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In many applications, the performance of the device will depend on the possibility of controlling the electrons by acting on the gate voltage.
At the nanometer scale, **quantum** effects such as interferences or tunneling become important and a **quantum** **transport** model is necessary. In this paper, we analyze the controllability of a simplified mathematical model of the **quantum** **transport** of electrons trapped in a two-dimensional device, typically a MOS field-effect transistor. The problem is modeled by a single Schr¨odinger equation, in a bounded domain Ω with homogeneous Dirichlet boundary conditions, coupled to the Poisson equation for the electrical potential. This work is a first step towards more realistic models. For instance, throughout the paper, the self-consistent potential modeling interactions between electrons is either neglected, or (in the last section of the paper) considered as a small perturbation of the applied potential.

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Closeness of bands in vicinity of the Fermi level as compared with those from VASP conrms the appropriateness of adopted ASAs for subsequent zero bias transport calculations.. The corre[r]

For simplicity yet still captures the essentials, in what follows we discuss a three-level QCL design with two wells per module as shown in Fig. 1 共Refs. 22 and 23 兲 in which
level 1 ⬘ is the injector state and the radiative transition is from level 3 →2. Even though typically QCL designs in- clude many more levels per period, the results obtained here hold for the triplet of levels consisting of the injector level and the two radiative levels 关levels 1 ⬘ , 3, and 2 in Fig. 1共b兲 兴, regardless of a particular design, and including the mid-IR designs. Due to the various intrasubband and intersubband scattering mechanisms that contribute to **quantum** **transport**, the electron wave packets undergo dephasing, which mani- fests itself as broadening of the energy levels. The tunnel coupling between the levels of the same module is strong, therefore, dephasing has a relatively negligible effect on the intramodule intersubband **transport**. 16 However, the inter-

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Büttiker[21, 19, 86].
Dynamical **transport** for electronic optic experiments and **quantum** computation using ying qu-bits
From that, one can ask if the large coherence lengths and ballistic trajectories of electrons in such devices could be used in order to perform the experiments of **quantum** optics, such as Hong-Ou-Mandel[63] or Bell's inequality[6] experiments. Indeed, the fermionic nature of electron make their emission one-per-one easier, in principle, than photons used in **quantum** optics which tend to be emitted by packets[42]. Moreover, the possibility of controlling electrons through the Coulomb interaction is of a great interest for **quantum** computation, by using "ying qu-bits" where the information is coded on the electronic trajectories[64][95]. But how manipulate only one electron among billions in a crystal? This major diculty has been overcame in the nineties with the rst manipulation of unique charges, performed into a serie of metallic islands, where the Coulomb blockade allows to transfer electron one-per-one[51, 102]. Another approach is to use the piezo- electric properties of the GaAs in order to generate Surface Acoustic Waves (SAW), which create a moving potential for electrons in a depleted 1D wire. It enables to transfer an electron above the Fermi sea from a **quantum** dot to another[61, 89]. An important step forward for the implementation of ying qu-bits was the realisation of coherent electron sources by injecting an electron just above the Fermi sea in a **quantum** wire. The rst has been realized in 2007[41] thanks to a mesoscopic capacitor playing the role of a **quantum** dot[46], which injects an electron at a well dened energy above the Fermi sea. Another idea is to use voltage pulses for the injection of a leviton, a single charge wavepacket with a Lorentzian shape for which the extra electron-hole excitations created when an arbitrary voltage is applied on the lead of a **quantum** wire[74] are cancelled. This has been experimentally demonstrated in our group[37] and we discuss below about the perspectives explored in this thesis. Thanks to these coherent electron sources, it has been possible to perform the electron tomography and Hong-Ou-Mandel experiments [70, 71, 12]. In parallel, the framework has been built thanks to the theoretical study of the dynamic of **quantum** **transport** in coherent ballistic conductors [16, 24, 27, 25, 20, 1, 110] and stimulates numerical simulations, for instance the study of the propagation of time- resolved pulses in **quantum** wires [49, 50].

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We have investigated **quantum** dots formed in silicon nanowire metal-oxide-semiconductor field-effect transis- tors (MOSFETs), fabricated using a microelectronics technology based on 300 mm silicon-on-insulator (SOI) wafers. The low-temperature electronic conductance prop- erties of such devices have been extensively studied in previous works [24 –32] , showing very robust Coulomb blockade characteristics. We performed conductance, current, and shot noise measurements in several small-size ( ≈20 × 30 × 10 nm) p-type devices using the setup described in Fig. 2 , at a temperature of 0.3 K in a cryogen-free He-3 refrigerator. We measure the excess shot noise S II in the **quantum** dot with a cross-correlation

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4.1 Sorting CQD solids
As we showed in the previous chapter, one strategy to maintain the highest charge carrier mobility in CQD solids could involve synthesizing monodisperse CQDs or nar- rowing the size dispersion from the as-synthesized polydisperse CQDs before deposit- ing into active layers. However, achieving perfectly monodisperse CQDs is currently unrealistic given the hot-injection methods used in CQD synthesis and lack of eﬃcient nanometer scale filtration methods, although recent work reported a ⇠ 5% size dis- persion; [92] even in this case our calculations show that 40% of the potential electron mobility is lost. Furthermore, several types of CQD systems including III-V compos- ites inherently have diﬃculties in being prepared with small size dispersion [93] due to their unique synthesis process. [94] Another approach to achieve eﬃcient charge **transport** in CQD films could be to redesign the CQD configurations within the film even though considerable size dispersion exists in the as-synthesized colloidal CQDs. While computational approaches allow for any distribution of CQDs to be tested, here we adopt ones that may be practically realized, such as a film possessing a gradient of colloidal CQD radii in diﬀerent directions: vertical (in the electric field) or horizontal (perpendicular to the electric field).

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ground-state spin-orbit splitting. Since one has to employ rather large basis sets (triple-ζ quality) to get a meaningful result, they again are not true FCI calculations, but FCI calculations in a limited CAS. The first one corresponds to a CAS composed of two electrons in the highest occupied (π 1/2 ) and the lowest unoccupied (π3/2) Kramers pairs [CAS(2,2)]. After the factorization of a Hamiltonian according to the **quantum** number and taking into account only one of the two degenerate z projections of (for = 1), the size of the CI space is 2 for the ground state (0 + ) and 1 for the excited state (1). The excited state is therefore trivial and the calculation of the ground state is in fact a complete analog of the already mentioned NR computations [ 14 , 15 ], because it needs just one qubit for the wave function (two in total). The controlled single-qubit gate can be decomposed using two controlled NOT

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I. STATEMENT OF THE PROBLEM AND RESULT
A **quantum** particle in a random potential can move diffusively, ballistically, or superbal- listically depending on the circumstances. In this note, we derive some results about the mean square displacement of a **quantum** particle subject to a time-dependent white-noise Gaussian potential V ω (x, t) that is correlated in space and uncorrelated in time. We prove

The paper deals with the nonequilibrium two-lead Anderson model, considered as an adequate description for **transport** through a dc biased **quantum** dot. Using a self-consistent equation-of-motion method generalized out of equilibrium, we calculate a fourth-order decoherence rate ␥ 共4兲 induced by a bias voltage V. This decoherence rate provides a cutoff to the infrared divergences of the self-energy showing up in the Kondo regime. At low temperature, the Kondo peak in the density of states is split into two peaks pinned at the chemical potential of the two leads. The height of these peaks is controlled by ␥ 共4兲 . The voltage dependence of the differential conductance exhibits a zero-bias peak followed by a broad Coulomb peak at large V, reflecting charge fluctuations inside the dot. The low-bias differential conductance is found to be a universal function of the normalized bias voltage V /T K , where T K is the Kondo temperature of the model, which has been improved in comparison with previous approaches. The universal scaling with a single energy scale T K at low-bias voltages is also observed for the renormalized decoherence rate ␥ 共4兲 /T K . We discuss the effect of ␥ 共4兲 on the crossover from strong- to weak-coupling regime when either the temperature or the bias voltage is increased.

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Finally, to consistently interpret all the experimental observed data from three independent measurements, we propose a model specially designed for the 2D perovskite system where a vertically stacked **quantum** well is present throughout the ﬁlm thickness. Based on that, we conduct theoretical device modeling to interpret all the data consistently as demonstrated in Fig. 5 . Figure 5 a schematically illustrates the energy band landscaped, reﬂecting the fact in a layered 2D perovskite **quantum** well sys- tem. Unlike the conventional **quantum** wells where wide band gap materials are stacked in a layer-by-layer fashion out of plane, in our case, those **quantum** wells are stacked vertically as demonstrated by our previous work 2 . Even though the thin ﬁlms were grown with preferred vertical out-of-plane direction, the slight mismatch and imperfect crystal packing in thin ﬁlms (in comparison to single crystals) manifests as potential barriers created by the partially intercepting organic spacers between conducting inorganic slabs that could interrupt the **transport** pathway (Fig. 5 i). This band diagram thus identiﬁes two types of

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second paper ( Curcio et al., 2018 ), the noncovalent proteins surface interactions were accurately evaluated by a **quantum** and molecular mechanics approach. This ab initio modeling allowed defining the actual structure of the first layer of adsorbed proteins and the equilibrium distance among them. In this way, a physical limit to both the volume fraction and the additional resistance, as due to adsorbed macromolecules, was rigorously calculated. However, in these papers ( De Luca et al., 2014; Curcio et al., 2018 ; Petrosino et al., 2019 ) only the interactions between a lim ited number of macromolecules and the surface was analyzed. Nevertheless, the methods used to simulate the phenomena in mesoscopic and macroscopic scales were founded on a major assumption: the formation of the protein deposit layers towards the bulk, in fact, was simulated through a force balance written with reference to a specific protein packing symmetry that yielded a compactly ordered cake. Although, the noncovalent proteins surface interactions were accurately evaluated by a **quantum** and molecular mechanics approach ( De Luca et al., 2014; Curcio et al., 2018 ) and, as a result, the structure of the first layer of pro teins adsorbed on membrane surface was obtained by calculating the equilibrium distance between them, a body centered cubic structure symmetry was assumed. A physical limit for both the vol ume fraction and the additional resistance, as due to either the compact or the loose proteins deposit, was rigorously calculated presuming that this symmetry held also for the loose layers.

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Much less investigated is the effect of magnetic field, see Fig. 1, on the coupling between electronic **transport** and mechanical oscillations (called magneto-elastic cou- pling hereafter). This coupling is at the origin of the mag- netomotive effect, which has been used to activate and detect the classical motion of micro and nano-mechanical resonators since a long time. However its manifestation in the **quantum** regime has been addressed only recently for a suspended carbon nanotube forming a **quantum** dot. 23–26 A particularly appealing interpretation of the

The method we propose is a **quantum** version of the Poincar´e section/Poincar´e map construction used to analyze the classical flow (see §1). Namely, around some scattering energy E > 0 we will construct a **quantum** transfer operator (or **quantum** monodromy operator), which contains the relevant information of the **quantum** dynamics at this energy, in a much reduced form: this operator has finite rank (which increases in the semiclassical limit), it allows to characterize the **quantum** resonances of the scattering system in the vicinity of the energy E. The **quantum** transfer operator is very similar with the open **quantum** maps studied as toy models for chaotic scattering [4, 19, 24].

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