F. Hassler, M. V. Suslov, G. M. Graf, M. V. Lebedev, G. B. Lesovik, G. Blatter
备注：
20 pages, 5 figures; major update, new figures and explanations included as well as a discussion about finite temperatures and subleading logarithmic terms
We make use of the first-quantized wave-packet formulation of the full counting statistics to describe charge transport of noninteracting electrons in a mesoscopic device. We derive various expressions for the characteristic function generating the full counting statistics, accounting for both energy and time dependence in the scattering process and including exchange effects due to finite overlap of the incoming wave packets. We apply our results to describe the generic statistical properties of a two-fermion scattering event and find, among other features, sub-binomial statistics for nonentangled incoming states (Slater rank 1), while entangled states (Slater rank 2) may generate super-binomial (and even super-Poissonian) noise, a feature that can be used as a spin singlet-triplet detector. Another application is concerned with the constant-voltage case, where we generalize the original result of Levitov-Lesovik to account for energy-dependent scattering and finite measurement time, including short time measurements, where Pauli blocking becomes important.
The coherent potential approximation (CPA) within full counting statistics (FCS) formalism is shown to be a suitable method to investigate average electric conductance, shot noise as well as higher order cumulants in disordered systems. We develop a similar FCS-CPA formalism for phonon transport through disordered systems. As a byproduct, we derive relations among coefficients of different phonon current cumulants. We apply the FCS-CPA method to investigate phonon transport properties of graphene systems in the presence of disorders. For binary disorders as well as Anderson disorders, we calcu…
We have investigated the role of pseudospin polarization in electron wave packet dynamics in pristine graphene and in a graphene antidot lattice subject to an external magnetic field. Employing a Green's function formalism, we show that the electron dynamics can be controlled by tuning pseudospin polarization. We find that in Landau quantized pristine graphene both the propagation of an electron wave packet and Zitterbewegung oscillations strongly depend on pseudospin polarization. The electron wave packet is found to propagate in the direction of initial pseudospin polarization. We also show …
The scattering theory of electron transport allows for a compact and powerful description in terms of $\check{g}^2 = 1$ Green functions, so-called circuit theory of quantum transport. A scatterer in the theory is characterized by an action, most generally a Keldysh one, that can be further used as a building bock of theories describing statistics of electron transport, superconducting correlations, time-dependent and interaction effects. The action is usually used in the form suitable for a two-terminal scatterer. Here we provide a comprehensive derivation of a more general form of the action …
We report the investigation of full-counting statistics (FCS) of transferred charge and spin in the transient regime where the connection between central scattering region (quantum dot) and leads are turned on at $t=0$. A general theoretical formulation for the generating function (GF) is presented using a nonequilibrium Green's function approach for the quantum dot system. In particular, we give a detailed derivation on how to use the method of path integral together with nonequilibrium Green's function technique to obtain the GF of FCS in electron transport systems based on the two-time quan…
We formulate a full-counting statistics description to study energy exchange in multi-terminal junctions. Our approach applies to quantum systems that are coupled either additively or non-additively (cooperatively) to multiple reservoirs. We derive a Markovian Redfield-type equation for the counting-field dependent reduced density operator. Under the secular approximation, we confirm that the cumulant generating function satisfies the heat exchange fluctuation theorem. Our treatment thus respects the second law of thermodynamics. We exemplify our formalism on a multi-terminal two-level quantum…
We develop a non-Markovian full counting statistics formalism taking into account both the sequential tunneling and cotunneling based on the exact particle number resolved time-convolutionless master equation and the Rayleigh-Schrödinger perturbation theory. Then, we study the influences of the quantum coherence and the cotunneling assisted sequential tunneling processes on the non-Markovian full counting statistics of electron tunneling through an open quantum system, which consists of a side-coupled double-quantum-dot molecule weakly coupled to two electron reservoirs. We demonstrate that in…
The Stationary Phase Method for a Wave Packet in a Semiconductor Layered System. The applicability of the method
使用Bohm在他的书{ \em“量子理论“}中所做的形式分析，Dover Publications Inc. New York（1979），为了近似地计算通过势垒的透射和反射波包的相位时间，我们计算了由不同介观层形成的半导体系统的相位时间。对透射波包和反射波包进行了分析，并根据波包的平稳相位，讨论了该方法在不同情况下的适用性。对于固定相位法的适用性，在仅取决于相位的导数的透射波的情况下，得到一个表达式，直到三阶。该条件指示系统的参数是否允许通过其前导项来定义波包。一个多屏障系统的情况下显示的结果的说明。这种形式包括使用传递矩阵来描述中心层，无论它是由一个层（单势垒情况）形成的，还是由两个势垒和一个内阱（DBRT系统）形成的，但是可以假设该层可以包括任何数量或任何种类的半导体层。
A general formalism for computing the full counting statistics of energy exchanged between 'N' squeezed thermal photon reservoirs weakly coupled to a cavity with 'M' photon modes is presented. The formalism is based on the two-point measurement scheme and is applied to two simple special cases, the relaxation dynamics of a single mode cavity in contact with a single squeezed thermal photon reservoir and the steady-state energy transport between two squeezed thermal photon reservoirs coupled to a single cavity mode. Using analytical results, it is found that the short time statistics is signifi…
We demonstrate that the probability distribution of the net number of electrons passing through a quantum system in a junction obeys a steady-state fluctuation theorem (FT) which can be tested experimentally by the full counting statistics (FCS) of electrons crossing the lead-system interface. The FCS is calculated using a many-body quantum master equation (QME) combined with a Liouville space generating function (GF) formalism. For a model of two coupled quantum dots, we show that the FT becomes valid for long binning times and provide an estimate for the finite-time deviations. We also demon…
The theory of full counting statistics allows complete characterization of charge transport processes through nanoscale systems. The majority of existing theoretical treatments used to obtain the current cumulants rely on perturbative approximations with respect to either the system-bath coupling or the electronic tunnelling coupling within the system. This is not generally well suited to electron transfer through organic molecules where these couplings can be on the same order of magnitude. Here we present a non-perturbative approach that uses the formalism of the hierarchical equations of mo…
Non-Hermitian wave-packet dynamics and its realization within a non-Hermitian chiral cavity
School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）；Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院吴文裕量子中心）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Shanghai Branch, Hefei National Laboratory（合肥国家实验室上海分部）
We consider a bipartite quantum conductor and analyze fluctuations of heat quantity in a subsystem as well as self-information associated with the reduced-density matrix of the subsystem. By exploiting the multi-contour Keldysh technique, we calculate the Rényi entropy, or the information generating function, subjected to the constraint of the local heat quantity of the subsystem, from which the probability distribution of conditional self-information is derived. We present an equality that relates the optimum capacity of information transmission and the Rényi entropy of order 0, which is the …
Quantum Dynamics of Full Counting Statistics in Fermionic Lattices with Localized Gain
Indian Institute of Science Education and Research Pune（印度科学教育研究所浦那分校）；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础研究院国际理论科学中心）
