Counting statistics of non-Markovian quantum stochastic processes

We derive a general expression for the cumulant generating function (CGF) of non-Markovian quantum stochastic transport processes. The long-time limit of the CGF is determined by a single dominating pole of the resolvent of the memory kernel from which we extract the zero-frequency cumulants of the current using a recursive scheme. The finite-frequency noise is expressed not only in terms of the resolvent, but also initial system-environment correlations. As an illustrative example we consider electron transport through a dissipative double quantum dot for which we study the effects of dissipation on the zero-frequency cumulants of high orders and the finite-frequency noise.     

Number-resolved master equation approach to quantum transport under the self-consistent Born approximation

We construct a particle-number(n)-resolved master equation(ME) approach under the self-consistent Born approximation(SCBA) for quantum transport through mesoscopic systems.The formulation is essentially non-Markovian and incorporates the interplay of the multi-tunneling processes and many-body correlations.The proposed n-SCBA-ME goes beyond the scope of the BornMarkov master equation,being applicable to transport under small bias voltage,in non-Markovian regime and with strong Coulomb correlations.For steady state,it can recover not only the exact result of noninteracting transport under arbitrary voltages,but also the challenging nonequilibrium Kondo efect.Moreover,the n-SCBA-ME approach is efcient for the study of shot noise.We demonstrate the application by a couple of representative examples,including particularly the nonequilibrium Kondo system.     

Time-Dependent Dephasing and Quantum Transport

The investigation of the phenomenon of dephasing assisted quantum transport, which happens when the presence of dephasing benefits the efficiency of this process, has been mainly focused on Markovian scenarios associated with constant and positive dephasing rates in their respective Lindblad master equations. What happens if we consider a more general framework, where time-dependent dephasing rates are allowed, thereby, permitting the possibility of non-Markovian scenarios? Does dephasing-assisted transport still manifest for non-Markovian dephasing? Here, we address these open questions in a setup of coupled two-level systems. Our results show that the manifestation of non-Markovian dephasing-assisted transport depends on the way in which the incoherent energy sources are locally coupled to the chain. This is illustrated with two different configurations, namely non-symmetric and symmetric. Specifically, we verify that non-Markovian dephasing-assisted transport manifested only in the non-symmetric configuration. This allows us to draw a parallel with the conditions in which time-independent Markovian dephasing-assisted transport manifests. Finally, we find similar results by considering a controllable and experimentally implementable system, which highlights the significance of our findings for quantum technologies.     

Quantum semi-Markov processes

We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes. General conditions for the complete positivity of the corresponding quantum dynamical maps are formulated. The resulting non-Markovian quantum processes allow the treatment of a variety of physical systems, as is illustrated by means of various examples and applications, including quantum optical systems and models of quantum transport.     

Exact dynamics of a continuous time random walker in the presence of a boundary: beyond the intuitive boundary condition approach

We derive the exact dynamics of a random walker with arbitrary non-Markovian transport and reaction rate distribution at a boundary, and present exact solutions in the continuum limit. We find that the ultimate escape probability of the particle is independent of the transport mechanism in contradiction to the long-standing belief based on the conventional approach. We also find a phase transition in the relaxation kinetics associated with the heterogeneity of the transport media.     

Nonequilibrium Shot Noise Spectrum Through a Quantum Dot in the Kondo Regime:A Master Equation Approach under Self-Consistent Born Approximation

We construct a number(n)-resolved master equation(ME)approach under self-consistent Born approximation(SCBA)for noise spectrum calculation.The formulation is essentially non-Markovian and incorporates properly the interlay of the multi-tunneling processes and many-body correlations.We apply this approach to the challenging nonequilibrium Kondo system and predict a profound nonequilibrium Kondo signature in the shot noise spectrum.The proposed n-SCBA-ME scheme goes completely beyond the scope of the Born-Markovian master equation approach,in the sense of being applicable to the shot noise of transport under small bias voltage,in non-Markovian regime,and with strong Coulomb correlations as favorably demonstrated in the nonequilibrium Kondo system.     

Non-Markovian transmission through two quantum dots connected by a continuum

We consider a transport setup that contains a double-dot connected by a continuum. Via an exact solution of the time-dependent Schrödinger equation, we demonstrate a highly non-Markovian quantum-coherence-mediated transport through this dot–continuum–dot (DCD) system, which is in contrast with the common premise since in typical case a quantum particle does not reenter the system of interest once it irreversibly decayed into a continuum (such as the spontaneous emission of a photon). We also find that this DCD system supports an unusual steady state with unequal source and drain currents, owing to electrons irreversibly entering the continuum and floating there.     

Derivation of non-Markovian transport equations for trapped cold atoms in nonequilibrium thermal field theory

The non-Markovian transport equations for the systems of cold Bose atoms confined by a external potential both without and with a Bose-Einstein condensate are derived in the framework of nonequilibrium thermal field theory (Thermo Field Dynamics). Our key elements are an explicit particle representation and a self-consistent renormalization condition which are essential in thermal field theory. The non-Markovian transport equation for the non-condensed system, derived at the two-loop level, is reduced in the Markovian limit to the ordinary quantum Boltzmann equation derived in the other methods. For the condensed system, we derive a new transport equation with an additional collision term which becomes important in the Landau instability.     

A quantum photonic dissipative transport theory

In this paper, a quantum transport theory for describing photonic dissipative transport dynamics in nanophotonics is developed. The nanophotonic devices concerned in this paper consist of on-chip all-optical integrated circuits incorporating photonic bandgap waveguides and driven resonators embedded in nanostructured photonic crystals. The photonic transport through waveguides is entirely determined from the exact master equation of the driven resonators, which is obtained by explicitly eliminating all the degrees of freedom of the waveguides (treated as reservoirs). Back-reactions from the reservoirs are fully taken into account. The relation between the driven photonic dynamics and photocurrents is obtained explicitly. The non-Markovian memory structure and quantum decoherence dynamics in photonic transport can then be fully addressed. As an illustration, the theory is utilized to study the transport dynamics of a photonic transistor consisting of a nanocavity coupled to two waveguides in photonic crystals. The controllability of photonic transport through the external driven field is demonstrated.     

Quantum statistical effects in nuclear reactions,fission, and open quantum systems

Quantum diffusion equations with time-dependent transport coefficients are derived from generalized non-Markovian Langevin equations. Generalized fluctuation-dissipation relations and analytical formulas for calculating friction and diffusion coefficients in nuclear processes are obtained. The asymptotics of the transport coefficients and of the correlation functions are investigated. The problem of correlation decay in quantum dissipative systems is studied. A comparative analysis of diffusion coefficients for the harmonic and inverted oscillators is performed. The role of quantum statistical effects during passage through a parabolic potential barrier is investigated. Sets of diffusion coefficient assuring the purity of states at any time instant are found in cases of non-Markovian dynamics. The influence of different sets of transport coefficients on the rate of decay from a metastable state is studied in the framework of the master equation for reduced density matrices describing open quantum systems. The approach developed is applied to investigation of fission processes and the processes of projectile-nuclei capture by target nuclei for bombarding energies in the vicinity of the Coulomb barrier. The influence of dissipation and fluctuation on these processes is taken into account in a self-consistent way. The evaporation residue cross sections for asymmetric fusion reactions are calculated from the derived capture probabilities averaged over all orientations of the deformed projectile and target nuclei.     

Entropy Production in Non-Markovian Collision Models: Information Backflow vs. System-Environment Correlations

We investigate the irreversible entropy production of a qubit in contact with an environment modelled by a microscopic collision model in both Markovian and non-Markovian regimes. Our main goal is to contribute to the discussions on the relationship between non-Markovian dynamics and negative entropy production rates. We employ two different types of collision models that do or do not keep the correlations established between the system and the incoming environmental particle, while both of them pertain to their non-Markovian nature through information backflow from the environment to the system. We observe that as the former model, where the correlations between the system and environment are preserved, gives rise to negative entropy production rates in the transient dynamics, the latter one always maintains positive rates, even though the convergence to the steady-state value is slower as compared to the corresponding Markovian dynamics. Our results suggest that the mechanism underpinning the negative entropy production rates is not solely non-Markovianity through information backflow, but rather the contribution to it through established system-environment correlations.     

The squeezing dynamics of two independent atoms by detuning in two non-Markovian environments

The squeezing dynamics of two independent two-level atoms off-resonantly coupled to two non-Markovian reservoirs is studied by the time-convolutionless master-equation approach. We find that the squeezing of two atoms is dependent on both detuning and the non-Markovian effect. Our results show that, in the non-Markovian regime, the bigger the detuning and the stronger the non-Markovian effect are, the larger the strength of the squeezing is. And the squeezing of two atoms can be effectively protected for a long time when both the non-Markovian effect and detuning are present simultaneously. The physical mechanism is that the detuning not only can promote the feedback of information from the environment into the atomic system but also can greatly suppress the atomic decay in the non-Markovian regime.     

Non-Markovian dynamics of a qubit in a reservoir: different solutions of non-Markovian master equation

We present a non-Markovian master equation for a qubit interacting with a general reservoir, which is derived according to the Nakajima-Zwanzig and the time convolutionless projection operator technique. The non-Markovian solutions and Markovian solution of dynamical decay of a qubit are compared. The results indicate the validity of non-Markovian approach in different coupling regimes and also show that the Markovian master equation may not precisely describe the dynamics of an open quantum system in some situation. The non-Markovian solutions may be effective for many qubits independently interacting with the heated reservoirs.     

二能级系统的马尔可夫与非马尔可夫方法比较

分别用马尔可夫与非马尔可夫方法推导出二能级系统与库相互作用的耗散动力学,并把失谐谱密度与一个光子带隙的谱密度下的计算结果与精确解进行比较。对于失谐谱密度,分别讨论在马尔可夫与非马尔可夫库的激发态布居数,发现无论是短时的弱耦合区域,还是长时间的强耦合区域,非马尔可夫方法比马尔可夫方法更加接近精确解,而马尔可夫近似主要适用于弱耦合条件;对于光子带隙谱密度,主要考虑了小带宽的布居数,结果显示马尔可夫方法主要适用于弱耦合条件,而非马尔可夫方法主要适用于强耦合情形。结果表明:对于不同谱密度、不同的耦合区域,只有选择合适的马尔可夫或非马尔可夫方法才能精确描述系统的动力学。     

Regression law and the renormalization of the transport coefficients

Using Mazur's lemma we show that the coarse-grained variables used in nonequilibrium statistical mechanics are the Onsager's regression variables. With this result we find a regression law for the fluctuations which is both non-Markovian and nonlinear. Considering the Markovian approximation and generalizing Onsager's ideas leading to the symmetry of the transport matrix, we formulate Mori and Fujisaka's method for the renormalization of transport coefficients due to nonlinear interactions.     

Non-Markovian effects in plasma hydrodynamics

A microscopic theory of the linearized plasma hydrodynamical equations is presented and important non-Markovian effects on the plasma transport coefficients are revealed.     

Non-Markovian quantum jumps

Open quantum systems that interact with structured reservoirs exhibit non-Markovian dynamics. We present a quantum jump method for treating the dynamics of such systems. This approach is a generalization of the standard Monte Carlo wave function (MCWF) method for Markovian dynamics. The MCWF method identifies decay rates with jump probabilities and fails for non-Markovian systems where the time-dependent rates become temporarily negative. Our non-Markovian quantum jump approach circumvents this problem and provides an efficient unraveling of the ensemble dynamics.     

Non-markovian continuous quantum measurement of retarded observables

We reconsider the non-Markovian time-continuous measurement of a Heisenberg observable x[over ] and show for the first time that it can be realized by an infinite set of entangled von Neumann detectors. The concept of continuous readout is introduced and used to rederive the non-Markovian stochastic Schr?dinger equation. We can prove that, contrary to recent doubts, the resulting non-Markovian quantum trajectories are true single system trajectories and correspond to the continuous measurement of a retarded functional of x[over ].     

Coulomb blockade and hopping transport behaviors of donor-induced quantum dots in junctionless transistors

The ionized dopants, working as quantum dots in silicon nanowires, exhibit potential advantages for the development of atomic-scale transistors. We investigate single electron tunneling through a phosphorus dopant induced quantum dots array in heavily n-doped junctionless nanowire transistors. Several subpeaks splittings in current oscillations are clearly observed due to the coupling of the quantum dots at the temperature of 6 K. The transport behaviors change from resonance tunneling to hoping conduction with increased temperature. The charging energy of the phosphorus donors is approximately 12.8 meV. This work helps clear the basic mechanism of electron transport through donor-induced quantum dots and electron transport properties in the heavily doped nanowire through dopant engineering.