arXiv subjects

Fei Liu

Publications and source records attributed to Fei Liu.

At least 325 records · Page 18Linked to original sources

arXiv2015

Recursive Sweeping Preconditioner for the 3D Helmholtz Equation

This paper introduces the recursive sweeping preconditioner for the numerical solution of the Helmholtz equation in 3D. This is based on the earlier work of the sweeping preconditioner with the moving perfectly matched layers (PMLs). The key idea is to apply the sweeping preconditioner recursively to the quasi-2D auxiliary problems introduced in the 3D sweeping preconditioner. Compared to the non-recursive 3D sweeping preconditioner, the setup cost of this new approach drops from $O(N^{4/3})$ to $O(N)$, the application cost per iteration drops from $O(N\log N)$ to $O(N)$, and the iteration count only increases mildly when combined with the standard GMRES solver. Several numerical examples are tested and the results are compared with the non-recursive sweeping preconditioner to demonstrate the efficiency of the new approach.

math.NA↗

arXiv2014

Calculating work in adiabatic two-level quantum Markovian master equations: A characteristic function method

We present a characteristic function method to calculate the probability density functions of the inclusive work in the adiabatic two-level quantum Markovian master equations. These systems are steered by some slowly varying parameters and the dissipations may depend on time. Our theory is based on the interpretation of the quantum jump for the master equations. In addition to the calculation, we also find that the fluctuation properties of the work can be described by the symmetry of the characteristic functions, which is exactly the same as the case of the isolated systems. A periodically driven two-level model is used to show the method.

cond-mat.stat-mech↗

arXiv2014

Generalized integral fluctuation relation with feedback control for diffusion processes

We extend a generalized integral fluctuation relation in diffusion processes that we obtained previously to the situation with feedback control. The general relation not only covers existing results but also predicts other unnoticed fluctuation relations. In addition, we find that its explanation of time-reversal automatically emerges in the derivation. This interesting observation leads into an alternative inequality about the entropy-like quantity with an improved lower bound. Two feedback-controlled Brownian models are used to verify the result.

cond-mat.stat-mech↗

arXiv2014

Equivalence of two Bochkov-Kuzovlev equalities in quantum two-level systems

We present two kinds of Bochkov-Kuzovlev work equalities in a two-level system that is described by a quantum Markovian master equation. One is based on multiple time correlation functions and the other is based on the quantum trajectory viewpoint. We show that these two equalities are indeed equivalent. Importantly, this equivalence provides us a way to calculate the probability density function of the quantum work by solving the evolution equation for its characteristic function. We use a numerical model to verify these results.

cond-mat.stat-mech↗

arXiv2014

Nonequilibrium work equalities in isolated quantum systems

We briefly introduce the quantum Jarzynski and Bochkov-Kuzovlev equalities in isolated quantum Hamiltonian systems, which includes the origin of the equalities, their derivations using a quantum Feynman-Kac formula, the quantum Crooks equality, the evolution equations governing the characteristic functions of the probability density functions for the quantum work, the recent experimental verifications. Some results are given here first time. We particularly emphasize the formally structural consistence between these quantum equalities and their classical counterparts, which shall be useful in understanding the existing equalities and pursuing new fluctuation relations in other complex quantum systems.

cond-mat.stat-mech↗

arXiv2013

Pocket doping method on Improving the Performance of Graphene Nanoribbons Tunneling FET

A tunneling field effect transistor based on armchair graphene nanoribbons is studied using ballistic quantum transport simulation based on 3D real space nonequilibrium Green's function formalism. By introducing a pocket doping region near the source, the performance of GNRs TFET is improved in terms of larger on current and steeper subthreshold swings compared to conventional tunneling FET. It is also found that pocket region introduces two interesting features. By increasing the pocket length the ambipolar can be effectively suppressed. Furthermore, there is negative trans-conductance at negative gate voltage due to resonance.

cond-mat.mes-hall↗

arXiv2013

Improved Performance of Tunneling FET Based on Hetero Graphene Nanoribbons

A heterojunction tunneling field effect transistor based on armchair graphene nanoribbons is proposed and studied using ballistic quantum transport simulation based on 3D real space nonequilibrium Green's function formalism. By using low band gap nanoribbons as the source/drain material, the hetero- structure shows better performance including higher on current, lower off current, and improved steep subthreshold swings compared with homostructure. It is also found the device performance greatly depends on the source/drain dopping density. High doping density leads to fewer density states in the source and degrades the device performance.

cond-mat.mes-hall↗

arXiv2012

Operator equality on entropy production in quantum Markovian master equations

An operator equality on the entropy production for general quantum Markovian master equations is derived without resorting quantum stochastic trajectory and priori quantum definition of entropy production. We find that, the equality can be still interpreted as a consequence of time-reversal asymmetry of the nonequilibrium processes of the systems. In contrast with the classical case, however, the first order expansion of the equality does not directly related to the mean entropy production, which arises from noncommute property of operators in quantum physics.

cond-mat.stat-mech↗

arXiv2012

A Bayesian model averaging approach for observational gene expression studies

Identifying differentially expressed (DE) genes associated with a sample characteristic is the primary objective of many microarray studies. As more and more studies are carried out with observational rather than well controlled experimental samples, it becomes important to evaluate and properly control the impact of sample heterogeneity on DE gene finding. Typical methods for identifying DE genes require ranking all the genes according to a preselected statistic based on a single model for two or more group comparisons, with or without adjustment for other covariates. Such single model approaches unavoidably result in model misspecification, which can lead to increased error due to bias for some genes and reduced efficiency for the others. We evaluated the impact of model misspecification from such approaches on detecting DE genes and identified parameters that affect the magnitude of impact. To properly control for sample heterogeneity and to provide a flexible and coherent framework for identifying simultaneously DE genes associated with a single or multiple sample characteristics and/or their interactions, we proposed a Bayesian model averaging approach which corrects the model misspecification by averaging over model space formed by all relevant covariates. An empirical approach is suggested for specifying prior model probabilities. We demonstrated through simulated microarray data that this approach resulted in improved performance in DE gene identification compared to the single model approaches. The flexibility of this approach is demonstrated through our analysis of data from two observational microarray studies.

stat.AP↗

arXiv2012

Operator perturbation theory in the backward Heisenberg picture

We present a simple operator perturbation theory in the backward Heisenberg picture. Compared with the well-known Heisenberg picture, the revised picture is based on the backward time instead of the forward time. The unique feature of the uncommon picture is that the perturbation expansion becomes very simple and the famous Dyson expansion is not directly involved. Its relationship with the perturbation expansion for the density operator developed by Kubo is also discussed.

quant-ph↗

arXiv2012

Derivation of quantum work equalities using quantum Feynman-Kac formula

On the basis of a quantum mechanical analogue of the famous Feynman-Kac formula and the Kolmogorov picture, we present a novel method to derive nonequilibrium work equalities for isolated quantum systems, which include the Jarzynski equality and Bochkov-Kuzovlev equality. Compared with previous methods in the literature, our method shows higher similarity in form to that deriving the classical fluctuation relations, which would give important insight when exploring new quantum fluctuation relations.

cond-mat.stat-mech↗

arXiv2011

Splitting rate matrix as a definition of time reversal in master equation systems

Motivated by recent progresses in nonequilibrium Fluctuation Relations, we present a generalized time reversal for stochastic master equation systems with discrete states that is defined as a splitting of the rate matrix into irreversible and reversible parts. An immediate advantage of this definition is that a variety of fluctuation relations can be attributed to different matrix splitting. Additionally, we also find that, the accustomed total entropy production formula and conditions of the detailed balance must be modified appropriately to account for the presence of the reversible part, which was completely ignored in the past a long time.

cond-mat.stat-mech↗

arXiv2010

Effect of Spatial Charge Inhomogeneity on 1/f Noise Behavior in Graphene

Scattering mechanisms in graphene are critical to understanding the limits of signal-to-noise-ratios of unsuspended graphene devices. Here we present the four-probe low frequency noise (1/f) characteristics in back-gated single layer graphene (SLG) and bilayer graphene (BLG) samples. Contrary to the expected noise increase with the resistance, the noise for SLG decreases near the Dirac point, possibly due to the effects of the spatial charge inhomogeneity. For BLG, a similar noise reduction near the Dirac point is observed, but with a different gate dependence of its noise behavior. Some possible reasons for the different noise behavior between SLG and BLG are discussed.

cond-mat.mes-hall↗

arXiv2009

Linear response theory and transient fluctuation theorems for diffusion processes: a backward point of view

On the basis of perturbed Kolmogorov backward equations and path integral representation, we unify the derivations of the linear response theory and transient fluctuation theorems for continuous diffusion processes from a backward point of view. We find that a variety of transient fluctuation theorems could be interpreted as a consequence of a generalized Chapman-Kolmogorov equation, which intrinsically arises from the Markovian characteristic of diffusion processes.

cond-mat.stat-mech↗

arXiv2009

Broadband Radio Spectral Observations of Solar Eclipse on 2008-08-01 and Implications on the Quiet Sun Atmospheric Model

Based on the joint-observations of the radio broadband spectral emissions of solar eclipse on August 1, 2008 at Jiuquan (total eclipse) and Huairou (partial eclipse) at the frequencies of 2.00 -- 5.60 GHz (Jiuquan), 2.60 -- 3.80 GHZ (Chinese solar broadband radiospectrometer, SBRS/Huairou), and 5.20 -- 7.60 GHz (SBRS/Huairou), the authors assemble a successive series of broadband spectrum with a frequency of 2.60 -- 7.60 GHz to observe the solar eclipse synchronously. This is the first attempt to analyze the solar eclipse radio emission under the two telescopes located at different places with broadband frequencies in the periods of total and partial eclipse. With these analyses, the authors made a new semiempirical model of the coronal plasma density of the quiet Sun and made a comparison with the classic models.

astro-ph.SR↗

arXiv2009

A generalized integral fluctuation theorem for general jump processes

Using the Feynman-Kac and Cameron-Martin-Girsanov formulas, we obtain a generalized integral fluctuation theorem (GIFT) for discrete jump processes by constructing a time-invariable inner product. The existing discrete IFTs can be derived as its specific cases. A connection between our approach and the conventional time-reversal method is also established. Different from the latter approach that was extensively employed in existing literature, our approach can naturally bring out the definition of a time-reversal of a Markovian stochastic system. Additionally, we find the robust GIFT usually does not result into a detailed fluctuation theorem.

cond-mat.stat-mech↗

arXiv2009

Response delay as a strategy for survival in fluctuating environment

Response time-delay is an ubiquitous phenomenon in biological systems. Here we use a simple stochastic population model with time-delayed switching-rate conversion to quantitatively study the biological influence of the response time-delay on the survival fitness of cells living in periodically fluctuating and stochastic environment, respectively. Our calculation and simulation show that for the cells having a slow rate transition into fit phenotype and a fast rate transition into unfit phenotype, the response time-delay can always enhance their fitness during the environment change. Particularly, in the periodic or stochastic environment with small variance, the optimal fitness achieved by these cells is superior to that of cells with reverse switching rates even if the latter exhibits rapid response. These results suggest that the response time delay may be utilized by cells to enhance their adaptation to the fluctuating environment.

q-bio.PE↗

arXiv2009

A generalized integral fluctuation theorem for diffusion processes

We present a generalized integral fluctuation theorem (GIFT) for general diffusion processes using the Feynman-Kac and Cameron-Martin-Girsanov formulas. Existing IFTs can be thought of to be its specific cases. We interpret the origin of this theorem in terms of time-reversal of stochastic systems.

cond-mat.stat-mech↗