Heuristic derivation of continuum kinetic equations from microscopic dynamics

We present an approximate and heuristic scheme for the derivation of continuum kinetic equations from microscopic dynamics for stochastic, interacting systems. The method consists of a mean-field type, decoupled approximation of the master equation followed by the `naive' continuum limit. The Ising model and driven diffusive systems are used as illustrations. The equations derived are in agreement with other approaches, and consequences of the microscopic dependences of coarse-grained parameters compare favorably with exact or high-temperature expansions. The method is valuable when more systematic and rigorous approaches fail, and when microscopic inputs in the continuum theory are desirable.Comment: 7 pages, RevTeX, two-column, 4 PS figures include

Unification of bulk and interface electroresistive switching in oxide systems

We demonstrate that the physical mechanism behind electroresistive switching in oxide Schottky systems is electroformation, as in insulating oxides. Negative resistance shown by the hysteretic current-voltage curves proves that impact ionization is at the origin of the switching. Analyses of the capacitance-voltage and conductance-voltage curves through a simple model show that an atomic rearrangement is involved in the process. Switching in these systems is a bulk effect, not strictly confined at the interface but at the charge space region.Comment: 4 pages, 3 figures, accepted in PR

Logarithmic perturbation theory for quasinormal modes

Logarithmic perturbation theory (LPT) is developed and applied to quasinormal modes (QNMs) in open systems. QNMs often do not form a complete set, so LPT is especially convenient because summation over a complete set of unperturbed states is not required. Attention is paid to potentials with exponential tails, and the example of a Poschl-Teller potential is briefly discussed. A numerical method is developed that handles the exponentially large wavefunctions which appear in dealing with QNMs.Comment: 24 pages, 4 Postscript figures, uses ioplppt.sty and epsfig.st

Eigenvector Expansion and Petermann Factor for Ohmically Damped Oscillators

Correlation functions $C(t) \sim$ in ohmically damped systems such as coupled harmonic oscillators or optical resonators can be expressed as a single sum over modes $j$ (which are not power-orthogonal), with each term multiplied by the Petermann factor (PF) $C_j$, leading to "excess noise" when $|C_j| > 1$. It is shown that $|C_j| > 1$ is common rather than exceptional, that $|C_j|$ can be large even for weak damping, and that the PF appears in other processes as well: for example, a time-independent perturbation \sim\ep leads to a frequency shift \sim \ep C_j. The coalescence of $J$ ($>1$) eigenvectors gives rise to a critical point, which exhibits "giant excess noise" ($C_j \to \infty$). At critical points, the divergent parts of $J$ contributions to $C(t)$ cancel, while time-independent perturbations lead to non-analytic shifts \sim \ep^{1/J}.Comment: REVTeX4, 14 pages, 4 figures. v2: final, 20 single-col. pages, 2 figures. Streamlined with emphasis on physics over formalism; rewrote Section V E so that it refers to time-dependent (instead of non-equilibrium) effect

Wave Propagation in Gravitational Systems: Completeness of Quasinormal Modes

The dynamics of relativistic stars and black holes are often studied in terms of the quasinormal modes (QNM's) of the Klein-Gordon (KG) equation with different effective potentials $V(x)$. In this paper we present a systematic study of the relation between the structure of the QNM's of the KG equation and the form of $V(x)$. In particular, we determine the requirements on $V(x)$ in order for the QNM's to form complete sets, and discuss in what sense they form complete sets. Among other implications, this study opens up the possibility of using QNM expansions to analyse the behavior of waves in relativistic systems, even for systems whose QNM's do {\it not} form a complete set. For such systems, we show that a complete set of QNM's can often be obtained by introducing an infinitesimal change in the effective potential

Coverage performance of MIMO-MRC in heterogeneous networks:a stochastic geometry perspective

We study the coverage performance of multi-antenna (MIMO) communications with maximum ratio combining (MRC) at the receiver in heterogeneous networks (HetNets). Our main interest in on multi-stream communications when BSs do not have access to channel state information. Adopting stochastic geometry we evaluate the network-wise coverage performance of MIMO-MRC assuming maximum signal- to-interference ratio (SIR) cell association rule. Coverage analysis in MIMO-MRC HetNets is challenging due to inter-stream interference and statistical dependencies among streams' SIR values in each communication link. Using the results of stochastic geometry we then investigate this problem and obtain tractable analytical approximations for the coverage performance. We then show that our results are adequately accurate and easily computable. Our analysis sheds light on the impacts of important system parameters on the coverage performance, and provides quantitative insight on the densification in conjunction with high multiplexing gains in MIMO HetNets. We further observe that increasing multiplexing gain in high- power tier can cost a huge coverage reduction unless it is practiced with densification in femto-cell tier

Coverage performance in multi-stream MIMO-ZFBF heterogeneous networks

We study the coverage performance of multiantenna (MIMO) communications in heterogenous networks (HetNets). Our main focus is on open-loop and multi-stream MIMO zero-forcing beamforming (ZFBF) at the receiver. Network coverage is evaluated adopting tools from stochastic geometry. Besides fixed-rate transmission (FRT), we also consider adaptive-rate transmission (ART) while its coverage performance, despite its high relevance, has so far been overlooked. On the other hand, while the focus of the existing literature has solely been on the evaluation of coverage probability per stream, we target coverage probability per communication link — comprising multiple streams — which is shown to be a more conclusive performance metric in multi-stream MIMO systems. This, however, renders various analytical complexities rooted in statistical dependency among streams in each link. Using a rigorous analysis, we provide closed-form bounds on the coverage performance for FRT and ART. These bounds explicitly capture impacts of various system parameters including densities of BSs, SIR thresholds, and multiplexing gains. Our analytical results are further shown to cover popular closed-loop MIMO systems, such as eigen-beamforming and space-division multiple access (SDMA). The accuracy of our analysis is confirmed by extensive simulations. The findings in this paper shed light on several important aspects of dense MIMO HetNets: (i) increasing the multiplexing gains yields lower coverage performance; (ii) densifying network by installing an excessive number of lowpower femto BSs allows the growth of the multiplexing gain of high-power, low-density macro BSs without compromising the coverage performance; and (iii) for dense HetNets, the coverage probability does not increase with the increase of deployment densities

Provisioning statistical QoS for coordinated communications with limited feedback

The capacity performance of ICIC has been extensively studied in coordinated multi-point transmissions (CoMP). In practice however, due to limited feedback, the acquired channel direction information (CDI), which is crucial for ICIC, is often partially available. Hence one may question whether the ICIC is able to meet the Quality-of-Service (QoS) requirements. This paper considers the optimal partitioning of the feedback bits in CoMP while accounting for the inter-cell interference cancellation (ICIC). In this paper, we adopt a statistical model of QoS in CoMP by using the notion of effective capacity (EC). Utilizing EC we then formulate the system function as an optimization problem with the objective of maximizing the total EC subject to the limited feedback available to the cluster of base stations (BSs). Analytical bounds are then obtained on the EC performance which are then utilized as the base for algorithms that assign feedback bits among the user equipments (UEs) and BSs. Using simulations we then investigate the accuracy of the obtained bounds and highlight practical system designs for dealing with stringent delay requirements. Of crucial practical importance, the findings of this paper also indicates that in CoMP there is an optimal cluster size for a given feedback capacity that maximizes the corresponding EC