Sharif Digital Repository

Within the standard weak-coupling limit, the reduced dynamics of open quantum spin chains with their two end spins coupled to two distinct heat baths at different temperatures are mainly derived using the so-called global and local approaches, in which, respectively, the spin self-interaction is and is not taken into account. In order to compare the differences between the two regimes, we concentrate on an open three-site XX spin chain, provide systematic techniques to address the global and local asymptotic states, and then compare the asymptotic spin-transport features by studying the spin flux through the middle site. Based on the analytical expressions of the stationary states in the two... 

We use a nonlinear analytic approach to predict the main oscillation mode power and spurious levels in ultrapure microwave optoelectronic oscillators (OEOs). This approach takes into account N simultaneously mode falling inside the RF filter bandwidth and calculates all the dominant InterModulation Products (IMPs) that fall in the fundamental zone. We show that nonlinear microwave photonic links exhibit the capture effect. By considering this effect, we derive analytical expressions that govern the behavior of the OEOs in the steady state. We find that when the small-signal open-loop gain is increased beyond a critical value, OEOs start a multimode operation from which the spurious levels... 

We introduce the capture effect concept in microwave photonic links (MWPLs) for the first time to our knowledge. The capture effect or the small-signal suppression is the change in the amplitude ratio of the two signals between input and output of the intensity-modulation direct-detection (IMDD) MWPLs. An analytical explanation of the performance of external IMDD MWPLs due to the effects of nonlinearity combined with sum of several input sinusoidal signals is given.We have investigated the suppression of a weaker signal in these links. General analytic expression for the small-signal suppression is derived using a nonlinear analytical approach. We show that the small-signal suppression is... 

The mechanism of gold nanowire (AuNW) and nanotube (AuNT) electrodeposition in a cyanide-free solution is investigated for the first time based on the analytical model of Szabo et al. (A. Szabo et al., J. Electroanal. Chem. 217 (1987) 417) for recessed cylindrical ultramicroelectrode (UME). Track-etched Polycarbonate Template (PCT) is served as cylindrical UME ensemble/arrays. Firstly, Au is nucleated through a charge transfer step and when the Nernst thickness exceeds the pore length, the radial diffusion is established around pore mouths. By overlapping of these domains, the planar diffusion toward the whole PCT surface is obtained. An analytic expression for global diffusion coefficient... 

In this paper, we investigate the diversity-multiplexing tradeoff (DMT) for multi-relay channels in finite-SNR regime. In our analysis, we consider the decode and forward (DF) relaying strategy and a line of sight path from source to destination. First, we determine the outage probability in a multi-relay scenario and obtain its exact analytical expressions. Then, the outage probability of a multi-relay channel with relay selection is calculated and provided as a closed-form expression. Based on these results, we determine the DMT in finite-SNR regime. Finally, using simulation results, we show that our analysis has accurate results which coincides with that of obtained from Monte-Carlo... 

This paper proposes a new experimental procedure for magnetic characterization of switched reluctance machines. In the existing methods, phase voltage and current data are captured and further processed to find the flux linkage. Conventionally, assuming zero initial flux value, the flux linkage can be found by integrating the corresponding voltage term. However, the initial flux value is usually unknown, e.g., it can be nonzero when the current is zero due to the residual flux effect, and, thus, imposes error in magnetic characterization. The proposed method addresses this issue by considering an additional equation in steady state. This method injects a low-frequency sinusoidal current to... 

Local noise can produce quantum correlations on an initially classically correlated state, provided that it is not represented by a unital or semiclassical channel. We find the power of any given local channel for producing quantum correlations on an initially classically correlated state. We introduce a computable measure for quantifying the quantum correlations in quantum-classical states, which is based on the noncommutativity of ensemble states in one party of the composite system. Using this measure we show that the amount of quantum correlations produced is proportional to the classical correlations in the initial state. The power of an arbitrary channel for producing quantum... 

The objective of this work is to create an analytical framework to study the non-linear dynamics of beam flexures with a tip mass undergoing large deflections. Hamilton's principal is utilized to derive the equations governing the nonlinear vibrations of the cantilever beam and the associated boundary conditions. Then, using a single mode approximation, these non-linear partial differential equations are reduced to two coupled non-linear ordinary differential equations. These equations are solved analytically using combination of the method of multiple time scales and homotopy perturbation analysis. Closed-form, parametric analytical expressions are presented for the time domain response of... 

I propose a novel method for designing a broadband THz absorber by using periodic arrays of graphene ribbons on a Salisbury-screen-like structure. The recently proposed analytical circuit model of graphene arrays is used for obtaining analytical expressions for the input admittance of the proposed device. The input admittance is then adjusted to be closely matched to the free space in a wide frequency range. Consequently, it is demonstrated that a bandwidth of 90% absorption can be extended up to 100% of the central frequency with only one layer of patterned graphene  

Using a general expression for the second term in the density expansion of the hard core potentials, we obtained an analytical expression for the direct correlation function of the hard core double Yukawa potential. The results of this calculation using the proposed direct correlation function and its related radial distribution function through the Ornstein-Zernike equation show good agreements with those obtained by the computer simulation of the same model  

In this study, several analytical expressions are obtained for the vibrational characteristics of a Jeffcott model for micro-rotor systems based on the strain gradient theory to investigate the small-scale effects on the model. The Jeffcott model consists of a massless microrotating shaft and a disk as a rotor with eccentricity. The disk is mounted on the middle of the shaft. Two second-order differential equations associated with the oscillating motion of the rotor in the plane perpendicular to the longitudinal axis are presented and transformed into a complex form. The stiffness of the system is determined by obtaining the deflection of a strain-gradient-based nonrotating microbeam... 

In this paper, we investigate cooling of a levitated nanosphere in a system of coupled cavities in the resolved sideband regime. Thanks to the presence of an extra resonance in the coupled cavity cooling system, the coupling strength can be maximized at the optimum detuning. In this fashion, the intracavity photon number is increased, and thereby the cooling rate is enhanced and the strong coupling regime is achieved without resorting to increased driving laser power. The underlying physics of the increased cooling efficiency in the system of coupled cavities in the resolved sideband regime proposed here and that of the already reported system of coupled cavities in the unresolved sideband... 

A sheet of graphene under magnetic bias attains anisotropic surface conductivity, opening the door for realizing compact devices such as Faraday rotators, isolators and circulators. In this paper, an accurate and analytical method is proposed for a periodic array of graphene ribbons under magnetic bias. The method is based on integral equations governing the induced surface currents on the coplanar array of graphene ribbons. For subwavelength size ribbons subjected to an incident plane wave, the current distribution is derived leading to analytical expressions for the reflection/transmission coefficients. The results obtained are in excellent agreement with full-wave simulations and predict... 

Metagrating is a new concept for wavefront manipulation that, unlike phase gradient metasurfaces, does not suffer from low efficiency and also has a less complicated fabrication process. In this paper, a compound metallic grating (a periodic metallic structure with more than one slit in each period) is proposed for anomalous reflection. We propose an analytical method for analyzing the electromagnetic response of this grating. Closed-form and analytical expressions are presented for the reflection coefficients of zeroth diffracted order and also higher diffracted orders. The proposed method is verified against full-wave simulations and the results are in excellent agreement. Thanks to the... 

Theoretical study of arrays of graphene ribbons is currently of high interest due to its potential application in beam splitters, absorbers, and polarizers. In this paper, an analytical method is presented for diffraction analysis of graphene ribbon arrays. Previous analytical studies were carried out in the regime where the lateral separation between the ribbons is much smaller than the wavelength of the incident wave. As such, they cannot be used to calculate the reflection coefficients of higher diffracted orders. In contrast, the method proposed here can predict the electromagnetic response of graphene ribbon arrays even when the array constant is larger than the wavelength. To reach our... 

We propose an analytical circuit model for accurate analysis of one-dimensional periodic array of metallic strips. The proposed model is valid not only in subwavelength regime, but also for wavelengths shorter than the period of structure. The working frequency can reach the visible range and thus electromagnetic properties of periodic arrays of nano-slits can be analyzed by the proposed model. The proposed model remains valid for arbitrary incident angles even when nonspecular diffracted orders become propagating. Analytical expressions are derived explicitly in order to describe the parameters of the proposed circuit model. The circuit model is derived by assuming that only one guided mode... 

Dynamic behavior of a electrostatically actuated MEMS resonator is investigated. A double clamped micro-beam under distributed DC and AC actuation is used. Corresponding single degree of freedom model is derived using Galerkin's decomposition method. Homotopy Perturbation Method (HPM) is implemented in order to derive analytical expression for frequency response of the micro-resonator. Comparison of the obtained results with the numerical simulations confirms that HPM agrees very well with numerical simulations for a wide range of parameters. Obtained analytical solution can be used for design and optimization of MEMS resonators  

Cooling and entanglement in optomechanical systems coupled through radiation pressure and photothermal force are studied. To develop the photothermal model, we derive an expression for deformation constant of the force. By exploiting linearized quantum Langevin equations, we investigate the dynamics of such systems. According to our analysis, in addition to separate action of radiation pressure and photothermal force, their cross-correlation effect plays an important role in the dynamics of the system. We also achieve an exact relation for the phonon number of the mechanical resonator in such systems, and then we derive an analytical expression for it at the weak-coupling limit. At the... 

Ground-state fidelity (GSF) and quantum renormalization group (QRG) theory have proven to be useful tools in the study of quantum critical systems. Here we lay out a general, unified formalism of GSF and QRG; specifically, we propose a method for calculating GSF through QRG, obviating the need for calculating or approximating ground states. This method thus enhances the characterization of quantum criticality as well as scaling analysis of relevant properties with system size. We illustrate the formalism in the one-dimensional Ising model in a transverse field (ITF) and the anisotropic spin-1/2 Heisenberg (XXZ) model. Explicitly, we find the scaling behavior of the GSF for the ITF model in... 

In this paper, enhanced spatial and temporal shifts in the reflection of Gaussian wave packets from twodimensional photonic crystal waveguides supporting above-the-light-line leaky modes are studied, for the first time to our best knowledge. Particular attention is given to two important special cases, namely, harmonic Gaussian beams and Gaussian-pulse uniform plane waves. Analytical expressions are given for enhanced spatial and temporal shifts when the stationary phase approximation holds and the incident wave excites above-the-light-line leaky modes. The enhanced spatial and temporal shifts of Gaussian wave packets are thereby related to each other via the group velocity of the excited...