C. Mukherjee

C. Mukherjee
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C. Mukherjee

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Mathematics - Probability (8)
Physics - Materials Science (3)
Physics - Soft Condensed Matter (3)
Physics - Disordered Systems and Neural Networks (2)
Physics - Mesoscopic Systems and Quantum Hall Effect (2)
Mathematics - Mathematical Physics (2)
Physics - Statistical Mechanics (2)
Mathematical Physics (2)
Physics - Other (1)
Mathematics - Analysis of PDEs (1)
Physics - Chemical Physics (1)

Publications Authored By C. Mukherjee

We prove a quenched large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on $\Z^d$ ($d\geq 2$). The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long-range correlations, like the random cluster model, the random interlacement and its vacant set (for $d\geq 3$) and the level sets of the Gaussian free field ($d\geq 3$). Inspired by the methods developed by Kosygina, Rezakhanlou and Varadhan ([KRV06]) for proving quenched LDP for elliptic diffusions with a random drift, and by Yilmaz ([Y08]) and Rosenbluth ([R06]) for similar results regarding elliptic random walks in random environment, we take the point of view of the moving particle and prove a large deviation principle for the quenched distribution of the pair empirical measures of the environment Markov chain in the non-elliptic case of SRWPC . Read More

The effect of gamma irradiation on the UV-Vis and FTIR spectroscopy of polymethyl methacrylate (PMMA) foils has been studied. A new absorption band is observed in the visible spectral range due to color centers induced in the gamma irradiated PMMA. This band shows maximum absorption (low transmission) for 10 kGy irradiation, which decreases and saturates after 50 kGy followed by a further increase at 500 kGy. Read More

We consider the smoothed multiplicative noise stochastic heat equation $$d u_{\eps,t}= \frac 12 \Delta u_{\eps,t} d t+ \beta \eps^{\frac{d-2}{2}}\, \, u_{\eps, t} \, d B_{\eps,t} , \;\;u_{\eps,0}=1,$$ in dimension $d\geq 3$, where $B_{\eps,t}$ is a spatially smoothed (at scale $\eps$) space-time white noise, and $\beta>0$ is a parameter. We show the existence of a $\bar\beta\in (0,\infty)$ so that the solution exhibits weak disorder when $\beta<\bar\beta$ and strong disorder when $\beta > \bar\beta$. The proof techniques use elements of the theory of the Gaussian multiplicative chaos. Read More

We consider mean-field interactions corresponding to Gibbs measures on interacting Brownian paths in three dimensions. The interaction is self-attractive and is given by a singular Coulomb potential. The logarithmic asymptotics of the partition function for this model were identified in the 1980s by Donsker and Varadhan \cite{DV83} in terms of the Pekar variational formula, which coincides with the behavior of the partition function corresponding to the polaron problem under strong coupling. Read More

We are interested in the analysis of Gibbs measures defined on two independent Brownian paths in $\R^d$ interacting through a mutual self-attraction. This is expressed by the Hamiltonian $\int\int_{\R^{2d}} V(x-y) \mu(\d x)\nu(\d y)$ with two probability measures $\mu$ and $\nu$ representing the occupation measures of two independent Brownian motions. We will be interested in class of potentials $V$ which is singular, e. Read More

We study the transformed path measure arising from the self-interaction of a three-dimensional Brownian motion via an exponential tilt with the Coulomb energy of the occupation measures of the motion by time $t$. The logarithmic asymptotics of the partition function were identified in the 1980s by Donsker and Varadhan \cite{DV83-P} in terms of a variational formula. Recently \cite{MV14} a new technique for studying the path measure itself was introduced, which allows for proving that the normalized occupation measure asymptotically concentrates around the set of all maximizers of the formula. Read More

We prove a {\it{quenched}} large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster on $\Z^d$, $d\geq 2$.. We take the point of view of the moving particle and first prove a quenched LDP for the distribution of the {\it{pair empirical measures}} of the environment Markov chain. Read More

The plasmonic properties of vacuum evaporated nanostructured gold thin films having different types of nanoparticles are presented. The films with more than 6 nm thickness show presence of nanorods having non cylindrical shape with triangular base. Two characteristics plasmon bands have been recoreded in absorption spectra. Read More

Epitaxy of ZnO layers on cubic GaP (111) substrates has been demonstrated using pulsed laser deposition. Out of plane and in-plane epitaxial relationship of ZnO layer with respect to GaP substrate determined using phi scans in high resolution X-ray diffraction measurements are (0001) ZnO || (111) GaP and (-1 2 -1 0) ZnO || (-1 1 0) GaP respectively. Our results of epitaxy of ZnO and its intense excitonic photoluminescence with very weak defect luminescence suggest that (111) oriented GaP can be a potential buffer layer choice for the integration of ZnO based optoelectronic devices on Si(111) substrates. Read More

Valence band onset (Ev), valence band tail (VBT) and valence plasmons (VPs) have been studied as a function of sputtering of SnO2 and In2-xSnxO3 (ITO) thin films, using ultraviolet photoemission spectroscopy (UPS). Decrease in Ev with respect to the Fermi level and increase in the density of energy levels of VBT have been observed after 5 minutes of sputtering using Ar+ ions (500V). Bulk and surface components of VPs of Sn, SnO and SnO2 in sputtered SnO2 thin films have been observed in UPS spectra. Read More

Understanding the nature of metal/1D-semiconductor contacts such as metal/carbon nanotubes is a fundamental scientific and technological challenge for realizing high performance transistors\cite{Francois,Franklin}. A Schottky Barrier(SB) is usually formed at the interface of the $2D$ metal electrode with the $1D$ semiconducting carbon nanotube. As yet, experimental\cite{Appenzeller,Chen, Heinze, Derycke} and numerical \cite{Leonard, Jimenez} studies have generally failed\cite{Svensson} to come up with any functional relationship among the relevant variables affecting carrier transport across the SB owing to their unique geometries and complicated electrostatics. Read More

In proving large deviation estimates, the lower bound for open sets and upper bound for compact sets are essentially local estimates. On the other hand, the upper bound for closed sets is global and compactness of space or an exponential tightness estimate is needed to establish it. In dealing with the occupation measure $L_t(A)=\frac{1}{t}\int_0^t{\1}_A(W_s) \d s$ of the $d$ dimensional Brownian motion, which is not positive recurrent, there is no possibility of exponential tightness. Read More

The effect of an electric field on conduction in a disordered system is an old but largely unsolved problem. Experiments cover an wide variety of systems - amorphous/doped semiconductors, conducting polymers, organic crystals, manganites, composites, metallic alloys, double perovskites - ranging from strongly localized systems to weakly localized ones, from strongly correlated ones to weakly correlated ones. Theories have singularly failed to predict any universal trend resulting in separate theories for separate systems. Read More

We consider $p$ independent Brownian motions in $\R^d$. We assume that $p\geq 2$ and $p(d-2)Read More

The \textit{I-V} characteristics of four conducting polymer systems like doped polypyrrole (PPy), poly 3,4 ethylene dioxythiophene (PEDOT), polydiacetylene (PDA) and polyaniline (PA) in as many physical forms have been investigated at different temperatures, quenched disorder and magnetic fields. Transport data clearly confirm the existence of a \textit{single} electric field scale in any system. Based upon this observation, a phenomenological scaling analysis is applied, leading to extraction of a concrete number $x_M$, called nonlinearity exponent. Read More

We present here a short review of mainly experimental properties of noise as disordered systems are driven into non-ohmic regimes by applying voltages of few volts only. It is found that the noise does not simply follow the resistance in that the direction of change of noise could be opposite to that of resistance. It is discussed how this and other properties make the noise a complementary and incisive tool for studying complex systems, particularly its dynamic properties. Read More

Noise has been measured in two types of coductor-insulator mixtures as a function of bias and composition. It was marked by a huge increase in magnitude as the resistance increased only slightly due to Joule heating. The noise (resistance) current scale $I_s$($I_r$) for nonlinearity were found to scale with the linear resistance $R_o$ as $I_s(I_r) \sim {{R_o}^ {-x_s(x_r)}}$ where the exponent $x_s$ is equal to 0. Read More

At a composition far above the percolation threshold, the resistance of a composite sample increases with time due to Joule heating as a constant current of sufficiently large value is passed through the sample. If the current is less than a certain breakdown current ($I_b$) the resistance eventually reaches a steady value with a characteristic relaxation time $\tau_h$. The latter diverges with current $I$ as $\tau_h \sim {(1-I^2/ {I_b}^2)}^{-z}$. Read More