Tuning the instability in static mode atomic force spectroscopy as obtained in an AFM by applying an electric field between the tip and the substrate.

We have investigated experimentally the role of cantilever instabilities in determination of the static mode force-distance curves in presence of a dc electric field. The electric field has been applied between the tip and the sample in an atomic force microscope working in ultra-high vacuum. We have shown how an electric field modifies the observed force (or cantilever deflection)-vs-distance curves, commonly referred to as the static mode force spectroscopy curves, taken using an atomic force microscope. The electric field induced instabilities shift the jump-into-contact and jump-off-contact points and also the deflection at these instability points. We explained the experimental results using a model of the tip-sample interaction and quantitatively established a relation between the observed static mode force spectroscopy curves and the applied electric field which modifies the effective tip-sample interaction in a controlled manner. The investigation establishes a way to quantitatively evaluate the electrostatic force in an atomic force microscope using the static mode force spectroscopy curves.

Dissipative quantum systems and the heat capacity.

We present a detailed study of the quantum dissipative dynamics of a charged particle in a magnetic field. Our focus of attention is the effect of dissipation on the low- and high-temperature behaviors of the specific heat at constant volume. After providing a brief overview of two distinct approaches to the statistical mechanics of dissipative quantum systems, viz., the ensemble approach of Gibbs and the quantum Brownian motion approach due to Einstein, we present exact analyses of the specific heat. While the low-temperature expressions for the specific heat, based on the two approaches, are in conformity with power-law temperature dependence, predicted by the third law of thermodynamics, and the high-temperature expressions are in agreement with the classical equipartition theorem, there are surprising differences between the dependencies of the specific heat on different parameters in the theory, when calculations are done from these two distinct methods. In particular, we find puzzling influences of boundary confinement and the bath-induced spectral cutoff frequency. Further, when it comes to the issue of approach to equilibrium, based on the Einstein method, the way the asymptotic limit (t-->infinity) is taken seems to assume significance.

The effect of intrinsic instability of cantilever on static mode atomic force spectroscopy.

We show that the static force spectroscopy curve taken in an atomic force microscope is significantly modified due to presence of intrinsic cantilever instability which occurs as a result of its movement in a nonlinear force field. This instability acts in tandem with such instabilities as water bridge or molecular bond rupture and makes the static force spectroscopy curve (including 'jump-off-contact') dependent on the step size of data collection. A theoretical model has been proposed to explain the data. We emphasize the necessity of taking care of this fundamental instability of the microcantilever in calculating the adhesive force and also in the interpretation of data taken using an atomic force microscope.

Dissipative dynamics of a harmonic oscillator: a nonperturbative approach.

Starting from a microscopic theory, we derive a master equation for a harmonic oscillator coupled to a bath of noninteracting oscillators. We follow a nonperturbative approach, proposed earlier by us for the free Brownian particle. The diffusion constants are calculated analytically and the positivity of the master equation is shown to hold above a critical temperature. We compare the long time behavior of the average kinetic and potential energies with known thermodynamic results. In the limit of vanishing oscillator frequency of the system, we recover the results of the free Brownian particle.

Nonperturbative approach to quantum Brownian motion.

Starting from the Caldeira-Leggett model, we derive the equation describing the quantum Brownian motion, which has been originally proposed by Dekker purely from phenomenological basis containing extra anomalous diffusion terms. This nonperturbative approach yields explicit analytical expressions for the temperature dependence of the diffusion constants. At high temperatures, additional momentum diffusion terms are suppressed and classical Langevin equation can be recovered and at the same time positivity of the density matrix is satisfied. At low temperatures, the diffusion constants have a finite positive value. However, below a certain critical temperature, the master equation does not satisfy the positivity condition as proposed by Dekker.

Low-temperature thermodynamics in the context of dissipative diamagnetism.

We revisit here the effect of quantum dissipation on the much studied problem of Landau diamagnetism and analyze the results in the light of the third law of thermodynamics. The case of an additional parabolic potential is separately assessed. We find that dissipation arising from strong coupling of the system to its environment qualitatively alters the low-temperature thermodynamic attributes such as the entropy and the specific heat.

Effects of nonlinear forces on dynamic mode atomic force microscopy and spectroscopy.

In this paper, we describe the effects of nonlinear tip-sample forces on dynamic mode atomic force microscopy and spectroscopy. The jumps and hysteresis observed in the vibration amplitude (A) versus tip-sample distance (h) curves have been traced to bistability in the resonance curve. A numerical analysis of the basic dynamic equation was used to explain the hysteresis in the experimental curve. It has been found that the location of the hysteresis in the A-h curve depends on the frequency of the forced oscillation relative to the natural frequency of the cantilever.

A method to quantitatively evaluate the Hamaker constant using the jump-into-contact effect in atomic force microscopy.

We find that the 'jump-into-contact' of the cantilever in the atomic force microscope (AFM) is caused by an inherent instability in the motion of the AFM cantilever. The analysis is based on a simple model of the cantilever moving in a nonlinear force field. We show that the 'jump-into-contact' distance can be used to find the interaction of the cantilever tip with the surface. In the specific context of the attractive van der Waals interaction, this method can be realized as a new method of measuring the Hamaker constant for materials. The Hamaker constant is determined from the deflection of the cantilever at the 'jump-into-contact' using the force constant of the cantilever and the tip radius of curvature, all of which can be obtained by measurements. The results have been verified experimentally on a sample of cleaved mica, a sample of Si wafer with natural oxide and a silver film, using a number of cantilevers with different spring constants. We emphasize that the method described here is applicable only to surfaces that have van der Waals interaction as the tip-sample interaction. We also find that the tip to sample separation at the 'jump-into-contact' is simply related to the cantilever deflection at this point, and this provides a method to exactly locate the surface.

Small-world properties of the Indian railway network.

Structural properties of the Indian railway network is studied in the light of recent investigations of the scaling properties of different complex networks. Stations are considered as "nodes" and an arbitrary pair of stations is said to be connected by a "link" when at least one train stops at both stations. Rigorous analysis of the existing data shows that the Indian railway network displays small-world properties. We define and estimate several other quantities associated with this network.

Growing smooth interfaces with inhomogeneous moving external fields: dynamical transitions, devil's staircases, and self-assembled ripples.

We study the steady state structure and dynamics of an interface in a pure Ising system on a square lattice placed in an inhomogeneous external field with a profile designed to stabilize a flat interface and translated with velocity v(e). For small v(e), the interface is stuck to the profile, is macroscopically smooth, and is rippled with a periodicity in general incommensurate with the lattice parameter. For arbitrary orientations of the profile, the local slope of the interface locks in to one of infinitely many rational values (devil's staircase) which most closely approximates the profile. These "lock-in" structures and ripples disappear as v(e) increases. For still larger v(e) the profile detaches from the interface.