A. M. Jayannavar

Persistent currents in the presence of a transport current.

We have considered a system of a metallic ring coupled to two electron reservoirs. We show that in the presence of a transport current, the persistent current can flow in a ring, even in the absence of a magnetic field. This is purely a quantum effect and is related to the current magnification in the loop. These persistent currents can be observed if one tunes the Fermi energy near the antiresonances of the total transmission coefficient or the two-port conductance.

EFFECT OF IMPURITIES ON THE CURRENT MAGNIFICATION IN MESOSCOPIC OPEN RINGS

We have considered an open system consisting of a metallic ring coupled to two electron reservoirs. We have recently shown that in the presence of a transport current, circulating currents can flow in such a ring even in the absence of magnetic field. This is related to the current magnification effect in the ring. In our present work we have studied the effect of impurity on the current magnification. We find that the presence of impurity can enhance the current magnification in the loop significantly and thus lead to large circulating currents in a certain range of Fermi energies. This is in contrast to the known fact that impurities can only decrease the persistent currents in closed ring in the presence of magnetic flux.

A Biologically Inspired Ratchet Model of Two Coupled Brownian Motors

A ratchet model for coupled Brownian motors, inspired by the motion of individual two-headed molecular motors on cytoskeletal filaments, is proposed. Such motors are modeled as two elastically coupled Brownian particles, each of which moves in a flashing ratchet potential. The ratchet potentials felt by the individual particles are anti-correlated, modeling the successive binding and unbinding of the two motor heads to the filament. We obtain, via Langevin simulations, steady-state currents as functions of noise strength, the equilibrium separation of the particles and the rate of switching between potential states. We observe an enhanced current due to coupling, noise-induced stability and phase-locked behaviour in the deterministic regime. A qualitative understanding of these features is provided.

Some stochastic phenomena in a driven double-well system

We study the overdamped motion of a Brownian particle in a driven double-well system to understand various physical phenomena observed experimentally. These phenomena include hysteresis, stochastic resonance, and net undirectional motion in a symmetric periodic system. We argue that the area of the hysteresis loop so defined is a good measure of synchronization (with respect to the applied field) of passages between the two wells. We find that stochastic resonance may be relevant even in case of large-amplitude driving field due to a recently discovered phenomena of noise-induced stability of unstable states. We try to find the relation between some of these apparently different phenomena.

Two simple models of classical heat pumps.

Motivated by recent studies of models of particle and heat quantum pumps, we study similar simple classical models and examine the possibility of heat pumping. Unlike many of the usual ratchet models of molecular engines, the models we study do not have particle transport. We consider a two-spin system and a coupled oscillator system which exchange heat with multiple heat reservoirs and which are acted upon by periodic forces. The simplicity of our models allows accurate numerical and exact solutions and unambiguous interpretation of results. We demonstrate that while both our models seem to be built on similar principles, one is able to function as a heat pump (or engine) while the other is not.

Nonequilibrium work distributions for a trapped Brownian particle in a time-dependent magnetic field.

We study the dynamics of a trapped, charged Brownian particle in the presence of a time-dependent magnetic field. We calculate work distributions for different time-dependent protocols numerically. In our problem, thermodynamic work is related to variation of the vector potential with time as opposed to the earlier studies where the work is related to time variation of the potentials, a quantity that depends only on the coordinates of the particle. Using the Jarzynski and the Crooks equalities, we show that the free energy of the particle is independent of the magnetic field, thus complementing the Bohr-van Leeuwen theorem. We also show that our system exhibits a parametric resonance in a certain parameter space.

Quantum current magnification in a multichannel mesoscopic ring

We have studied the current magnification effect in a multi-channel open mesoscopic ring. We show that the current magnification effect is robust even in the presence of several propagating modes inspite of mode mixing and cancellation effects. The magnitude of circulating currents in the multichannel regime can be much larger than that in a single channel case. Impurities can enhance or degrade the current magnification effect depending sensitively on the system parameters. Circulating currents are mostly associated with Fano resonances in the total transport current. We further show that system-lead coupling qualitatively changes the current magnification effect.

Effect of nonlinearity on the dynamics of a particle in field-induced systems

Dynamics of a particle in a perfect chain with one nonlinear impurity and in a perfect nonlinear chain under the action of dc field is studied numerically. The nonlinearity appears due to the coupling of the electronic motion to optical oscillators that are treated in the adiabatic approximation. We study both the cases of low and high values of field strength. Three different ranges of nonlinearity are obtained each of which has a different dynamics. In the low and intermediate ranges of nonlinearity, the localization effects are reduced. In fact, in the intermediate range case subdiffusive behavior in the perfect nonlinear chain is obtained for a long time. In all cases a critical value of nonlinear strength exists where a self-trapping transition takes place. This critical value depends on the system and the field strength. Beyond the self-trapping transition, nonlinearity enhances the localization.

NOVEL INTERFERENCE EFFECTS IN MULTIPLY CONNECTED NORMAL METAL RINGS

We have investigated the magnetoconductance of a normal metal loop connected to ideal wires in the presence of magnetic flux. The quantum mechanical potential, V, in the loop is much higher than that in the connecting wires (V=0). The electrons with energies less than the potential height on entering the loop propagate as evanescent modes. In such a situation, the contribution to the conductance arises from two non-classical effects, namely, Aharonov-Bohm effect and quantum tunneling. For this case we show that, on application of a small magnetic field, the conductance initially always decreases, or small field magnetoconductance is always negative. This is in contrast to the behavior in the absence of the barrier, wherein the small field magnetoconductance is either positive or negative depending on the Fermi energy and other geometric details. We also discuss the possibility of a better switch action based on quantum interference effects in such structures.

Aharonov-Bohm effect in the presence of evanescent modes

It is known that differential magnetoconductance of a normal metal loop connected to reservoirs by ideal wires is always negative when an electron travels as an evanescent modes in the loop. This is in contrast to the fact that the magnetoconductance for propagating modes is very sensitive to small changes in geometric details and the Fermi energy and moreover it can be positive as well as negative. Here we explore the role of impurities in the leads in determining the magnetoconductance of the loop. We find that the change in magnetoconductance is negative and can be made large provided the impurities do not create resonant states in the systems. This theoretical finding may play a useful role in quantum switch operations.