• A M Jayannavar

      Articles written in Pramana – Journal of Physics

    • A note on traversal time for tunneling

      A M Jayannavar

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      A simple approach to study the traversal time for tunneling is given. By using the WKB wave function to evaluate the velocity field of particles in the barrier region, an expression for the traversal time τ=εdx[m/2(V(x)-E)]1/2 is obtained in conformity with the recent results.

    • The wavefunction envelope in one-dimensional random potentials

      A Mookerjee A M Jayannavar

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      We propose a formalism for the study of mean resistance of a one dimensional chain of random potentials. We obtain the resistance as a function of the length of the chain. In the asymptotic limit, this is related to the wavefunction envelope. The formalism demands loss of translational symmetry, but is general enough to include potentials with spatial correlations which are not long ranged and also those whose randomness is inhomogeneous.

    • Scaling theory of quantum resistance distributions in disordered systems

      A M Jayannavar

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      We have derived explicitly, the large scale distribution of quantum Ohmic resistance of a disordered one-dimensional conductor. We show that in the thermodynamic limit this distribution is characterized by two independent parameters for strong disorder, leading to a two-parameter scaling theory of localization. Only in the limit of weak disorder we recover single parameter scaling, consistent with existing theoretical treatments.

    • Self-segregation in chemical reactions, diffusion in a catalytic environment and an ideal polymer near a defect

      P K Datta A M Jayannavar

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      We study a family of equivalent continuum models in one dimension. All these models map onto a single equation and include simple chemical reactions, diffusion in presence of a trap or a source and an ideal polymer chain near an attractive or repulsive site. We have obtained analytical results for the survival probability, total growth rate, statistical properties of nearest-neighbour distribution between a trap and unreacted particle and mean-squared displacement of the polymer chain. Our results are compared with the known asymptotic results in the theory of discrete random walks on a lattice in presence of a defect.

    • State reduction theories, their classical analogs and some comments

      A M Jayannavar

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      Recently several theories have been proposed to account for the state reduction due to measurement. The resulting evolution is given by a new density matrix equation which suppresses linear superpositions of states with large spatial separations. We raise some pertinent questions regarding these theories. We also show that the evolution for the density matrix obtained in these theories has a classical analog.

    • Macroscopic equation of motion in inhomogeneous media: A microscopic treatment

      A M Jayannavar Mangal C Mahato

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      The dynamical evolution of a Brownian particle in an inhomogeneous medium with spatially varying friction and temperature field is important to understand conceptually. It requires to address the basic problem of relative stability of states in nonequilibrium systems which has been a subject of debate for over several decades. The theoretical treatments adopted so far are mostly phenomenological in nature. In this work we give a microscopic treatment of this problem. We derive the Langevin equation of motion and the associated Fokker-Planck equation. The correct reduced description of the Kramers equation in the overdamped limit (Smoluchowski equation) is obtained. Our microscopic treatment may be helpful in understanding the working of thermal ratchets, a problem of much current interest.

    • Novel interference effects and a new quantum phase in mesoscopic systems

      P Singha Deo A M Jayannavar

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      Mesoscopic systems have provided an opportunity to study quantum effects beyond the atomic realm. In these systems quantum coherence prevails over the entire sample. We discuss several novel effects related to persistent currents in open systems which do not have analogues in closed systems. Some phenomena arising simultaneously due to two non-classical effects namely, Aharonov-Bohm effect and quantum tunneling are presented. Simple analysis of sharp phase jumps observed in double-slit Aharonov-Bohm experiments is given. Some consequences of parity violation are elaborated. Finally, we briefly describe the dephasing of Aharonov-Bohm oscillations in Aharonov-Bohm ring geometry due to spin-flip scattering in one of the arms. Several experimental manifestations of these phenomena and their applications are given.

    • Universal fluctuations in orbital diamagnetism


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      Bohr–van Leuween theorem has attracted the notice of physicists for more than 100 years. The theorem states about the absence of magnetisation in classical systems in thermal equilibrium. In this paper, we discuss about fluctuations of magnetic moment in classical systems. In recent years, this topic has been investigated intensivelyand it is not free from controversy.We have considered a system consisting of a single particle moving in a plane. A magnetic field is applied perpendicular to the plane. The system is in contact with a thermal bath.We have considered three cases: (a) particle moving in a homogeneous medium, (b) particle moving in a medium with space-dependent friction and (c) particle moving in a medium with space-dependent temperature. For all the three cases, the averagemagnetic moment and fluctuations in magnetic moment have been calculated. Average magnetic moment saturates to a finite value in the case of free particle but goes to zero when the particle is confined by a 2D harmonic potential. Fluctuations in magnetic moment shows universal features in the presence of arbitrary friction inhomogeneity. For this case, the system reaches equilibrium asymptotically. In the case of space-dependent temperature profile, the stationary distribution is non-Gibbsian and fluctuations deviate from universal value for the bounded system only.

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