• Volume 51, Issue 5

      November 1998,   pages  547-661

    • Preface

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    • The Ithaca interpretation of quantum mechanics

      N David Mermin

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      I list several strong requirements for what I would consider a sensible interpretation of quantum mechanics and discuss two simple recent theorems which have important implications for such an interpretation. My talk will not clear everything up; indeed, you may conclude that it has not cleared anything up. But I hope it will provide a different perspective from which to view some old and vexing puzzles (or, if you believe nothing needs to be cleared up, some ancient verities.)

    • Measurement problem in quantum mechanics: Characteristics of an apparatus

      Deepak Kumar

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      The problem of measurement in Quantum Mechanics will be briefly reviewed. Since the measurement process involves a macroscopic apparatus, the attention is focussed on the dynamics of a pointer-like variable of the apparatus when it interacts with a quantum system. It is argued that since the measurement process requires an apparent collapse of the wave function in a certain basis, and collapse is an irreversible process, understanding of irreversibility in a quantum macroscopic system is crucial. The chief characteristics of an apparatus that are important in understanding measurement process are (a) its closely spaced energy levels and (b) its interaction with environment. The coupling with the environment drives the density matrix of the apparatus to diagonal form, but to have persistent correlations between system and apparatus states, it seems necessary to have a pointer variable that has a classical limit

    • Hindered decay of an unstable system: A quantum zeno effect

      Saverio Pascazio Larry S Schulman

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      A direct test of the so-called “quantum Zeno effect” is proposed for a truly decaying system. It is suggested that the lifetime of an unstable atom can be extended by illuminating it with an intense laser beam at the frequency of another of its transitions. The “Zeno” time is also compared to the lifetime

    • de Broglie-Bohm formulation of quantum mechanics, quantum chaos and breaking of time-reversal invariance

      F H M Faisal U Schwengelbeck

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      A recently developed unified theory of classical and quantum chaos, based on the de Broglie-Bohm (Hamilton-Jacobi) formulation of quantum mechanics is presented and its consequences are discussed. The quantum dynamics is rigorously defined to be chaotic if the Lyapunov number, associated with the quantum trajectories in de Broglie-Bohm phase space, is positive definite. This definition of quantum chaos which under classical conditions goes over to the well-known definition of classical chaos in terms of positivity of Lyapunov numbers, provides a rigorous unified definition of chaos on the same footing for both the dynamics. A demonstration of the existence of positive Lyapunov numbers in a simple quantum system is given analytically, proving the existence of quantum chaos. Breaking of the time-reversal symmetry in the corresponding quantum dynamics under chaotic evolution is demonstrated. It is shown that the rigorous deterministic quantum chaos provides an intrinsic mechanism towards irreversibility of the Schrodinger evolution of the wave function, without invoking ‘wave function collapse’ or ‘measurements’

    • Maximally causal quantum mechanics

      S M Roy

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      We present a new causal quantum mechanics in one and two dimensions developed recently at TIFR by this author and V Singh. In this theory both position and momentum for a system point have Hamiltonian evolution in such a way that the ensemble of system points leads to position and momentum probability densities agreeing exactly with ordinary quantum mechanics

    • Tunneling time based on the quantum diffusion process approach in multichannel and optical potential cases

      Ichiro Ohba Kentaro Imafuku Yoshiya Yamanaka

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      We analyze the effects of inelastic scattering on the tunneling time theoretically, using generalized Nelson’s quantum mechanics. This generalization enables us to describe quantum system with channel couplings and optical potential in a real time stochastic approach, which seems to give us a new insight into quantum mechanics beyond Copenhagen interpretation

    • The structure of the quantum mechanical state space and induced superselection rules

      Joachim Kupsch

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      The role of superselection rules for the derivation of classical probability within quantum mechanics is investigated and examples of superselection rules induced by the environment are discussed

    • Energy basis via decoherence

      Anu Venugopalan

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      The question of the emergence of a preferred basis which is generally understood as that basis in which the reduced density matrix is driven to a diagonal (classically interpretable) form via environment induced decoherence is addressed. The exact solutions of the Caldeira-Leggett Master Equation are analyzed for a free particle and a harmonic oscillator system. In both cases, we see that the reduced density matrix is driven diagonal in the energy basis, which is momentum for the free particle and the number states for the harmonic oscillator. This seems to single out the energy basis as the preferred basis which is contrary to the general notion that it is the position basis which is selected since the coupling to the environment is via the position coordinates

    • Quantum correlations in optics

      R Ghosh

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      In many nonlinear optical problems, for example in down-conversion and four-wave mixing, the photons are generated in pairs. The strong correlation between the photons in a pair, characterized by either the correlations between operators corresponding to observables associated with individual photons, or the correlated state describing the two photons, may lead to various nonclassicalities. We discuss some of these nonclassical effects and their experimental demonstrations in nonlinear optical processes

    • Hierarchies of non-classical states in quantum optics

      N Mukunda

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      The conventional separation of states of the quantised radiation field into “classical” and “nonclassical” types is expressed in a dual operator form and then refined. This is based on new features of the normal ordering rule for passage from classical to quantum dynamical variables. The cases of single and two-mode radiation fields are discussed

    • Wave-particle duality: The mystery keeps unfolding

      Partha Ghose

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      The current status of wave particle duality using single photon sources is briefly reviewed

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