Lectures in Theoretical Physics

“…However, calculation of the pnn values directly from (2.3) is problematic because (2.3) involves both diagonal and off-diagonal elements of the density matrix. Zwanzig [2] and others [3,4] have shown how to construct a closed equation of motion involving only the site probabilities and an appropriate memory function. For a localised initial condition [2,3], the appropriate equation for the time evolution of the site probabilities (P,(t)) is the generalised master equation (GME)…”

Section: Equations Of Motionmentioning

confidence: 99%

“…Zwanzig [2] and others [3,4] have shown how to construct a closed equation of motion involving only the site probabilities and an appropriate memory function. For a localised initial condition [2,3], the appropriate equation for the time evolution of the site probabilities (P,(t)) is the generalised master equation (GME)…”

Section: Equations Of Motionmentioning

confidence: 99%

“…We propose here to study the Anderson transition with the nearest-neighbour approximation to the memory for (2.1). Using the procedure outlined by Zwanzig [2], it is straightforward to show that is the nearest-neighbour approximation to the memory function for equation (2.1). For a one-dimensional system then, the corresponding equation of motion for the site probabilities is…”

Section: P =mentioning

confidence: 99%

“…The central quantity in any GME [2-71 is the memory function which in this case describes the interaction of the electron with the disordered environment. In our analysis we employ a nearest-neighbour approximation [2] to the exact memory function for a tight-binding Hamiltonian. The question on which we focus is as follows: can a GME with a nearest-neighbour memory function for a tight-binding Hamiltonian describe Anderson localisation?…”

Section: Introductionmentioning

confidence: 99%

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Anderson localisation from a generalised master equation

Dunlap

Kundu

Phillips³

1989

J. Phys.: Condens. Matter

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We consider here a tight-binding model for the motion of a single electron and an energetically disordered lattice. We show that the Anderson transition in this model can be studied using a generalised master equation with a nearest-neighbour memory function. It is first demonstrated that because the generalised master equation with a nearest-neighbour memory function is isomorphic to a classical bond-percolation problem, an exact expansion can be constructed for the diffusion constant using the bond flux method of Kundu, Parris and Phillips. We show that at the effective medium level, the diffusion constant vanishes for any non-zero value of the disorder. We then calculate the probability distribution of the selfenergy for the bond flux Green function on a Cayley tree of connectivity K. Our approach predicts an Anderson transition at W/V = 13 for K = 2 and W/V = 20 for K = 3. W is the width of the distribution for the site energies and V , the nearest-neighbour matrix element. These results are in good agreement with the exact values of W/V = 17 ( K = 2) and W/V = 29 ( K = 3). Further applications of the generalised master equation to disordered systems and the prospect of constructing the exact memory function for Anderson localisation are discussed.

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Decoherence and Fluctuations in Quantum Interference Experiments

2001

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We analyze the notion of quantum coherence in an interference experiment. We let the phase shifts fluctuate according to a given statistical distribution and introduce a decoherence parameter, defined in terms of a generalized visibility of the interference pattern. One might naively expect that a particle ensemble suffers a greater loss of quantum coherence by interacting with an increasingly randomized distribution of shifts. As we shall see, this is not always true.

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Lectures in Theoretical Physics

Cited by 783 publications

References 0 publications

Bound states of (1+1)-dimensional Dirac equation with kink-like vector potential and delta interaction

Bound states of (1+1)-dimensional Dirac equation with kink-like vector potential and delta interaction

Anderson localisation from a generalised master equation

Decoherence and Fluctuations in Quantum Interference Experiments

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