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WORLD SCIENTIFIC eBooks

A garden of quanta : essays in honor of Hiroshi Ezawa

次郎 荒船, 洋 江沢

Published Jan 1, 2003• 1 citation
OpenAlex

Abstract

Quantum mechanics path integral and stochastic processes quantum field theory statistical mechanics mathematical problems history.

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Some Observaiions on Stochastic vs. Quantum Dynamics-Following Ezawa, Klauder & Shepp

Ludwig Streit

The message of Hiroshi Ezawa, John Klauder, and Shepp for Euclidean quantum dynamics was contrary to the prevalent method of imposing quantum dynamics on trajectories by killing them; more naturally, quantum dynamics should translate itself into specific dynamical evolutions of the paths. This chapter reviews some of the work that the observation has triggered. In the mid-seventies the prevalent path space approach to quantum dynamics was via Brownian paths that is the paths are killed with probability. Instead of this, Ezawa, Klauder, and Shepp proposed to deform the paths according to the dynamics with obeying a stochastic differential equation, the quantum dynamics is now encoded in the drift term that depends on the potential and more directly on the ground state of the dynamics. Ground states are always smoother than the corresponding potentials, so that the former may survive in limiting cases where the latter fail to exist.

CRC Press eBooks•Nov 27, 2020•0 citations
The message of Hiroshi Ezawa, John Klauder, and Shepp for Euclidean quantum dynamics was contrary to the prevalent method of imposing quantum dynamics on trajectories by killing them; more naturally, quantum dynamics should translate itself into specific dynamical evolutions of the paths. This chapter reviews some of the work that the observation has triggered. In the mid-seventies the prevalent path space approach to quantum dynamics was via Brownian paths that is the paths are killed with probability. Instead of this, Ezawa, Klauder, and Shepp proposed to deform the paths according to the dynamics with obeying a stochastic differential equation, the quantum dynamics is now encoded in the drift term that depends on the potential and more directly on the ground state of the dynamics. Ground states are always smoother than the corresponding potentials, so that the former may survive in limiting cases where the latter fail to exist.