Quantum dissipative systems from theory of continuous measurements

Abstract

We apply the restricted-path-integral (RPI) theory of non-minimally disturbing continuous measurements for correct description of frictional Brownian motion. The resulting master equation is automatically of the Lindblad form, so that the difficulties typical of other approaches do not exist. In the special case of harmonic oscillator the known familiar master equation describing its frictionally driven Brownian motion is obtained. A thermal reservoir as a measuring environment is considered.

Quantum particle localization by frequent coherent monitoring

“…The parameter phase space can thus be partitioned into exclusion and localization parts. The timing onset and its intricate interplay with the intermonitoring interval essentially differ from previously considered dynamics, whether by static detection or by repeated measurements [7][8][9][11][12][13][14][15][16][17].…”

“…The predicted effects are essentially different from the quantum Zeno effect [9] or its inverse (the anti-Zeno effect) [10][11][12][13][14], i.e., the respective slowdown or speedup of quantum-state change by frequent observations. Although such effects have mostly been studied for discrete variables [7][8][9]13,[15][16][17][18][19], frequent observations of position have also been considered [8] under the idealized assumption of projective measurements that fully localize the particles (which would create nearly infinite effective potential barriers). We here adopt an experimentally feasible model of frequent PM monitoring that may appear to be the quantum analog of the Zeno arrow paradox, whereby a frequently watched arrow does not fly.…”

“…We here adopt an experimentally feasible model of frequent PM monitoring that may appear to be the quantum analog of the Zeno arrow paradox, whereby a frequently watched arrow does not fly. Yet, remarkably, excessively frequent PMs are shown to hamper localization, which requires specific timings, contrary to either Zeno-like or anti-Zeno evolution [7][8][9][10][11][12][13][14][15][16][17][18][19]. Hence, we are dealing with an essentially different monitoring regime.…”

Path summation and von Neumann–like quantum measurements

“…In this limit, a sequence of values f j , j = 1, 2, ...M is replaced by a continuous function f (t), f → f (t). Continuous measurements, which model a particle in a 'measuring medium', are analysed in [25,26,27,28,29,30,31,32]. This list is not exhaustive, and one can envisage various sequences and combinations of von Neumann, finite time and continuous measurements.…”

“…Equally, an analysis purely in terms of quantum histories, such as Feynman paths [7,8], has the disadvantage of leaving open the question of how, if at all, the obtained amplitudes can be observed. There are also different types of quantum measurements to be considered: (quasi)instantaneous von Neumann measurements [2], most commonly used in applications such as quantum information theory, finite time measurements [9] studied in [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24] in connection with the tunnelling time problem and continuous measurements [25,26,27,28,29,30,31,32], where a record of particle's evolution is produced by a 'measuring medium'. In addition, measurements of the same type differ in accuracy, depending on the strength of interaction between the system an a meter or an environment.…”