Microscopic theory of decaying many-particle systems

In this paper, the non-exponential decay is analyzed with the help of simple computer experiments performed by T. Petrosky, simulating classical radiation damping. The non-exponential decay is studied and shown to depend on the preparation of the system. However, whatever the initial preparation, the system reaches the decay predicted by classical radiation theory after a short time we call the Zeno's time. The similitude of Petrosky's results with computer experiments for the approach to equilibrium in many-body systems is emphasized. However, while there one deals with times which are multiple of the relaxation time, the irreversibility manifest in radiation theory occurs always over a much shorter time scale, the Zeno's time. In atomic systems, this would be a time order of 10/sup /minus/18/ seconds. These results are of great interest for the understanding of the microscopic mechanism of radiation. Let us consider a charged oscillator. In a first stage, this oscillator has to produce the field oscillators to which it may transfer energy through the usual resonance mechanism. Radiation appears therefore as a kind of non linear autocatalytic process, involving a self-organization mechanism. The behavior during the Zeno period can be explained easily in terms of subdynamics as introduced by the Brussel's group. We see that there is no transition from reversibility to irreversibility. Irreversible processes start at the very moment at which the system is prepared. It is important to stress that an unstable particle is itself the result of irreversible processes. As a result, an unstable particle (or an excited atomic state) can no more be described in terms of wave functions, as irreversible processes are not included in Schroedinger's equation. 14 refs. 3 figs.In this paper, the non-exponential decay is analyzed with the help of simple computer experiments performed by T. Petrosky, simulating classical radiation damping. The non-exponential decay is studied and shown to depend on the preparation of the system. However, whatever the initial preparation, the system reaches the decay predicted by classical radiation theory after a short time we call the Zeno's time. The similitude of Petrosky's results with computer experiments for the approach to equilibrium in many-body systems is emphasized. However, while there one deals with times which are multiple of the relaxation time, the irreversibility manifest in radiation theory occurs always over a much shorter time scale, the Zeno's time. In atomic systems, this would be a time order of 10/sup /minus/18/ seconds. These results are of great interest for the understanding of the microscopic mechanism of radiation. Let us consider a charged oscillator. In a first stage, this oscillator has to produce the field oscillators to which it may transfer energy through the usual resonance mechanism. Radiation appears therefore as a kind of non linear autocatalytic process, involving a self-organization mechanism. The behavior during the Zeno period can be explained easily in terms of subdynamics as introduced by the Brussel's group. We see that there is no transition from reversibility to irreversibility. Irreversible processes start at the very moment at which the system is prepared. It is important to stress that an unstable particle is itself the result of irreversible processes. As a result, an unstable particle (or an excited atomic state) can no more be described in terms of wave functions, as irreversible processes are not included in Schroedinger's equation. 14 refs. 3 figs.

Jan 1, 19871 citation

Long-range correlations in nonequilibrium quantum Lorentz gases

M. Yoshimura, T. R. Kirkpatrick

Spatial correlation functions in noninteracting disordered electronic systems maintained in a nonequilibrium steady state are studied using diagrammatic perturbation theory. The classical result obtained in a previous study is recovered for the correlation function of microscopic number densities of the moving particle and scatterer; it decays as 1/ ${\mathit{r}}^{2}$ in three dimensions. The number-density correlation function of moving particles is also calculated. We find that spatial correlations at second order in a concentration gradient decay linearly in three dimensions at low temperatures. The connection of this result with mesoscopic fluctuations is discussed. \textcopyright{} 1996 The American Physical Society.Spatial correlation functions in noninteracting disordered electronic systems maintained in a nonequilibrium steady state are studied using diagrammatic perturbation theory. The classical result obtained in a previous study is recovered for the correlation function of microscopic number densities of the moving particle and scatterer; it decays as 1/${\mathit{r}}^{2}$ in three dimensions. The number-density correlation function of moving particles is also calculated. We find that spatial correlations at second order in a concentration gradient decay linearly in three dimensions at low temperatures. The connection of this result with mesoscopic fluctuations is discussed. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matterSep 1, 19967 citations

General Theory of Many-Particle Systems

Stephen J. Gustafson, Israel Michael Sigal

UniversitextJan 1, 20200 citations

Certified Quantum Randomness

Serge Massar

Randomness is a phenomena which we are confronted with all the time. Will it rain today? Will the train be on time? What present(s) will I receive at Christmas? But are such phenomena truly random?Good randomness is essential for many applications. For instance, cryptography, the art of hiding information from malicious parties, is only as good as the sources of randomness that underlie it. Quantum mechanics, the theory of microscopic phenomena, can only predict the probability of events. For instance quantum theory can only predict the probability that a radioactive nucleus will decay, not when the nucleus will decay. Does this mean that microscopic phenomena are truly random?By studying systems of two entangled particles, it can be shown both theoretically and experimentally that events at the microscopic scale are truly random, truly unpredictable. Beyond its philosophical implications, this result also has important potential applications. Indeed it implies that one can build random number generators whose output is random and certifies that the device works correctly. That is, if the random number generator malfunctions in some way, if the numbers it produces cease to be random, this will automatically be detected. By extending this idea, one could also build quantum cryptographic systems and quantum computers that certify that they work correctly. We discuss the perspectives for practical implementations.Randomness is a phenomena which we are confronted with all the time. Will it rain today? Will the train be on time? What present(s) will I receive at Christmas? But are such phenomena truly random?Good randomness is essential for many applications. For instance, cryptography, the art of hiding information from malicious parties, is only as good as the sources of randomness that underlie it. Quantum mechanics, the theory of microscopic phenomena, can only predict the probability of events. For instance quantum theory can only predict the probability that a radioactive nucleus will decay, not when the nucleus will decay. Does this mean that microscopic phenomena are truly random?By studying systems of two entangled particles, it can be shown both theoretically and experimentally that events at the microscopic scale are truly random, truly unpredictable. Beyond its philosophical implications, this result also has important potential applications. Indeed it implies that one can build random number generators whose output is random and certifies that the device works correctly. That is, if the random number generator malfunctions in some way, if the numbers it produces cease to be random, this will automatically be detected. By extending this idea, one could also build quantum cryptographic systems and quantum computers that certify that they work correctly. We discuss the perspectives for practical implementations.

Jan 1, 20170 citations

{\mathit{r}}^{2}

in three dimensions. The number-density correlation function of moving particles is also calculated. We find that spatial correlations at second order in a concentration gradient decay linearly in three dimensions at low temperatures. The connection of this result with mesoscopic fluctuations is discussed. \textcopyright{} 1996 The American Physical Society.