Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Surveys In High Energy Physics

Effect of monitoring on almost stable systems

C. H. Woo

Published Jan 1, 1984• 0 citations
Publisher

Abstract

There are large discrepancies between the various estimates in the literature for the time interval below which the decay of a resonance may be significantly inhibited by monitoring. The disagreements arose because of our lack of knowledge of the detailed energy spectrum of the composite system undergoing decay. We emphasize here that for a large class of metastable systems the problem can be reduced to essentially kinematical considerations independent of the details of the spectrum, and point out that certain monitoring procedure can prevent even a free wave packet from spreading. If the proton is unstable, its decay will not be significantly suppressed unless the monitoring interval is shorter than 10−23 s.

DOI
10.1080/01422418408242493

Related papers

Real successive measurements on unstable quantum systems take nonvanishing time intervals and do not prevent them from decaying

Marta C. Bunge, Andrés J. Kálnay

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B•Sep 1, 1983•13 citations

Quantum dynamics of the Henon–Heiles system

Mordechai Bixon, Joshua Jortner

In this paper, we investigate the quantum dynamics of wave packets of bound states in the nonlinear Henon–Heiles (HH) system. The time evolution of a wave packet was separated into two processes involving (a) the motion of its first moments and (b) its spreading. On the time scale when wave packet spreading can be neglected, we were able to establish relations between wave packet quantum dynamics expressed in terms of the initial-state population probability P(t) and classical trajectory dynamics. We have demonstrated that the initial states, which are characterized by a periodic time evolution of P(t) over many periods, are related to the five elliptic periodic orbits in the HH system. The decay of P(t) over a few vibrational periods is related to the classical features of quasiperiodic trajectories and can be accounted for in terms of overlap reduction effects. When the center of the initial wave packet is moved further away from the classical periodic orbits, P(t) is characterized by a single initial peak followed by a ’’noisy’’ background. There is no qualitative distinction between the ’’short-time’’ behavior of a wave packet initiated in distant integrable regions and in classical stochastic regions. For long times, wave packet spreading effects set in. Quantum mechanical estimates for the spreading time τs, which depends on the initial conditions, were provided. For wave packets initiated on periodic trajectories, τs is very long, becoming shorter as one moves away from the fixed points. The quantum mechanical long time (t≫τs) behavior of P(t) exhibits small-amplitude noisy time dependence for all initial conditions. This behavior may be described as ’’quantum mechanical stochasticity’’ and is related to the universal feature of irregularity of the spectral resolution of all wave packets in a nonlinear system. From this point of view, all wave packets exhibit ’’quantum stochastic behavior,’’ but there are vast quantitative differences for different initial conditions that are manifested in terms of the values of τs and of the average noisy amplitude. It should be emphasized that this ’’quantum stochasticity’’ is not related to classical stochasticity phenomena.

The Journal of Chemical Physics•Oct 15, 1982•32 citations

Point Interactions in Systems of Fermions

Moser, Thomas

In this thesis we will discuss systems of point interacting fermions, their stability and other spectral properties. Whereas for bosons a point interacting system is always unstable this ques- tion is more subtle for a gas of two species of fermions. In particular the answer depends on the mass ratio between these two species. Most of this work will be focused on the N + M model which consists of two species of fermions with N, M particles respectively which interact via point interactions. We will introduce this model using a formal limit and discuss the N + 1 system in more detail. In particular, we will show that for mass ratios above a critical one, which does not depend on the particle number, the N + 1 system is stable. In the context of this model we will prove rigorous versions of Tan relations which relate various quantities of the point-interacting model. By restricting the N + 1 system to a box we define a finite density model with point in- teractions. In the context of this system we will discuss the energy change when introducing a point-interacting impurity into a system of non-interacting fermions. We will see that this change in energy is bounded independently of the particle number and in particular the bound only depends on the density and the scattering length. As another special case of the N + M model we will show stability of the 2 + 2 model for mass ratios in an interval around one. Further we will investigate a different model of point interactions which was discussed before in the literature and which is, contrary to the N + M model, not given by a limiting procedure but is based on a Dirichlet form. We will show that this system behaves trivially in the thermodynamic limit, i.e. the free energy per particle is the same as the one of the non-interacting system.

•Jan 1, 2018•0 citations

Effect of the Measurement on the Decay Rate of a Quantum System

B. Elattari, S. A. Gurvitz

Springer eBooks•Nov 28, 2007•1 citation

A Critical Discussion on the Decay of Quantum Unstable Systems

Luciano Fonda

De Gruyter eBooks•Dec 31, 1977•1 citation

Transition state theory for wave packet dynamics: I. Thermal decay in metastable Schrödinger systems

Andrej Junginger, Jörg Main, Günter Wunner +1 more

We demonstrate the application of transition state theory to wave packet dynamics in metastable Schrödinger systems which are approached by means of a variational ansatz for the wavefunction and whose dynamics is described within the framework of a time-dependent variational principle. The application of classical transition state theory, which requires knowledge of a classical Hamilton function, is made possible by mapping the variational parameters to classical phase space coordinates and constructing an appropriate Hamiltonian in action variables. This mapping, which is performed by a normal form expansion of the equations of motion and an additional adaptation to the energy functional, as well as the requirements to the variational ansatz are discussed in detail. The applicability of the procedure is demonstrated for a cubic model potential for which we calculate thermal decay rates of a frozen Gaussian wavefunction. The decay rate obtained with a narrow trial wavefunction agrees perfectly with the results using the classical normal form of the corresponding point particle. The results with a broader trial wavefunction go even beyond the classical approach, i.e. they agree with those using the quantum normal form. The method presented here will be applied to Bose–Einstein condensates in the following paper (Junginger et al 2012 J. Phys. A: Math. Theor. 45 155202).

arXiv:1202.2758•Journal of Physics A Mathematical and Theoretical•Mar 27, 2012•9 citations
There are large discrepancies between the various estimates in the literature for the time interval below which the decay of a resonance may be significantly inhibited by monitoring. The disagreements arose because of our lack of knowledge of the detailed energy spectrum of the composite system undergoing decay. We emphasize here that for a large class of metastable systems the problem can be reduced to essentially kinematical considerations independent of the details of the spectrum, and point out that certain monitoring procedure can prevent even a free wave packet from spreading. If the proton is unstable, its decay will not be significantly suppressed unless the monitoring interval is shorter than 10−23 s.
In this paper, we investigate the quantum dynamics of wave packets of bound states in the nonlinear Henon–Heiles (HH) system. The time evolution of a wave packet was separated into two processes involving (a) the motion of its first moments and (b) its spreading. On the time scale when wave packet spreading can be neglected, we were able to establish relations between wave packet quantum dynamics expressed in terms of the initial-state population probability P(t) and classical trajectory dynamics. We have demonstrated that the initial states, which are characterized by a periodic time evolution of P(t) over many periods, are related to the five elliptic periodic orbits in the HH system. The decay of P(t) over a few vibrational periods is related to the classical features of quasiperiodic trajectories and can be accounted for in terms of overlap reduction effects. When the center of the initial wave packet is moved further away from the classical periodic orbits, P(t) is characterized by a single initial peak followed by a ’’noisy’’ background. There is no qualitative distinction between the ’’short-time’’ behavior of a wave packet initiated in distant integrable regions and in classical stochastic regions. For long times, wave packet spreading effects set in. Quantum mechanical estimates for the spreading time τs, which depends on the initial conditions, were provided. For wave packets initiated on periodic trajectories, τs is very long, becoming shorter as one moves away from the fixed points. The quantum mechanical long time (t≫τs) behavior of P(t) exhibits small-amplitude noisy time dependence for all initial conditions. This behavior may be described as ’’quantum mechanical stochasticity’’ and is related to the universal feature of irregularity of the spectral resolution of all wave packets in a nonlinear system. From this point of view, all wave packets exhibit ’’quantum stochastic behavior,’’ but there are vast quantitative differences for different initial conditions that are manifested in terms of the values of τs and of the average noisy amplitude. It should be emphasized that this ’’quantum stochasticity’’ is not related to classical stochasticity phenomena.
In this thesis we will discuss systems of point interacting fermions, their stability and other spectral properties. Whereas for bosons a point interacting system is always unstable this ques- tion is more subtle for a gas of two species of fermions. In particular the answer depends on the mass ratio between these two species. Most of this work will be focused on the N + M model which consists of two species of fermions with N, M particles respectively which interact via point interactions. We will introduce this model using a formal limit and discuss the N + 1 system in more detail. In particular, we will show that for mass ratios above a critical one, which does not depend on the particle number, the N + 1 system is stable. In the context of this model we will prove rigorous versions of Tan relations which relate various quantities of the point-interacting model. By restricting the N + 1 system to a box we define a finite density model with point in- teractions. In the context of this system we will discuss the energy change when introducing a point-interacting impurity into a system of non-interacting fermions. We will see that this change in energy is bounded independently of the particle number and in particular the bound only depends on the density and the scattering length. As another special case of the N + M model we will show stability of the 2 + 2 model for mass ratios in an interval around one. Further we will investigate a different model of point interactions which was discussed before in the literature and which is, contrary to the N + M model, not given by a limiting procedure but is based on a Dirichlet form. We will show that this system behaves trivially in the thermodynamic limit, i.e. the free energy per particle is the same as the one of the non-interacting system.
We demonstrate the application of transition state theory to wave packet dynamics in metastable Schrödinger systems which are approached by means of a variational ansatz for the wavefunction and whose dynamics is described within the framework of a time-dependent variational principle. The application of classical transition state theory, which requires knowledge of a classical Hamilton function, is made possible by mapping the variational parameters to classical phase space coordinates and constructing an appropriate Hamiltonian in action variables. This mapping, which is performed by a normal form expansion of the equations of motion and an additional adaptation to the energy functional, as well as the requirements to the variational ansatz are discussed in detail. The applicability of the procedure is demonstrated for a cubic model potential for which we calculate thermal decay rates of a frozen Gaussian wavefunction. The decay rate obtained with a narrow trial wavefunction agrees perfectly with the results using the classical normal form of the corresponding point particle. The results with a broader trial wavefunction go even beyond the classical approach, i.e. they agree with those using the quantum normal form. The method presented here will be applied to Bose–Einstein condensates in the following paper (Junginger et al 2012 J. Phys. A: Math. Theor. 45 155202).