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Register a new userOscillating decay of an unstable system
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We study the short-time and medium-time behavior of the survival probability in the frame of the $N$-level Friedrichs model. The time evolution of an arbitrary unstable initial state is determined. We show that the survival probability may oscillate significantly during the so-called exponential era. This result explains qualitatively the experimental observations of the NaI decay.
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We consider a model of a unstable state defined by the truncated Breit-Wigner energy density distribution function. An analytical form of the survival amplitude $a(t)$ of the state considered is found. Our attention is focused on the late time properties of $a(t)$ and on effects generated by the non--exponential behavior of this amplitude in the late time region: In 1957 Khalfin proved that this amplitude tends to zero as $t$ goes to the infinity more slowly than any exponential function of $t$. This effect can be described using a time-dependent decay rate $gamma(t)$ and then the Khalfin result means that this $gamma(t)$ is not a constant but at late times it tends to zero as $t$ goes to the infinity. It appears that the energy $E(t)$ of the unstable state behaves similarly: It tends to the minimal energy $E_{min}$ of the system as $t to infty$. Within the model considered we find two first leading time dependent elements of late time asymptotic expansions of $E(t)$ and $gamma (t)$. We discuss also possible implications of such a late time asymptotic properties of $E(t)$ and $gamma (t)$ and cases where these properties may manifest themselves.
The role played by Time in the quantum theory is still mysterious by many aspects. In particular it is not clear today whether the distribution of decay times of unstable particles could be described by a Time Operator. As we shall discuss, different approaches to this problem (one could say interpretations) can be found in the literature on the subject. As we shall show, it is possible to conceive crucial experiments aimed at distinguishing the different approaches, by measuring with accuracy the statistical distribution of decay times of entangled particles. Such experiments can be realized in principle with entangled kaon pairs.
We report the first observation of the Quantum Zeno and Anti-Zeno effects in an unstable system. Cold sodium atoms are trapped in a far-detuned standing wave of light that is accelerated for a controlled duration. For a large acceleration the atoms can escape the trapping potential via tunneling. Initially the number of trapped atoms shows strong non-exponential decay features, evolving into the characteristic exponential decay behavior. We repeatedly measure the number of atoms remaining trapped during the initial period of non-exponential decay. Depending on the frequency of measurements we observe a decay that is suppressed or enhanced as compared to the unperturbed system.
We consider an unstable bound system of two supersymmetric Dirichlet branes of different dimensionality ($p,p$ with $p<p$) embedded in a flat non-compactified IIA or IIB type background. We study the decay, via tachyonic condensation, of such unstable bound states leading to a pair of bound D$(p-1)$, D$p$-branes. We show that only when the gauge fields carried by the D$p$-brane are localised perependicular to the tachyon direction, then tachyon condensation will indeed take place. We perform our analysis by combining both, the Hamiltonian and the Lagrangian approach.
Starting from the formal solution to the Heisenberg equation, we revisit an universal model for a quantum open system with a harmonic oscillator linearly coupled to a boson bath. The analysis of the decay process for a Fock state and a coherent state demonstrate that this method is very useful in dealing with the problems in decay process of the open system. For finite temperature, the calculations of the reduced density matrix and the mean excitation number for the open system show that an initial coherent state will evolve into a temperature-dependant coherent state after tracing over the bath variables. Also in short-time limit, a temperature-dependant effective Hamiltonian for the open system characterizes the decay process of the open system.
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