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Added by
Krzysztof Urbanowski
Publication date
2015
fields
Physics
and research's language is
English
Authors
K. Urbanowski
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Results presented in a recent paper Which is the Quantum Decay Law of Relativistic particles?, arXiv: 1412.3346v2 [quant--ph]], are analyzed. We show that approximations used therein to derive the main final formula for the survival probability of finding a moving unstable particle to be undecayed at time $t$ force this particle to almost stop moving, that is that, in fact, the derived formula is approximately valid only for $gamma cong 1$, where $gamma = 1/sqrt{1-beta^{2}}$ and $beta = v/c$, or in other words, for the velocity $v simeq 0$.
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Late time properties of moving relativistic particles are studied. Within the proper relativistic treatment of the problem we find decay curves of such particles and we show that late time deviations of the survival probability of these particles from the exponential form of the decay law, that is the transition times region between exponential and non-expo-nen-tial form of the survival amplitude, occur much earlier than it follows from the classical standard approach boiled down to replace time $t$ by $t/gamma_{L}$ (where $gamma_{L}$ is the relativistic Lorentz factor) in the formula for the survival probability. The consequence is that fluctuations of the corresponding decay curves can appear much earlier and much more unstable particles have a chance to survive up to these times or later. It is also shown that fluctuations of the instantaneous energy of the moving unstable particles has a similar form as the fluctuations in the particle rest frame but they are seen by the observer in his rest system much earlier than one could expect replacing $t$ by $t/gamma_{L}$ in the corresponding expressions for this energy and that the amplitude of these fluctuations can be even larger than it follows from the standard approach. All these effects seems to be important when interpreting some accelerator experiments with high energy unstable particles and the like (possible connections of these effects with GSI anomaly are analyzed) and some results of astrophysical observations.
We analyze the achievable limits of the quantum information processing of the weak interaction revealed by hyperons with spin. We find that the weak decay process corresponds to an interferometric device with a fixed visibility and fixed phase difference for each hyperon. Nature chooses rather low visibilities expressing a preference to parity conserving or violating processes (except for the decay $Sigma^+longrightarrow p pi^0$). The decay process can be considered as an open quantum channel that carries the information of the hyperon spin to the angular distribution of the momentum of the daughter particles. We find a simple geometrical information theoretic interpretation of this process: two quantization axes are chosen spontaneously with probabilities $frac{1pmalpha}{2}$ where $alpha$ is proportional to the visibility times the real part of the phase shift. Differently stated the weak interaction process corresponds to spin measurements with an imperfect Stern-Gerlach apparatus. Equipped with this information theoretic insight we show how entanglement can be measured in these systems and why Bells nonlocality (in contradiction to common misconception in literature) cannot be revealed in hyperon decays. We study also under which circumstances contextuality can be revealed.
Results of theoretical studies of the quantum unstable systems caused that there are rather widespread belief that a universal feature od the quantum decay process is the presence of three time regimes of the decay process: the early time (initial) leading to the Quantum Zeno (or Anti Zeno) Effects, exponential (or canonical) described by the decay law of the exponential form, and late time characterized by the decay law having inverse--power law form. Based on the fundamental principles of the quantum theory we give the proof that there is no time interval in which the survival probability (decay law) could be a decreasing function of time of the purely exponential form but even at the exponential regime the decay curve is oscillatory modulated with a smaller or a large amplitude of oscillations depending on parameters of the model considered.
Methods based on the use of Greens functions or the Jost functions and the Fock-Krylov method are apparently very different approaches to understand the time evolution of unstable states. We show that the two former methods are equivalent up to some constants and as an outcome find an analytic expression for the energy density of states in the Fock-Krylov amplitude in terms of the coefficients introduced in the Greens functions and the Jost functions methods. This model-independent density is further used to obtain an analytical expression for the survival amplitude and study its behaviour at large times. Using these expressions, we investigate the origin of the oscillatory behaviour of the decay law in the region of the transition from the exponential to the non-exponential at large times. With the objective to understand the failure of nuclear and particle physics experiments in observing the non-exponential decay law predicted by quantum mechanics for large times, we derive analytical formulae for the critical transition time, $t_c$, from the exponential to the inverse power law behaviour at large times. Evaluating $tau_c = Gamma t_c$ for some particle resonances and narrow nuclear states which have been tested experimentally to verify the exponential decay law, we conclude that the large time power law in particle and nuclear decay is hard to find experimentally.
We present the probability preserving description of the decaying particle within the framework of quantum mechanics of open systems taking into account the superselection rule prohibiting the superposition of the particle and vacuum. In our approach the evolution of the system is given by a family of completely positive trace preserving maps forming one-parameter dynamical semigroup. We give the Kraus representation for the general evolution of such systems which allows one to write the evolution for systems with two or more particles. Moreover, we show that the decay of the particle can be regarded as a Markov process by finding explicitly the master equation in the Lindblad form. We also show that there are remarkable restrictions on the possible strength of decoherence.
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