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arXiv:1509.07681 · Physical Review A

Neutral kaons as an open quantum system in a second quantization approach

Kordian A. Smoliński

Published Sep 24, 2015• 5 citations
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Abstract

We have shown that it is possible to formulate the consistent and probability-preserving description of the $\mathit{CP}$-symmetry-violating evolution of a system of decaying particles. This has been done within the framework of quantum mechanics of open systems. This approach allows the description of both the exponential decay and flavor oscillations. We have solved explicitly the Kossakowski-Lindblad master equation for a system of particles with violated $\mathit{CP}$ symmetry and found the evolution of any observable bilinear in creation and annihilation operators. The choice of a concrete observable can be done by the proper choice of initial conditions for the system of differential equations. We have calculated the evolution as well as mean values of the observables most interesting from the physical point of view, and we have found their lowest order difference with the $\mathit{CP}$-preserved values.

DOI
10.1103/physreva.92.032128

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We postulate a master equation, written in the language of creation and annihilation operators, as a candidate for unambiguous quantum mechanical description of unstable particles. We have found Kraus representation for the evolution driven by this master equation and study its properties. Both Schrödinger and Heisenberg picture of the system evolution are presented. We show that the resulting time evolution leads to exponential decay law. Moreover, we analyse mixing of particle flavours and show that it can lead to flavour oscillation phenomenon.
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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 a 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.
The study and characterisation of quantum entanglement represents an extended effort within the field of quantum information. This thesis addresses two problems. The first regards entanglement in open systems, where it’s more difficult to define a dichotomic (two outcome) observable due to population loss. The second problem concerns genuine multipartite entanglement, that is entanglement between many particles in states that cannot be separable with respect to any possible bipartition of a system.\nThe first chapter consists of an introduction to the basic elements of quantum mechanics and quantum information theory. We briefly describe a few historical facts about quantum mechanics and the study of entanglement, to help put things into perspective.\nThe second chapter is a detailed discussion of the neutral kaon system. These particles are produced in pairs and are described as a particle-antiparticle system. This system displays some unique properties like the violation of CP-symmetry, and shares some characteristics with other mesons, such as neutral particle oscillation and decay. This makes formulating Bell-type inequalities for them more difficult, but also provides the opportunity for new tests.\nThe third chapter continues with the presentation of an already existent effective formalism for performing Bell tests on neutral kaons. The essence of the formalism is a switch to the Heisenberg picture, transferring the time evolution and dependence on measurement directions to a so-called effective operator. This has many advantages, some of the most important being a proper normalization during population loss (due to decay), an easy application to\nthe case of multiple particles and the fact that it allows one to observe entanglement within the system for a relatively long amount of time. The final part presents a way to simulate neutral kaons with atomic systems, namely with Ytterbium isotopes and discuss what are the differences between these atomic systems and neutral kaons.\nThe second part of the thesis treats the problem of proving genuine multipartite entanglement from separable two-body marginals. For this, an introduction to semidefinite programming is necessary due to the fact that the problem under study can be formulated in terms of this method. We will briefly discuss linear and semidefinite programming as well as the concept of duality and provide some basic examples.\nThe formal description of this problem and previous results are provided in the fifth chapter. Our result shows that, through a cyclic iteration between two SDPs, one obtains states with the desired properties. Using this method we managed to go up to six qubit states for various configurations. From this we can construct higher-dimensional states having the same properties.
Decays of heavier neutrino mass eigenstates into lighter ones, while very slow in the Standard Model, can be significantly enhanced in scenarios with more than three neutrino flavours, or in models with new ultra-light particles such as Majorons. A full theoretical description is challenging due to the intricate interplay between oscillations and decay, interference between different decay channels, and the possibility of multi-step decay cascades. In this paper, we develop a fully general description of arbitrarily complex systems of oscillating and decaying neutrinos using methods from the theory of open quantum systems. Notably, we demonstrate how such systems can be implemented using the Lindblad master equation, the Liouvillian superoperator, as well as Kraus operators. The last two methods eschew the need for solving a differential equation, thereby showing superior numerical performance.
We investigate the open dynamics of quantum particles in relativistic scattering. Specifically, we consider the scattering process of quantum particles coupled to an environment initially in a vacuum state. Tracing out the environment and using the unitarity of an S operator, we find the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) generator that describes the evolution of the particles. The GKSL generator is exemplified by focusing on the concrete processes: one is the decay of scalar particle ($\ensuremath{\phi}\ensuremath{\rightarrow}\ensuremath{\chi}\ensuremath{\chi}$), and the others are the pair annihilation and the $2\ensuremath{\rightarrow}2$ scattering of scalar particles ($\ensuremath{\phi}\ensuremath{\phi}\ensuremath{\rightarrow}\ensuremath{\chi}\ensuremath{\chi}$ and $\ensuremath{\phi}\ensuremath{\phi}\ensuremath{\rightarrow}\ensuremath{\phi}\ensuremath{\phi}$). The GKSL generator for $\ensuremath{\phi}\ensuremath{\rightarrow}\ensuremath{\chi}\ensuremath{\chi}$ has a parameter with the coupling between $\ensuremath{\phi}$ and $\ensuremath{\chi}$ and the masses of the fields. The GKSL generator associated with $\ensuremath{\phi}\ensuremath{\phi}\ensuremath{\rightarrow}\ensuremath{\chi}\ensuremath{\chi}$ is characterized by a Lorentz-invariant function of initial momenta. Notably, in the pair annihilation process, we show that the probability of pair annihilation varies depending on the superposition state of incident scalar $\ensuremath{\phi}$ particles. Furthermore, we observe that the GKSL generators derived in this paper have Poincar\'e symmetry. This means that GKSL generators with Poincar\'e symmetry provide an effective description of the asymptotic behavior of open quantum dynamics in the long-term processes considered here.