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Register a new userEffects of phase space variables on oscillations of modified combinants
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It has been shown recently that additional information can be obtained from charged particle multiplicity distribution by investigating their modified combinants $C_j$, which exhibit periodic oscillatory behaviour. The modified combinants obtained from experimental data can be expressed in a recurrent form involving the probability of obtaining $N$ charged particles $P(N)$, scaled by the void probability $P(0)$. The effects of various experimental observables such as $|eta|$, $p_T$ and centre-of-mass collision energy $sqrt{s}$ on the oscillatory behaviour of $C_j$ will be discussed.
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The experimentally measured multiplicity distributions exhibit, after closer inspection, peculiarly enhanced void probability and oscillatory behavior of the modified combinants. We show that both these features can be used as additional sources of information, not yet fully explored, on the mechanism of multiparticle production. We provide their theoretical understanding within the class of compound distributions.
As shown recently, one can obtain additional information from the measured charged particle multiplicity distributions, $P(N)$, by investigating the so-called modified combinants, $C_j$, extracted from them. This information is encoded in the observed specific oscillatory behaviour of $C_j$, which phenomenologically can be described only by some combinations of compound distributions based on the Binomial Distribution. So far this idea has been checked in $pp$ and $e^+e^-$ processes (where observed oscillations are spectacularly strong). In this paper, we continue observation of multiparticle production from the modified combinants perspective by investigating dependencies of the observed oscillatory patterns on type of colliding particles, their energies and the phase space where they are observed. We also offer some tentative explanations based on different types of compound distributions and stochastic branching processes.
We present a comprehensive insight into counting distributions from the perspective of the combinants extracted from them. In particular, we focus on cases where these combinants exhibit oscillatory behavior that can provide an invaluable new source of information about the dynamics of the process under study. We show that such behavior can be described only by specific combinations of compound distributions based on the Binomial Distribution and provide their analytical forms which can be used in further investigations and which can be helpful in the analysis of all other types of counting distributions.
An hidden variable (hv) theory is a theory that allows globally dispersion free ensembles. We demonstrate that the Phase Space formulation of Quantum Mechanics (QM) is an hv theory with the position q, and momentum p as the hv. Comparing the Phase space and Hilbert space formulations of QM we identify the assumption that led von Neumann to the Hilbert space formulation of QM which, in turn, precludes global dispersion free ensembles within the theory. The assumption, dubbed I, is: If a physical quantity $mathbf{A}$ has an operator $hat{A}$ then $f(mathbf{A})$ has the operator $f(hat{A})$. This assumption does not hold within the Phase Space formulation of QM. The hv interpretation of the Phase space formulation provides novel insight into the interrelation between dispersion and non commutativity of position and momentum (operators) within the Hilbert space formulation of QM and mitigates the criticism against von Neumanns no hidden variable theorem by, virtually, the consensus.
This dissertation serves as a general introduction to Wigner functions, phase space, and quantum metrology but also strives to be useful as a how-to guide for those who wish to delve into the realm of using continuous variables, to describe quantum states of light and optical interferometry. We discuss the advantages of Wigner functions and their use to describe many quantum states of light. Throughout our metrology discussions, we will also discuss various quantum limits and use quantum Fisher information to show optimal bounds. When applicable, we also discuss the use of quantum Gaussian information and how it relates to our Wigner function treatment. The remainder of our discussion focuses on investigating the effects of photon addition and subtraction to various states of light and analyze the nondeterministic nature of this process. We use examples of $m$ photon additions to a coherent state as well as discuss the properties of an $m$ photon subtracted thermal state. We also provide an argument that this process must always be a nondeterministic one, or the ability to violate quantum limits becomes apparent. We show that using phase measurement as ones metric is much more restrictive, which limits the usefulness of photon addition and subtraction. When we consider SNR however, we show improved SNR statistics, at the cost of increased measurement time. In this case of SNR, we also quantify the efficiency of the photon addition and subtraction process.
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