In the Maze of Data Languages

In data languages the positions of strings and trees carry a label from a finite alphabet and a data value from an infinite alphabet. Extensions of automata and logics over finite alphabets have been defined to recognize data languages, both in the string and tree cases. In this paper we describe and compare the complexity and expressiveness of such models to understand which ones are better candidates as regular models

Quantum Parametric Resonance of a dissipative oscillator: fading and persistent memory in the long-time evolution

The evolution of a quantum oscillator, with periodically varying frequency and damping, is studied in the two cases of parametric resonance (PR) producing a limited, or unlimited stretching of the wave function. The different asymptotic behaviors of the energy distribution, show the non trivial interplay between PR and the initial quantum state. In the first case, the oscillator's mean energy tends asymptotically to a fully classical value, independent of the initial state, with vanishing relative quantum fluctuations. In the second case, the memory of the initial state persists over arbitrary long time scales, both in the mean value and in the large quantum fluctuations of the energy.Comment: 20 pages, 2 figure

The nitrite anion: the key intermediate in alkyl nitrates degradative mechanism.

Alkyl nitrates, _in vivo_, are metabolized to yield nitric oxide, and thiol groups are considered necessary cofactors. This statement is based on studies that underline how these species potentiate hemodynamic responsiveness to nitrates in patients with ischemic heart disease. However, the role of thiols might be mediated by the formation of corresponding S-nitrosothiols, and a redox process is responsible for the nitrates' degradation: an enzyme, probably the cytochrome P450, is involved _in vivo_. Here, we report evidence that, in vitro, no reaction between thiols and alkyl nitrates takes place, but that stronger reducing agents, such as iron (II) derivatives, are necessary: alkoxy radicals and the nitrite anion are the reaction intermediates. The latter, in slightly acidic conditions, for instance mimicking ischemic conditions, is shown to nitrosilate thiols to the corresponding S-nitrosothiols: the real NO suppliers. Therefore, the direct release of NO from nitrates is excluded. Finally, the in vivo role of thiols on depletion and tolerance is also accounted for

Bogoliubov theory of interacting bosons: new insights from an old problem

In a gas of $N$ interacting bosons, the Hamiltonian $H_c$, obtained by dropping all the interaction terms between free bosons with moment $\hbar\mathbf{k}\ne\mathbf{0}$, is diagonalized exactly. The resulting eigenstates $|\:S,\:\mathbf{k},\:\eta\:\rangle$ depend on two discrete indices $S,\:\eta=0,\:1,\:\dots$, where $\eta$ numerates the \emph{quasiphonons} carrying a moment $\hbar\mathbf{k}$, responsible for transport or dissipation processes. $S$, in turn, numerates a ladder of \textquoteleft vacua\textquoteright$\:|\:S,\:\mathbf{k},\:0\:\rangle$, with increasing equispaced energies, formed by boson pairs with opposite moment. Passing from one vacuum to another ($S\rightarrow S\pm1$), results from creation/annihilation of new momentless collective excitations, that we call \emph{vacuons}. Exact quasiphonons originate from one of the vacua by \textquoteleft creating\textquoteright$\:$an asymmetry in the number of opposite moment bosons. The well known Bogoliubov collective excitations (CEs) are shown to coincide with the exact eigenstates $|\:0,\:\mathbf{k},\:\eta\:\rangle$, i.e. with the quasiphonons created from the lowest-level vacuum ($S=0$). All this is discussed, in view of existing or future experimental observations of the vacuons (PBs), a sort of bosonic Cooper pairs, which are the main factor of novelty beyond Bogoliubov theory.Comment: 13 pages, 1 figur

Exact canonic eigenstates of the truncated Bogoliubov Hamiltonian in an interacting bosons gas

In a gas of $N$ weakly interacting bosons \cite{Bogo1, Bogo2}, a truncated canonic Hamiltonian $\widetilde{h}_c$ follows from dropping all the interaction terms between free bosons with momentum $\hbar\mathbf{k}\ne\mathbf{0}$. Bogoliubov Canonic Approximation (BCA) is a further manipulation, replacing the number \emph{operator} $\widetilde{N}_{in}$ of free particles in $\mathbf{k}=\mathbf{0}$, with the total number $N$ of bosons. BCA transforms $\widetilde{h}_c$ into a different Hamiltonian $H_{BCA}=\sum_{\mathbf{k}\ne\mathbf{0}}\epsilon(k)B^\dagger_\mathbf{k}B_\mathbf{k}+const$, where $B^\dagger_\mathbf{k}$ and $B_\mathbf{k}$ create/annihilate non interacting pseudoparticles. The problem of the \emph{exact} eigenstates of the truncated Hamiltonian is completely solved in the thermodynamic limit (TL) for a special class of eigensolutions $|\:S,\:\mathbf{k}\:\rangle_{c}$, denoted as \textquoteleft s-pseudobosons\textquoteright, with energies $\mathcal{E}_{S}(k)$ and \emph{zero} total momentum. Some preliminary results are given for the exact eigenstates (denoted as \textquoteleft $\eta$-pseudobosons\textquoteright), carrying a total momentum $\eta\hbar\mathbf{k}$ ($\eta=\:1,\:2,\: \dots$). A comparison is done with $H_{BCA}$ and with the Gross-Pitaevskii theory (GPT), showing that some differences between exact and BCA/GPT results persist even in the TL. Finally, it is argued that the emission of $\eta$-pseudobosons, which is responsible for the dissipation $\acute{a}$ \emph{la} Landau \cite{L}, could be significantly different from the usual picture, based on BCA pseudobosons