Study of the chemical structures of the photo-cross-linking products between Tyr and the 5-azido-2-nitrobenzoyl residue

Irradiation of N-(tyrosyl)-N'-(5-azido-2-nitrobenzoyl)-1,2-diaminoethane (I) initiates chemical reactions that lead to different products depending on the experimental conditions. All of these products are attributed to the reactions of triplet 4-nitrobenzoyl nitrene (4NBN). The reactions of triplet 4NBN with the tyrosyl residue result in the formation of two distinct products: compound II, which is unstable in aqueous solution, and the stable compound cyclo-[1-(4'-nitro-3'-benzoyl)-2-(aminotyrosyl)-N,N'-ethylenediami ne] (III). The formation of II is detected only in aerobic conditions. The unstable photoproduct II converts almost completely into compound III when its solution is concentrated. The photoproducts II and III have absorption spectra that are close to those of the photolabelled peptides. This finding is important for speculating about the chemical nature of the photomodification products of protein tyrosyl residues by the arylazide group.     

Quenching of tryptophan fluorescence of firefly luciferase by substrates

The interaction of firefly luciferase with substrates (luciferin and MgATP) by steady-state and time-resolved fluorescence is studied. The efficient quenching of tryptophan fluorescence of the active enzyme takes place upon its binding with substrates. In the presence of ATP the quenching is of dynamic type and is caused by structural changes in the protein molecule upon ATP binding. A model is proposed in which the complex has smaller fluorescence quantum yield than the free enzyme because of partial quenching of tryptophan fluorescence by the new microenvironment. Quenching of tryptophan fluorescence by luciferin due to the efficient energy transfer from tryptophan to luciferin is discussed. The calculated distance between Trp-419 and luciferin for the L. mingrelica luciferase in the enzyme-substrate complex is less than 12 A.     

Quantum rule for detection probability from Brownian motion in the space of classical fields

We obtain Born’s rule from the classical theory of random waves in combination with the use of thresholdtype detectors. We consider a model of classical random waves interacting with classical detectors and reproducing Born’s rule. We do not discuss complicated interpretational problems of quantum foundations. The reader can select between the “weak interpretation,” the classical mathematical simulation of the quantum measurement process, and the “strong interpretation,” the classical wave model of the real quantum (in fact, subquantum) phenomena.     

Non-Archimedean Analogues of Orthogonal and Symmetric Operators and p-adic Quantization

We study orthogonal and symmetric operators in non-Archimedean Hilbert spaces in the connection with p-adic quantization. This quantization describes measurements with finite precision. Symmetric (bounded) operators in the p-adic Hilbert spaces represent physical observables. We study spectral properties of one of the most important quantum operators, namely, the operator of the position (which is represented in the p-adic Hilbert L₂-space with respect to the p-adic Gaussian measure). Orthogonal isometric isomorphisms of p-adic Hilbert spaces preserve precisions of measurements. We study properties of orthogonal operators. It is proved that each orthogonal operator in the non-Archimedean Hilbert space is continuous. However, there exist discontinuous operators with the dense domain of definition which preserve the inner product. There also exist nonisometric orthogonal operators. We describe some classes of orthogonal isometric operators and we study some general questions of the theory of non-Archimedean Hilbert spaces (in particular, general connections between topology, norm and inner product).     

Quantum correlations from classical Gaussian correlations

Already Schrödinger tried to proceed towards a purely wave theory of quantum phenomena. However, he should give up and accept Born’s probabilistic interpretation of the wave function. A simple mathematical fact was behind this crucial decision. The wave function of a composite system S = (S ₁, S ₂) belongs to the tensor product of two L2 spaces and not to their Cartesian product. It was impossible to consider it as a vector function ψ(x) = (ψ ₁(x), ψ ₂(x)), x ∈ R ³. Here we solved this problem. It is shown that there exists a mathematical formalism that provides a possibility to describe composite quantum systems without appealing to the tensor product of the Hilbert state space, and one can proceed with their Cartesian product. It may have important consequences for the understanding of entanglement and applications to quantum information theory. It seems that “quantum algorithms” can be realized on the basis of classical wave mechanics. However, the interpretation of the proposed mathematical formalism is a difficult problem and needs additional studies.     

p-Adic physics, non-well-founded reality and unconventional computing

We consider perspectives of application of coinductive and corecursive methods of non-well-founded mathematics to modern physics, especially to adelic and p-adic quantum mechanics. We also survey perspectives of relationship between modern physics and unconventional computing.     

Born's rule from classical random fields

This Letter is an attempt to go beyond QM. In our approach density operators of QM can be represented as covariance operators of classical random fields. Born's rule can be obtained from measurement theory for classical random field under the assumption that the probability of detection of field is proportional to the power of this field.     

New experimental tests of the photon’s indivisibility

We consider the old foundational problem of quantum/classical optics ?C indivisibility of photon. Quantum theory predicts that in experiments on coincidence detection double clicks are impossible (up to noise); on the other hand, the known semiclassical and classical models predict a relatively high rate of coincidence. We present a model of the classical (random) wave type which predicts that in the same way as in quantum optics coincidence of clicks is a rare event. However, this model has a new prediction compared to quantum optics, namely, that the rate of double clicks depends substantially on the discrimination threshold of a detector. We propose to perform new detailed tests to check the discrimination threshold dependence predicted by our model. In experiments on coincidence detection performed to date, for example, the Grangier experiment does not contain statistical data on the threshold dependence.     

p-adic dynamic systems

Dynamic systems in non-Archimedean number fields (i.e., fields with non-Archimedean valuations) are studied. Results are obtained for the fields of p-adic numbers and complex p-adic numbers. Simple p-adic dynamic systems have a very rich structure—attractors, Siegel disks, cycles, and a new structure called a “fuzzy cycle”. The prime number p plays the role of a parameter of the p-adic dynamic system. Changing p radically changes the behavior of the system: attractors may become the centers of Siegel disks, and vice versa, and cycles of different lengths may appear or disappear. Alexander von Humboldt Fellowship and SFB 237 Essen-Bochum-Düsseldorf, on leave from Moscow State Institute of Electronic Engineering. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 114, No. 3, pp. 349–365, March, 1998.