A new approach to quantum theory of multimode coupled parametric processes
A new approach is proposed to solve the quantum evolution problem for a system with an arbitrary number of coupled optical parametric processes. Our method is based on the canonical transformations which define the evolution of the system in the Heisenberg picture. This theory overcomes the difficulties arising in the Wei–Norman method. The application of the approach developed is illustrated with the example of generation of a three-mode entangled light field.
For a generic quantum integrable system, we describe the asymptotics of the eigenstate density and of the trace of the evolution operator in all orders of the quantization parameter. This is done by using quantum symplectic geometry, which makes the given quantum system to be equivalent to a deformed classical system with arbitrary accuracy with respect to the quantization parameter. The asymptotics is explicitly given via the deformed symplectic form, deformed Liouville–Arnold tori, and deformed Maslov class.
I discuss the ontological nature and heuristic value of psychedelic experience. I argue that psychedelic phenomena may manifest the activity of certain mental formations and brain mechanisms that otherwise remain hidden. Thus, psychedelic phenomena can be heuristic tools and intriguing objects of the scientific study. I consider two types of psychedelic phenomena in particular. The first is the moral cleansing that may accompany a psychedelic trip. The second is the appearance of visual and auditory hallucinations. I establish a unified explanatory ground for the phenomena that are commonly viewed as distinct in their genesis. I explain both types of phenomena as products of the amplified imaginative ability of the brain under a substance’s influence. I suggest that the activation of imagination causes an increased empathy and thus accentuates moral feelings. I propose the hypothesis that hallucinations are mental objects of a quantum nature. I argue that no ontologically separate reality stands behind psychedelic visions.
Quantum fluctuations in quasi-one-dimensional superconducting channels leading to spontaneous changes of the phase of the order parameter by 2, alternatively called quantum phase slips (QPS), manifest themselves as the finite resistance well below the critical temperature of thin superconducting nanowires and the suppression of persistent currents in tiny superconducting nanorings. Here we report the experimental evidence that in a current-biased superconducting nanowire the same QPS process is responsible for the insulating state—the Coulomb blockade. When exposed to rf radiation, the internal Bloch oscillations can be synchronized with the external rf drive leading to formation of quantized current steps on the I-V characteristic. The effects originate from the fundamental quantum duality of a Josephson junction and a superconducting nanowire governed by QPS—the QPS junction
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.
A form for an unbiased estimate of the coefficient of determination of a linear regression model is obtained. It is calculated by using a sample from a multivariate normal distribution. This estimate is proposed as an alternative criterion for a choice of regression factors.