Improvement of the design method of thermal networks: serial connection of heat exchangers

The mathematical model of the system is considered consisting of a series connection of three heating devices. A system of equations based on the energy conservation law is constructed, which turns out to be incomplete. It is shown that, given the known requirements for the system, expressed only in the efficiency of the system, the formalization of design often becomes insoluble. The system of equations is supplemented with expressions in accordance with the hypothesis of the proportionality of the amount of energy in an element and is presented in matrix form. The design task is reduced to determining the elements of the matrix by the value of the determinants. Analysis of the mathematical model made it possible to obtain an expression for the efficiency of the system as a function of energy exchange in its elements. This made it possible to obtain solutions for flows and their relationships in the elements of the system. In addition, the efficiency of inter-network and intra-network energy exchange has been determined, which satisfy the principles of equilibrium and minimum uncertainty in the values of the average parameters of the system. As an application, one of the main parameters, NTU, is considered, which determines the area of heat exchange with the external environment and the mass and dimensional characteristics of the heat exchange system. Models of direct and opposite switching on of flows with variations of flows and the value of the surface of devices when meeting the requirements for the efficiency of the system are considered. The results of comparing the design process with the iterative calculation method are presented and the advantages of the proposed approach are shown

Measurement-based extrapolation of spectral responsivity by using a low-NEP pyroelectric detector

In case the primary realization of the spectral responsivity scale is not conducted at all target wavelengths but at only a small part of them, one needs to extrapolate values at the specific wavelengths to an extended range. In this work, we present a fully experimental procedure to extrapolate a single value of spectral responsivity at 633 nm into the whole working wavelength range (250 – 1100) nm of Si photodiodes. It is based on spectral responsivity comparison between a Si trap detector and a low-NEP pyroelectric detector of nearly flat spectral response. For this purpose, we developed a setup specialized to compare a Si-trap detector of dc-current output with a pyroelectric detector of ac-voltage output by using a modulated probing light source and a monitoring technique. To keep the probing light chopped even for the dc-photocurrent readout, we adopted a low chopping frequency of 4 Hz and a triggered readout for the Si-trap detector, which leads to a speedy comparison between the Si-trap detector and the pyroelectric detector. For the reference pyroelectric detector, we characterized the spectral absorptivity of the black-coating and the nonlinearity of the lock-in amplifier readout. Compiling all the required information, the spectral responsivity of the Si trap detector could be measured with the minimum uncertainty of 0.3 % (k = 2), which was validated by comparing with that of our previous method based on a numerical extrapolation.

Minimum-uncertainty coherent states of the hyperbolic and trigonometric Rosen–Morse oscillators

A mixed supersymmetric-algebraic approach is employed to generate the minimum uncertainty coherent states of the hyperbolic and trigonometric Rosen–Morse oscillators. The method proposed produces the superpotentials, ground state eigenfunctions and associated eigenvalues as well as the Schrödinger equation in the factorized form amenable to direct treatment in the algebraic or supersymmetric scheme. In the standard approach the superpotentials are calculated by solution of the Riccati equation for the given form of potential energy function or by differentiation of the ground state eigenfunction. The procedure applied is general and permits derivation the exact analytical solutions and coherent states for the most important model oscillators employed in molecular quantum chemistry, coherent spectroscopy (femtochemistry) and coherent nonlinear optics.

Position, momentum, and wave spreading in curved space

The effect of the geometry (deviation from the flat space) on the quantum evolution of the momentum and position of a free particle is discussed. It is shown that beginning with a wave-packet of minimum uncertainty (a Gaussian wave), there is a usual increase in the product of the volume uncertainties in the momentum and position space, as seen in the quantum mechanics on a flat spaces. But there is also a contribution from geometry. The leading order of this contribution is calculated.

Zero uncertainty states in the presence of quantum memory

The uncertainty principle imposes a fundamental limit on predicting the measurement outcomes of incompatible observables even if complete classical information of the system state is known. The situation is different if one can build a quantum memory entangled with the system. Zero uncertainty states (in contrast with minimum uncertainty states) are peculiar quantum states that can eliminate uncertainties of incompatible von Neumann observables once assisted by suitable measurements on the memory. Here we determine all zero uncertainty states of any given set of nondegenerate observables and determine the minimum entanglement required. It turns out all zero uncertainty states are maximally entangled in a generic case, and vice versa, even if these observables are only weakly incompatible. Our work establishes a simple and precise connection between zero uncertainty and maximum entanglement, which is of interest to foundational studies and practical applications, including quantum certification and verification.

New family of parasupercoherent states: entanglement, uncertainties, and statistical properties

The general parasupersymmetric annihilation operator of arbitrary order does not reduce to the Kornbluth–Zypman general supersymmetric annihilation operator for the first order. In this paper, we introduce an annihilation operator for a parasupersymmetric harmonic oscillator that in the first order matches with the Kornblouth–Zypman results. Then, using the latter operator, we obtain the parasupercoherent states and calculate their entanglement, uncertainties, and statistics. We observe that these states are entangled for any arbitrary order of parasupersymmetry and their entanglement goes to zero for the large values of the coherency parameter. In addition, we find that the maximum of the entanglement of parasupercoherent states is a decreasing function of the parasupersymmetry order. Moreover, these states are minimum uncertainty states for large and also small values of the coherency parameter. Furthermore, these states show squeezing in one of the quadrature operators for a wide range of the coherency parameter, while no squeezing in the other quadrature operator is observed at all. In addition, using the Mandel parameter, we find that the statistics of these new states are subPoissonian for small values of the coherency parameter.