Complex Reaction Kinetics in Chemistry: A unified picture suggested by Mechanics in Physics

Complex biochemical pathways or regulatory enzyme kinetics can be reduced to chains of elementary reactions, which can be described in terms of chemical kinetics. This discipline provides a set of tools for quantifying and understanding the dialogue between reactants, whose framing into a solid and consistent mathematical description is of pivotal importance in the growing field of biotechnology. Among the elementary reactions so far extensively investigated, we recall the socalled Michaelis-Menten scheme and the Hill positive-cooperative kinetics, which apply to molecular binding and are characterized by the absence and the presence, respectively, of cooperative interactions between binding sites, giving rise to qualitative different phenomenologies. However, there is evidence of reactions displaying a more complex, and by far less understood, pattern: these follow the positive-cooperative scenario at small substrate concentration, yet negative-cooperative effects emerge and get stronger as the substrate concentration is increased. In this paper we analyze the structural analogy between the mathematical backbone of (classical) reaction kinetics in Chemistry and that of (classical) mechanics in Physics: techniques and results from the latter shall be used to infer properties on the former

Symmetries and criticality of generalised van der Waals models

We consider a family of thermodynamic models such that the energy density can be expressed as an asymptotic expansion in the scale formal parameter and whose terms are suitable functions of the volume density. We examine the possibility to construct solutions for the Maxwell thermodynamic relations relying on their symmetry properties and deduce the critical properties implied in terms of the the dynamics of coexistence curves in the space of thermodynamic variables

Unified Treatment of Heterodyne Detection: the Shapiro-Wagner and Caves Frameworks

A comparative study is performed on two heterodyne systems of photon detectors expressed in terms of a signal annihilation operator and an image band creation operator called Shapiro-Wagner and Caves' frame, respectively. This approach is based on the introduction of a convenient operator $\hat \psi$ which allows a unified formulation of both cases. For the Shapiro-Wagner scheme, where $[\hat \psi, \hat \psi^{\dag}] =0$, quantum phase and amplitude are exactly defined in the context of relative number state (RNS) representation, while a procedure is devised to handle suitably and in a consistent way Caves' framework, characterized by $[\hat \psi, \hat \psi^{\dag}] \neq 0$, within the approximate simultaneous measurements of noncommuting variables. In such a case RNS phase and amplitude make sense only approximately.Comment: 25 pages. Just very minor editorial cosmetic change

Integrable extended van der Waals model

Inspired by the recent developments in the study of the thermodynamics of van der Waals fluids via the theory of nonlinear conservation laws and the description of phase transitions in terms of classical (dissipative) shock waves, we propose a novel approach to the construction of multi-parameter generalisations of the van der Waals model. The theory of integrable nonlinear conservation laws still represents the inspiring framework. Starting from a macroscopic approach, a four parameter family of integrable extended van der Waals models is indeed constructed in such a way that the equation of state is a solution to an integrable nonlinear conservation law linearisable by a Cole–Hopf transformation. This family is further specified by the request that, in regime of high temperature, far from the critical region, the extended model reproduces asymptotically the standard van der Waals equation of state. We provide a detailed comparison of our extended model with two notable empirical models such as Peng–Robinson and Soave’s modification of the Redlich–Kwong equations of state. We show that our extended van der Waals equation of state is compatible with both empirical models for a suitable choice of the free parameters and can be viewed as a master interpolating equation. The present approach also suggests that further generalisations can be obtained by including the class of dispersive and viscous-dispersive nonlinear conservation laws and could lead to a new type of thermodynamic phase transitions associated to nonclassical and dispersive shock waves

Effects of quenching protocols based on parametric oscillators

We consider the problem of understanding the basic features displayed by quantum systems described by parametric oscillators whose time-dependent frequency parameter varies continuously during evolution so to realize quenching protocols of different types. To this scope we focus on the case where behaves like a Morse potential, up to possible sign reversion and translations in the plane. We derive closed form solution for the time-dependent amplitude of quasi-normal modes, which is the very fundamental dynamical object entering the description of both classical and quantum parametric oscillators, and highlight its significant characteristics for distinctive cases arising based on the driving specifics. After doing so, we provide an insight on the way quantum states evolve by paying attention on the position–momentum Heisenberg uncertainty principle and the statistical aspects implied by second-order correlation functions over number-type states

Non-autonomous Hamiltonian quantum systems, operator equations and representations of Bender-Dunne Weyl ordered basis under time-dependent canonical transformations

We solve the problem of integrating operator equations for the dynamics of nonautonomous quantum systems by using time-dependent canonical transformations. The studied operator equations essentially reproduce the classical integrability conditions at the quantum level in the basic cases of one-dimensional nonautonomous dynamical systems. We seek solutions in the form of operator series in the Bender–Dunne basis of pseudodifferential operators. Together with this problem, we consider quantum canonical transformations. The minimal solution of the operator equation in the representation of the basis at a fixed time corresponds to the lowest-order contribution of the solution obtained as a result of applying a canonical linear transformation to the basis elements