Localized open systems in a thermodynamically closed system of chemical reactions

A thermodynamically closed system of chemical reactions becomes unstable against transforming spontaneously a locally planar reaction network into a spherically shaped one if the mean lifetime of the composite two-monomers is greater than the mean collision time of the polymers.     

Electrical transport in open and closed systems

Electrical conductance is typically calculated by approaches which view the electrical field as a causative source and the motion of carriers as a response. An alternative viewpoint, which starts from the flux of carriers maintained at the edges of a sample, and then calculates how charges build up and fields develop, has gained acceptance in the treatment of disordered systems, the solid state Aharanov-Bohm effect, and universal fluctuations. We analyze some of the less appreciated concomitants of this viewpoint, emphasizing both the generality and limitations of the viewpoint. Particular emphasis is given to the Residual Resistivity Dipole; localized scatterers in metallic conductivity are accompanied by highly localized transport fields. Closed Hamiltonian systems, e.g. a metallic ring with elastic scattering and driven by a time-dependent magnetic flux, are conservative. They cannot exhibit dissipation, under our conventionally accepted forms of physics. It is suggested that the limited precision available,in principle, in calculating the behavior of physical systems limits our ability to retrieve energy from supposedly conservative systems. This can be regarded as the ultimate source of dissipative processes.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Dynamics and steady states in excitable mobile agent systems

We study the spreading of excitations in 2D systems of mobile agents where the excitation is transmitted when a quiescent agent keeps contact with an excited one during a nonvanishing time. We show that the steady states strongly depend on the spatial agent dynamics. Moreover, the coupling between exposition time (omega) and agent-agent contact rate (CR) becomes crucial to understand the excitation dynamics, which exhibits three regimes with CR: no excitation for low CR, an excited regime in which the number of quiescent agents (S) is inversely proportional to CR, and, for high CR, a novel third regime, model dependent, where S scales with an exponent xi-1, with xi being the scaling exponent of omega with CR.     

Factorised steady states and condensation transitions in nonequilibrium systems

Systems driven out of equilibrium can often exhibit behaviour not seen in systems in thermal equilibrium —for example phase transitions in one-dimensional systems. In this talk I will review a simple model of a nonequilibrium system known as the ‘zero-range process’ and its recent developments. The nonequilibrium stationary state of this model factorises and this property allows a detailed analysis of several ‘condensation’ transitions wherein a finite fraction of the constituent particles condenses onto a single lattice site. I will then consider a more general class of mass transport models, encompassing continuous mass variables and discrete time updating, and present a necessary and sufficient condition for the steady state to factorise. The property of factorisation again allows an analysis of the condensation transitions which may occur.     

Quasistationary states in open disordered systems

Institute of Radiophysics and Electronics, Academy of Sciences of the Ukrainian SSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 33, No. 1, pp. 61–64, January, 1990.     

Control of unstable steady states in neutral time-delayed systems

We present an analysis of time-delayed feedback control used to stabilize an unstable steady state of a neutral delay differential equation. Stability of the controlled system is addressed by studying the eigenvalue spectrum of a corresponding characteristic equation with two time delays. An analytic expression for the stabilizing control strength is derived in terms of original system parameters and the time delay of the control. Theoretical and numerical results show that the interplay between thecontrol strength and two time delays provides a number of regions in the parameter space where the time-delayed feedback control can successfully stabilize an otherwise unstable steady state.     

Stability and fluctuation in chemical systems

Fluctuations around the steady state in chemical reactions are discussed. The connection between the two approaches in the literature, the Langevin equation approach and the master equation approach, is shown in terms of a path integral.     

Preferred states of open electronic systems

System-environment interaction may introduce dynamic destruction of quantum coherence, resulting in a special representation named as pointer states. In this work, pointer states of an open electronic system are studied. The decoherence effect is taken into account through two different ways which are Büttiker's virtual probe model and strong electron-phonon interaction in the polaron picture. The pointer states of the system with different coupling strength are investigated. The pointer states are identified by tracking the eigenstates of the density matrix in real-time propagation. It is found that the pointer states can emerge for arbitrary coupling strength. And the pointer states deform to the eigenstates of the system in the strong coupling limit, which indicates the vanish of quantumness in the strong coupling limit.     

Quantum fidelity of Gaussian states in open systems

Using the expression of the fidelity for the most general Gaussian quantum states, the behaviour of the quantum fidelity is described for the states of a harmonic oscillator interacting with an environment, in particular with a thermal bath. By taking a correlated squeezed Gaussian state as initial state, we calculate the quantum fidelity for both kinds of undisplaced and displaced states, and for different values of the squeezing and correlation parameters and of the environment temperature.     

Entropy,information, and complexity of the steady states of open systems not satisfying the principle of local equilibrium

The entropy of the steady state of an open electronic system is determined, and its relation to the entropy arriving at the environment is established. The notion of system ordering is defined, and quantitative parameters characterizing ordering are introduced. The information and conditional complexity of the system versus the state of thermodynamic chaos are determined. These values are numerically estimated for vacuum, magnetron, and Gunn diodes.     

Stability and equilibrium states of infinite classical systems

We prove that any stationary state describing an infinite classical system which is stable under local perturbations (and possesses some strong time clustering properties) must satisfy the classical KMS condition. (This in turn implies, quite generally, that it is a Gibbs state.) Similar results have been proven previously for quantum systems by Haag et al. and for finite classical systems by Lebowitz et al.Supported by N.S.F. Grant MPS 71-03375 A03. Part of this work carried out at the Courant Institute where it was supported by N.S.F. Grant GP-37069X.Supported in part by AFOSR Grant #73-2430 and N.S.F. Grant MP S75-20638.Supported by N.S.F. Grant # GP33136X-2. Part of this work was carried out at the Institute for Advanced Study.     

Invariant integral and the transition to steady states in separable dynamical systems

We show that the transition between fixed points in a separable dynamical system is fully described by an invariant integral. We discuss in detail the case of a system with two temporal variables with bilinear coupling, where the new stable state is attained asymptotically through spiraling into the fixed point. Through the invariance, it is possible to establish conditions for the control parameter that permit a (targeted) transition in finite time and without relaxation oscillations.     

Quantum-to-classical crossover of quasibound states in open quantum systems

In the semiclassical limit of open ballistic quantum systems, we demonstrate the emergence of instantaneous decay modes guided by classical escape faster than the Ehrenfest time. The decay time of the associated quasibound states is smaller than the classical time of flight. The remaining long-lived quasibound states obey random-matrix statistics, renormalized in compliance with the recently proposed fractal Weyl law for open systems [W.T. Lu, S. Sridhar, and M. Zworski, Phys. Rev. Lett. 91, 154101 (2003)]. We validate our theory numerically for a model system, the open kicked rotator.     

Quasi-gradient models of the dynamics of closed chemical systems

A new class of models of the chemical dynamics of closed systems, quasi-gradient models, is suggested. According to these models, the evolution of a chemically reacting system to the equilibrium state occurs along a thermodynamic potential gradient with an accuracy to a positive definite multiplier.     

Stochastic theory of nonequilibrium steady states. Part II: Applications in chemical biophysics

The mathematical theory of nonequilibrium steady state (NESS) has a natural application in open biochemical systems which have sustained source(s) and sink(s) in terms of a difference in their chemical potentials. After a brief introduction in Section 1, in Part II of this review, we present the widely studied biochemical enzyme kinetics, the workhorse of biochemical dynamic modeling, in terms of the theory of NESS (Section 2.1). We then show that several phenomena in enzyme kinetics, including a newly discovered activation-inhibition switching (Section 2.2) and the well-known non-Michaelis-Menten-cooperativity (Section 2.3) and kinetic proofreading (Section 2.4), are all consequences of the NESS of driven biochemical systems with associated cycle fluxes. Section 3 is focused on nonlinear and nonequilibrium systems of biochemical reactions. We use the phosphorylation-dephosphorylation cycle (PdPC), one of the most important biochemical signaling networks, as an example (Section 3.1). It starts with a brief introduction of the Delbrück-Gillespie process approach to mesoscopic biochemical kinetics (Sections 3.2 and 3.3). We shall discuss the zeroth-order ultrasensitivity of PdPC in terms of a new concept — the temporal cooperativity (Sections 3.4 and 3.5), as well as PdPC with feedback which leads to biochemical nonlinear bistability (Section 3.6). Also, both are nonequilibrium phenomena. PdPC with a nonlinear feedback is kinetically isomorphic to a self-regulating gene expression network, hence the theory of NESS discussed here could have wide applications to many other biochemical systems.     

Laser synthesis of chiral molecules in isotropic racemic media

The problem of directional laser synthesis of enantiomers in an isotropic racemic mixture of chiral molecules is analyzed taking into account rotational degrees of freedom of molecules. It is shown that the chirality of the polarization structure of a laser field is the most general necessary condition for the laser distillation of an isotropic non-racemic mixture of chiral molecules with the isotropic distribution over the Eulerian angles. In the approximation of the electric-dipole interaction, the required field configuration can be provided due to noncoplanarity of the polarization vectors of laser-pump components. A relevant experimental scheme is proposed and calculated for the transformation of an isotropic racemic mixture with the help of a three-component pulsed laser field. It is shown that the possibility of the laser control of chirality in an isotropic medium corresponds to nonzero information on coupling between the input and output in the laser field-chiral molecular state information channel.     

On stability of steady states

Conditions of stability with respect to finite perturbations of a steady transport state are derived on the basis of a statistical theory for a very general type of equations of motion for the state change. Infinitesimal perturbations yield the stability condition of Glansdorff and Prigogine.