Two-state Theory Research Articles

Stochastic resonance: the role of potential asymmetry and non Gaussian noises

Within the two state theory (TST) for stochastic resonance (SR) we analize two different aspects: (a) the extension of the TST in order to include potential asymmetry (i.e.: the states show different stabilities); (b) the evaluation of transition rates for systems whose stationary distribution is non Gaussian. We apply the results of (a) to study the role of the potential symmetry for SR in bistable systems, observing that the signal-to-noise ratio increases with the symmetry of the potential of the system indicating that it is this feature that governs the optimization of the response. We apply the results of (b) to discuss SR in situations where we can assume that the noise is non Gaussian, and discuss its relation with experimental results in sensory systems.

Reversing-Pulse Electric Birefringence of Montmorillonite K10 in Aqueous Media: Electric Moments, Field Orientation, and Changes in Sign and Profile of Signals Observed in the Low-Field Region

The reversing-pulse electric birefringence (RPEB) of a montmorillonite K10 (MK-10) sample was measured at 25°C and 633 nm in aqueous suspensions in the concentration range 0.005–0.145 g/L in the 0–200 V/cm region. The sign of the RPEB signals was negative and the profile was associated with a deep dip in the reverse process in all cases at weak fields lower than the sign-inversion point,Esi. AboveEsi, the sign became positive, whereas the signal profile usually showed a hump in the buildup process and a larger hump in the reverse process. A complex signal pattern appeared at the highest MK-10 concentration (0.145 g/L). For the multicomponent equilibrium system, theoretical RPEB expressions were derived in terms of three electric dipole moments: the permanent moment, the fluctuating counterion polarizability (ς3) with ionic relaxation time (τI) along the symmetry axis, and the covalent polarizability anisotropy (Δα′). Analysis of profiles of the observed RPEB signals showed that the MK-10 particle possesses no permanent dipole moment. The ratio ς3/Δα′ was less than −1, and τ1was comparable with the overall rotational relaxation time τ of the disklike MK-10 particle. RPEB signals at 0.145 g/L were analyzed with the two-state equilibrium theory and the MK-10 particle was found to form thin platelike aggregates with partially overlapping surfaces. The field-strength dependence of the steady-state birefringence was fitted with SUSID orientation functions. The field orientation mechanism of MK-10 particles in aqueous media was discussed.

Study of the Binding of Anions by a Cationic Polyelectrolyte Using Equilibrium Dialysis. 1. Chromate Anions

Equilibrium dialysis is used to investigate the binding of chromate anions to the cationic polyelectrolyte, poly(diallyldimethylammonium chloride), in the presence and in the absence of added sodium chloride. The binding of chromate to the polyelectrolyte is predicted by using a model which combines thermodynamic relations with the Oosawa two-state polyelectrolyte theory. Allowances are made for the nonideality of the bulk aqueous phase by introducing ion activities and ion activity coefficients. The model quite successfully accounts for the experimental data when the theoretical value of a potential parameter is utilized and when the fraction of the apparent volume containing the bound counterions is determined by considering the dimensions of the bound chromate ions.

Semiclassical theory of multi-channel curve crossing problems: Nonadiabatic tunneling case

Based on the new two-state theory of curve crossing recently completed by the authors, a compact and powerful theory is formulated for a general resonant multi-channel scattering with nonadiabatic tunneling (NT) type curve crossings. This theory is demonstrated to work remarkably well by comparing with the numerical solutions of close-coupling equations. Even detailed structures of overlapping resonances are nicely reproduced by the theory. Furthermore, this theory is very simple, not requiring any nonunique diabatization procedure, any complex calculus and any information on the couplings, neither diabatic nor nonadiabatic. The theory is based only on the adiabatic potentials on the real axis. Together with the previously proposed theory for the Landau-Zener (LZ) type curve crossings, the present semiclassical theory provides a complete picture of and a very powerful tool for multi-channel curve crossing problems.

Usefulness of the newly completed semiclassical theory of curve crossing: multi-channel resonant scattering

A resonant multi-channel curve crossing problem is investigated by using the two-state semiclassical theory recently completed by the authors. The complex phase integral in the non-adiabatic tunneling type curve crossing is accurately replaced by the phase integral on the real axis. Thanks to this, the transition matrix propagation method based on the two-state theory can be applied to multi-state curve crossing problems without any restriction on the number of crossings and states. The present theory can handle even the case that the collision energy is lower than the highest avoided crossing. Numerical comparisons with the exact quantum results for a three-state problem demonstrate the excellence of the theory. Even the detailed feature of dense resonances is accurately reproduced. The theory does not require any complex calculus, any diabatization procedure nor any information on the couplings.

Semiclassical theory of multi-channel curve crossing problems: Landau-Zener case

A two-by-two diabatic propagation method is developed to deal with general one-dimensional multi-channel curve crossing problems. Each crossing is treated within the newly completed two-state semiclassical theory in the diabatic representation and is represented by a nonadiabatic transition matrix (I-matrix). A product of all the I-matrices yields the reduced scattering matrix for the entire system. This theory can handle the multi-channel curve crossing problems as simply as a two-state problem. An analysis of the complex crossing points in the momentum space can provide a comprehensive illustrative criterion of this method. A detailed severe numerical test is made by taking a seven-state system with 6 and 12 nonzero diabatic couplings. It is demonstrated that dominant processes among the state-to-state transitions are well reproduced by the present semiclassical theory.

On modeling possibilistic uncertainty in two-state reliability theory

In this paper, we show how a possibilistic uncertainty model can be used to represent and manipulate uncertainty about the states of a system and of its components. At the same time, we present a thorough study of the incorporation of this possibilistic uncertainty model in classical, two-state reliability theory. The possibilistic reliability of a component or system is introduced and studied. Furthermore, we introduce the important notion of a possibilistic structure function, based upon the concept of a classical, two-valued structure function. Under certain conditions of possibilistic independence, it allows us to calculate the possibilistic reliability of a system in terms of the possibilistic reliabilities of its components. Finally, we give straightforward methods for determining a possibilistic structure function from its classical, two-valued counterpart. In this way, we intend to show that a possibilistic uncertainty model in two-state reliability theory is formally analogous to, and certainly not more complicated than, a probabilistic uncertainty model.

Generalized Nikitin model: strong-coupling approximation

The Delos-Thorson-type generalization of the exponential model of Nikitin in the two-state theory of atomic collisions is presented. The generalized Nikitin model defines a class of pairs of energy differences and couplings of which the original Nikitin model is a particular case. The transition probability is expressed in terms of the confluent hypergeometric function. It is shown that the generalized Nikitin model has the same peculiarity found recently in the generalized Demkov model: to derive the correct leading term of the strong-coupling asymptotic expansion of the transition probability, it is necessary to go beyond the leading terms of the strong-coupling expansions of the confluent hypergeometric functions involved. The strong-coupling approximation to the transition probability has all the correct limits and is shown to be very accurate in wide ranges of values of the free parameters.

Statistical theory of fatigue in ferroelectric devices

Abstract A simple model of fatigue in ferroelectric thin-films is developed from first principles. The core of the model is the distribution of pinning and coercive energies due to the polycrystalline nature of the material. Also, because domain nucleation for thin-films seem to be surface dominant, and surface space-charges are usually present, the model assumes that the pinning energies are field activated due to surface screening effects. The model is based on the well known two-state cluster theory in statistical physics. Further results from the model include the log (t) dependence of fatigue as a direct consequence of a gaussian distribution of pinning energies. And, for the first time a theoretical description of the V−1 dependence of fatigue is also described. The model is tested using fatigue data of sol-gel derived integrated (Si) PZT capacitors.

Photophysics of doubly-charged quinine: Steady state and time-dependent fluorescence

The quinine dication in aqueous solution (1 N H 2SO 4) gives two fluorescence lifetimes (τ 1 = 2.80 ns and τ 2 = 19.36 ns) at ambient temperature. τ 2 shows a small increase with an increase in acid concentration between 0.1 N and 15 N. Quenching by Cl − shows that τ 1 and τ 2 are differentially quenched. The Stern—Volmer quenching constant K SV for τ 1 is 10 M −1 and for τ 2 is 75 M −1. In addition, K SV is dependent on emission wavelength. In acidified solution, τ 2 increases with an increase in emission wavelength, whereas τ 1 exhibits a behaviour which resembles a two-state mechanism with a negative amplitude in the region of longer emission wavelength. However, the two-state theory does not give an entirely satisfactory mechanism for the time-dependent emission. Time-resolved emission spectroscopy (TRES) shows a spectral relaxation which partially explains the dependence of τ 2 on emission wavelength in accordance with Bakhshiev formulation. Transient and steady state fluorescence studies from 80 to 290 K show that at 160 K there is a rapid relaxation process resulting in an increase in τ 2 and a sudden spectral shift. We propose that the complex behaviour of quinine decay consists of two major relaxation processes: a charge-transfer process which occurs around 160 K and a solvent reorientation process which occurs in the fluid medium.

Quasistatic wing behavior of collisional-radiative line profiles.

It is shown that the conventional two-state theory of laser-induced collisional energy transfer (LICET) cannot be expected to provide an adequate description of the quasistatic wing behavior observed in a number of high-resolution LICET experiments. The theory breaks down whenever the detuning parameter \ensuremath{\Delta} of the LICET reaction is comparable to some frequency mismatch \ensuremath{\delta}\ensuremath{\omega} between either the initial or final state and a (virtual) intermediate state in the reaction. A simple extension of the conventional two-state theory is presented which leads to good agreement with experiment. For a van der Waals collisional interaction, the quasistatic wing is shown to fall off as \ensuremath{\Vert}\ensuremath{\Delta}${\ensuremath{\Vert}}^{\mathrm{\ensuremath{-}}1/2}$(\ensuremath{\delta}\ensuremath{\omega}+\ensuremath{\Vert}\ensuremath{\Delta}\ensuremath{\Vert}${)}^{\mathrm{\ensuremath{-}}3/2}$ instead of \ensuremath{\Vert}\ensuremath{\Delta}${\ensuremath{\Vert}}^{\mathrm{\ensuremath{-}}1/2}$ predicted by the two-state theory.

Phase space bottlenecks and statistical theories of isomerization reactions

We examine the dynamics of isomerization reactions and point out the existence of important phase space bottlenecks. A three-state statistical theory based on the behavior of trajectories and the properties of the phase space bottlenecks is proposed; this theory is better than standard two-state RRKM theory under some circumstances and offers a new way of conceptualizing isomerization. We test our ideas on the simple system, consisting of an equivalent double well coupled to a Morse oscillator, which was studied by DeLeon and Berne. Approximate methods of obtaining the required elementary rate constants in our theory are also discussed.

Studies on the mechanism of action of picrotoxinin and other convulsants at the crustacean muscle GABA receptor.

The actions of picrotoxinin, bicuculline and penicillin-G were investigated on the GABA-receptor system of lobster muscle by using intracellular recording. The highly potent antagonist, picrotoxinin, produced a lateral shift and depression in the maximum of the GABA dose--conductance curve (designated as mixed antagonism); bicuculline, a weak antagonist, caused only a depression in the maximum with little or no lateral shift, whereas penicillin-G, an even weaker antagonist, produced a greater depression at the top of the dose--response curve. The possible sites of antagonist action were examined, with a critical re-evaluation of a drug-receptor model previously proposed to account for the antagonistic behaviour of picrotoxinin (the mixed antagonistic model); this model was extended to include the actions of bicuculline and penicillin-G. Antagonism was examined (i) towards different GABA receptor agonists; (ii) in various external anion media; (iii) at varying external pH; and (iv) when two different antagonists were combined. The GABA agonists were differentially antagonized by picrotoxinin and bicuculline, but external pH and substituent anions caused only minor perturbations to the inhibition. Combination experiments suggested at least three sites for GABA antagonists binding on crustacean muscle: (i) the GABA recognition site or sites; (ii) the ionic selectivity site in the ionophore; and (iii) a highly lipophilic site which may be part of the GABA receptor or ionophore. The mixed antagonism model accounted for the pH and external anion data but required modification to a cyclic scheme to explain the antagonism of a partial agonist. A model based on two-state receptor theory could only account for the antagonism of GABA if picrotoxinin was assumed not only to perturb L (the R rightleftharpoons T conformation constant) but also to affect the agonist binding affinity. It is suggested that picrotoxinin and bicuculline may antagonize GABA responses by stabilizing the closed form of the activated channel, whereas penicillin-G may block the channel in the open state.

An alternative index for the reliability of telecommunication networks : D. Trstensky and P. Bowron. IEEE Trans. Reliab.R-33 (4) 343 (October 1984)

A resonant multi-channel curve crossing problem is investigated by using the two-state semiclassical theory recently completed by the authors. The complex phase integral in the non-adiabatic tunneling type curve crossing is accurately replaced by the phase integral on the real axis. Thanks to this, the transition matrix propagation method based on the two-state theory can be applied to multi-state curve crossing problems without any restriction on the number of crossings and states. The present theory can handle even the case that the collision energy is lower than the highest avoided crossing. Numerical comparisons with the exact quantum results for a three-state problem demonstrate the excellence of the theory. Even the detailed feature of dense resonances is accurately reproduced. The theory does not require any complex calculus, any diabatization procedure nor any information on the couplings.

Reliability analysis of two special three-state devices : J. L. Roca. Microelectron. Reliab.24 (5) 899 (1984)

A resonant multi-channel curve crossing problem is investigated by using the two-state semiclassical theory recently completed by the authors. The complex phase integral in the non-adiabatic tunneling type curve crossing is accurately replaced by the phase integral on the real axis. Thanks to this, the transition matrix propagation method based on the two-state theory can be applied to multi-state curve crossing problems without any restriction on the number of crossings and states. The present theory can handle even the case that the collision energy is lower than the highest avoided crossing. Numerical comparisons with the exact quantum results for a three-state problem demonstrate the excellence of the theory. Even the detailed feature of dense resonances is accurately reproduced. The theory does not require any complex calculus, any diabatization procedure nor any information on the couplings.

H(2s) formation in non-adiabatic ground-state hydrogen atom collisions

H(2s) formation in collisions between ground-state hydrogen atoms for impact energies in the region 1-9 keV is investigated. By allowing for rotation of the internuclear axis in a two-state non-adiabatic theory the authors obtain results on the 1s to 2s single-transition cross section. The results obtained are compared with previous theoretical calculations and with experimental data. They believe this to be the first correct theoretical treatment of exchange for this process.

State selected ion–molecule reactions by a TESICO technique. VIII. Vibronic-state dependence of the cross sections in the reaction NO+(a 3Σ+, v ; b 3Π, v)+Ar → NO+Ar+

Charge transfer reactions NO++Ar → Ar++NO (1) have been studied by selecting the vibronic states of NO+ using the threshold electron–secondary ion coincidence (TESICO) technique. The vibronic states selected were a 3Σ+, v=0–5 and b 3Π, v=0, for each of which the relative cross sections have been determined at two collision energies 1.4 and 5.8 eV. The cross section for the a 3Σ+ state has been found to show a resonancelike enhancement at v=2. This feature is reproduced fairly well by the simple two-state theory of Rapp and Francis combined with the consideration of the Franck–Condon factors. However, a closer comparison of the theoretical and experimental results over the entire range of v reveals that the reaction cross sections for the a 3Σ+ reactant ion state consist of two components, one in which the vibrational-state dependence is determined simply by the energy defects and Franck–Condon factors, and the other in which the vibrational-state dependence cannot be interpreted by those factors. The cross section for the b 3Π, v=0 state has been found to be much smaller than those for the exoergic reactions of the a 3Σ+ state (v=1–5). This has been attributed to the difference in the nature of the molecular orbitals that play primary roles in the a 3Σ+ and b 3Π reactions.

Regulation of surface-membrane enzymes by lipid ordering. A model based on allosteric transition theory.

This paper shows for the first time that effects of lipid ordering on the activity of surface-membrane enzymes can be interpreted in terms of the two-state allosteric transition theory. In this mathematical modelling, the conversion of an active molecule into a catalytically inactivated one of a given enzyme can be directly triggered by a change in the order parameter of lipids. Depending on the lipid order, the tendency for this conversion is either independent of the state of other enzyme molecules or co-operatively aided through intermolecular interactions that in turn depend on lipid ordering. The theory so developed is then applied to (Na+ + K+)-dependent adenosine triphosphatase (EC 3.6.1.3). On comparison of the relevant theoretical expression and published measurements, the fit to experimental results is shown to support the model. Furthermore, the model accounts for much of the data in the literature of the behaviour of this enzyme.

Asymmetric rearrangement collisions: VUV emission spectra in keV He and Ne ion-atom collisions with Ar

The authors report observations of vacuum ultraviolet spectra from He+ and Ne++Ar single collisions and the inverse collisions Ar++He, Ne in the 500 to 1100 AA range, and energy range 8-30 keV. Comparison is made with available theory for excitation of the Ar+ 920-932 AA doublet, involving two-state and four-state quasimolecular calculations with and without electron translation factors. None of the simple theoretical calculations available fits the shape of the data accurately, but the data suggest that a refined two-state theory incorporating electron translation factors may give reasonable agreement in the He++Ar case. The large cross section near 2 keV amu-1 for Ar II 920-932 AA doublet excitation in a rearrangement collision with He+ implies a possible ion-beam-pumped VUV laser candidate.

Order-order transition in a macromolecular system—poly-L-proline I and II

Ising model formalism developed for order-disorder transition in poly-peptides has been modified for the study of order-order transition in a macromolecular system. A two-state theory is developed and applied to poly-L-proline I and II. Various transition curves for different chain lengths are obtained as a function of solvent composition. Transition curves and crossing point for a solvent system are in excellent agreement with the experimental data on poly-L-proline.