Non-adiabatic Operation Research Articles

Gate errors in solid-state quantum-computer architectures

We theoretically consider possible errors in solid-state quantum computation due to the interplay of the complex solid-state environment and gate imperfections. In particular, we study two examples of gate operations in the opposite ends of the gate speed spectrum, an adiabatic gate operation in electron-spin-based quantum dot quantum computation and a sudden gate operation in Cooper-pair-box superconducting quantum computation. We evaluate quantitatively the nonadiabatic operation of a two-qubit gate in a two-electron double quantum dot. We also analyze the nonsudden pulse gate in a Cooper-pair-box-based quantum-computer model. In both cases our numerical results show strong influences of the higher excited states of the system on the gate operation, clearly demonstrating the importance of a detailed understanding of the relevant Hilbert-space structure on the quantum-computer operations.

Nonadiabatic detection of the geometric phase of the macroscopic quantum state with a symmetric SQUID

We give a simple way to detect the geometric phase shift and the conditional geometric phase shift with Josephson junction system. Comparing with the previous work(Falcl G, Fazio R, Palma G.M., Siewert J and Verdal V, {\it Nature} {\bf 407}, 355(2000)), our scheme has two advantages. We use the non-adiabatic operation, thus the detection is less affected by the decoherence. Also, we take the time evolution on zero dynamic phase loop, we need not take any extra operation to cancel the dynamic phase.

Benzene adsorption and hot purge regeneration in activated carbon beds

Experimental and theoretical studies were performed on adsorption of benzene from nitrogen gas stream and thermal regeneration by hot nitrogen purge, in fixed beds charged with activated carbon. System temperature and effluent concentration data were collected during adsorption-regeneration runs. A mathematical model was developed to simulate temperature and concentration data of adsorption and regeneration. The model developed was based on non-equilibrium, non-isothermal and non-adiabatic conditions. Three heat transfer resistances were considered in interfaces of gas–solid, gas–wall, and wall–atmosphere. A linear driving force mass transfer model with a variable lumped-resistances coefficient was found to provide an acceptable fit to the experimental data. Experimental and modelling results were used to study the effects of adiabatic and non-adiabatic operations, contact time, gas velocity, regeneration temperature and initial bed loading on the regeneration efficiency. Besides, the specific energy requirement and purge gas consumption were evaluated to discuss the process efficiency.

Cancellation of heat effects in catalytic distillation

Abstract Heat effects in distillation, especially those caused by unequal heats of vaporization of components and highly nonadiabatic operation, were shown in earlier papers to cancel favorably in binary distillation when measuring and computing composition profiles along column height. We show here that the same favorable cancellation takes place in multicomponent catalytic distillation where heat effects are caused by a release or consumption of heat of reaction. A generic profile in terms of pseudo-composition of vapor, solved analytically by applying the linearized theory of multicomponent mass transfer, is given for exothermic reactions as a function of two dimensionless parameters, an eigenvalue of the number of mass transfer units matrix and an eigenvalue of the mass transfer rate factor matrix. Comparison with the solution that ignores the heat effects completely is made in terms of both pseudo-composition and actual composition. The final conclusion of the study is that nonequimolarity can be safely ignored in most practical cases of multicomponent catalytic distillation when computing bulk compositions on a plate in the reaction zone of a column.

Born-Oppenheimer expansion: From muon distribution to dissipation in fission

It is shown that a consistent treatment of momentum translation by a muon in the problem of the distribution of muons among prompt-fission fragments modifies the nonadiabatic transition operator in the Born-Oppenheimer expansion and removes difficulties indicated in earlier calculations. The muon distribution for very asymmetric prompt fission proves to be highly sensitive to the velocity of the primary fragments at the scission point. The mean collective energy dissipated during saddle-to-scission descent due to the one-body mechanism is calculated within the same approach.

Electronic Coherence in Mixed-Valence Systems: Spectral Analysis

The electron transfer kinetics of mixed-valence systems is studied via solving the eigenstructure of the two-state nonadiabatic diffusion operator for a wide range of electronic coupling constants and energy bias constants. The calculated spectral structure consists of three branches in the eigendiagram: a real branch corresponding to exponential or multiexponential decay, and two symmetric branches corresponding to population oscillations between donor and acceptor states. The observed electronic coherence is shown as a result of underdamped Rabi oscillations in an overdamped solvent environment. The time evolution of electron population is calculated by applying the propagator constructed from the eigensolution to the nonequilibrium initial preparation, and it agrees perfectly with the result of a direct numerical propagation of the density matrix. The resulting population dynamics confirms that increasing the energy bias destroys electronic coherence.

Conformation‐transitional rate in protein folding

AbstractBased on the conformation dynamics of macromolecules, the rate of conformational transition is deduced from the nonadiabaticity operator method which can be used to explain the time scale of milliseconds for protein folding. It is proved that (1) the dependence of the transition rate on inertial moment I of the atomic group obeys the I−2.5 law; (2) its dependence on numbers n of torsional angles participating in the transition obeys the n1.5 law; and (3) the temperature dependence of the transitional rate shows an abnormal character in the high‐ temperature region. © 1995 John Wiley & Sons, Inc.

Analysis of steady‐state reaction fronts in a porous medium

AbstractA pseudohomogeneous model is used to analyze the steady state of a sharp reaction front in a porous medium. The reaction rate is described by the flame sheet approximation, and an asymptotic matching analysis is used to determine the temperature, conversion and position of the reaction front. Both adiabatic and nonadiabatic operations are considered, and the effect of radiation is included in the adiabatic case. The results show that there exists a maximum molar flux before blowout occurs. The critical molar flux is decreased by higher activation energies, but it is increased by higher rate constants and flame temperatures. Radiation further stabilizes the flame against blowout. Expressions are provided for the flame temperature, reactant conversion and the conditions when blowout occur. It is also shown that under certain conditions the front has two steady‐state positions.

A COMPARATIVE STUDY OF TOOLS FOR ASSESSING THE EFFECTS OF FORCED PERIODIC OPERATION OF CATALYTIC REACTORS

Two methods for assessing the effects of forced periodic catalytic reactor operation are presented. The vibrational control method is an analytical technique which evaluates the effects of high frequency forcing of system parameters by the method of averaging. The second technique is a numerical tool based on a shooting algorithm. These methods are capable of handling multiple input forcing and various shapes of forcing functions. Both methods are applied to isothermal, adiabatic and nonadiabatic operation of an internal recycle reactor in which the catalytic oxidation of ethylene takes place. The basic features of both techniques are discussed and the results obtained by using these methods are compared. Effects of single and multiple input parameter forcing are investigated. Experimental verification of the theoretical results is also performed for the isothermal case.

Comparison between static and adiabatic coupling mechanisms for nonradiative multiphonon transitions in semiclassical approximation

Semiclassical versions of the static (diabatic) and adiabatic coupling schemes are applied to a two-level-one-mode system at total energies above the cross-over level. The corresponding rates of nonradiative multiphonon transitions reduce to alternativemonotonous dependences on the usual Landau-Zener parameterγ. Static coupling gives an increasing transition probability (per oscillation) of the familiar formPst(γ) = 4πγ. Adiabatic coupling associated with a sufficiently low mechanism-specific potential barrier of Born's type produces a decreasing transition probability of the formPad(γ) exp (−2πγ). The underlying “Beyond-Non-Condon” calculation procedure shows that (1) the weak dependence of the pre-exponential factorPad is a consequence of theγ-independent normalization of the electronic matrix element governing the non-adiabaticity operator and (2) the occurrence of the mechanism-specific tunnelling factor exp(−2πγ) is due to the avoided crossing of adiabatic oscillator potentials. Ranges of applicability of both alternative coupling schemes are limited by comparison with earlier non-perturbational results.

Numerical evaluation of non-radiative multi-phono transition rate from different electronic bases

Rigorous numerical calculations on the non-radiative multi-phonon transition probability based on the adiabatic approximation (AA) and the static approximation (SA) have been accomplished in a model of two electronic levels coupled to one-phonon mode. The numerical results indicate that both the diagonal non-adiabatic operator and the mixture and split of the potential sheets have a significant effect on the adiabatic vibrational states near or above the classical cross point and on the transition rates between these states. For strong electron-phonon coupling, the calculated transition rates based on AA are more reliable; on the other hand, for weak coupling the difference between transition rates near or beyond the crossing region based on different approximations can be beyond an order of magnitude. When the transition occurs far below the crossing point, both approximations give the same results. The relationship among the transition matrix element and the vibration level shift, the Huang-Rhys factor, the separation of the electronic levels and the electron-phonon coupling are analysed and discussed.

Dynamic responses to perturbations in the non-isothermal, continuous-flow stirred-tank reactor (CSTR)—II. Nonadiabatic operation: The general case

Abstract When an exothermic reaction is carried out in an open system, discontinuous jumps between stationary states may occur in response to continuous variation of control parameters such as average residence-time. Our previous paper examined the dynamics of such jumps for reaction in a CSTR operating adiabatically. Here the general case of marginally supercritical conditions during non-adiabatic operation in a CSTR is considered. It is again found that: (i) times to ignition and (ii) times for decay to a stationary state both obey universal formulae characteristic of the category of instability, lengthening rapidly as criticality is approached. For example: time-to-ignition ∝ (degree of supercriticality) − 1 2 . We illustrate our results chiefly by reference to a single, first-order, deceleratory reaction with the usual strong dependence on temperature, but the treatment is quite general and can cope with any concentration-dependence and any temperature-dependence of reaction rate.

Static and adiabatic approaches to nonradiative multiphonon transitions: correct transition matrix elements of order Δ

The static base approach (SBA) and adiabatic base approach (ABA) are analysed for an electronic two-level system coupled to a single vibrational mode. In the ABA due account is taken of the non-adiabatic contribution to the oscillatory potential. This permits the introduction of a suitable model potential whose eigensolutions can be calculated exactly. It is proven that the calculation of the non-adiabatic transition matrix elements by means of these model eigenfunctions yields the correct first-order result in the promoting-mode coupling constant Delta and thus provides the same accuracy as the SBA calculation. The analysis evinces the importance of the diagonal non-adiabaticity operator, which has been neglected in earlier work. The transition matrix elements of the two approaches are compared. It is found that the absolute value of the SBA result is always larger than that of the ABA result and rises up to about a factor of two times the latter for higher Huang-Rhys factors. The authors finding resolves an old controversy.

Adiabatic approach to non-radiative transitions: Exact transition rates of order Δ 2

Abstract The static (SBA) and adiabatic base (ABA) approaches are analyzed for an electronic two-level system coupled to a single vibrational mode. In the ABA due account is taken of the non-adiabatic contribution to the oscillatory potential. This permits the introduction of a suitable model potential whose eigenfunctions can be exactly calculated. It is proven that the calculation of the non-adiabatic transition matrix elements by means of these model eigenfunctions yields the exact first order result in the promoting mode coupling constant Δ. The calculation evinces the importance of the diagonal non-adiabaticity operator, which has been neglected in earlier work. The transition matrix elements of the two approaches are compared. It is found that the absolute value of the SBA-result is always larger than that of the ABA-result and rises up to a factor 2 of the latter for higher Huang-Rhys factors. Our finding resolves an old controversy.

On the theory of the radical radiation formation in a solid host

Abstract The calculation of the radical formation rate constant in solid organic compounds is carried out. This formation is a result of the cleavage of the hydrogen atom from the carbon atom via a radiationless electronic transition in an electronically excited molecule. The electronic transition is supposed to be stipulated by the nonadiabaticity operator and the perturbation theory with respect to this operator is supposed to be applicable. The vibrational interaction of an electronically excited molecule with the host environment is assumed not to be small. The calculation is carried out within the framework of a model in which the whole molecule is represented by a CH group this being treated as a Morse oscillator. The specific features of the different substances in such a model are simulated by different values of the CH bond parameters.

Quantitative dynamic modelling of a continuous stirred reactor

Abstract In this paper an attempt was made to obtain quantitative predictions of various aspects of the dynamic behaviour of a pilot-plant CSTR by means of a model synthesized from different laboratory kinetic studies and heat transfer measurements taken on the reactor vessel itself. Generally, it was found possible to bound the observed behaviour within the spread of the kinetic data, although the bounds were often far apart. No single source of kinetic data proved satisfactory for predicting all aspects of reactor behaviour considered, which included adiabatic and non-adiabatic batch operation and continuous flow experiments subject to upsets in the catalyst flow. Considerable progress still needs to be made in reaction kinetic studies before secure predictions of reactor performance can be made, even for relatively simple reaction systems such as the one studied here. Particular attention needs to be paid to the systematic sources of error in kinetic data which show up when the reaction kinetics are gathered from different types of laboratory reactor employing different measurement techniques.

Theory of radiationless transitions in a crystalline host material

Abstract Consistent calculations of the rate constant of radiationless electron transition are reported for a diatomic molecule in a crystal at zero temperature. The transition between electronic states occurs due to nonadiabaticity. Relaxation of the vibrational energy is stimulated by the interaction of the molecule with the crystal. The calculations have been carried out under the assumption that perturbation theory with respect to the nonadiabaticity operator is applicable. The vibrational interaction of the molecule with the environment is assumed not to be small. The electronic terms of the molecule are approximated by Morse potentials.

Effects of vibrational relaxation on molecular electronic transitions

In this paper we explore the implications of the coupling between nonradiative electronic relaxation and vibrational relaxation in excited electronic states of large molecules. The physical model involved a two electronic level molecular system interacting with a harmonic medium via linear coupling terms in the molecular nuclear coordinates. Two models were advanced for the molecule-medium coupling which involve single phonon decay and alternatively double phonon (or rather phonon-vibron) decay. The functional form of our final results is independent of the specific model adopted for the vibrational relaxation. The molecular Hamiltonian and the intramolecular coupling were recast in terms of second quantization formalism where the nonadiabatic coupling operator was modified by a Franck Condon shift operator. The coupling between electronic and vibrational relaxation processes was formulated in terms of a generalized interaction picture, where the intramolecular coupling was treated to second order while the vibrational relaxation was handled to ``infinite order'' by the Wigner Weisskopf approximation as applied to the equations of motion for the nuclear operators for the normal molecular modes. The nonradiative decay rate of an excited electronic state was expressed in terms of a generalized time correlation function. We were able to demonstrate that our general expressions reduce to the (time independent) decay rate of a single vibronic level in the limit of slow vibrational relaxation and to a modified expression for the (time independent) decay rate of the thermally averaged electronic manifold in the limit of fast vibrational relaxation. In the general case of coupled electronic-vibrational relaxation the decay probability is time dependent. In the low temperature limit the nonradiative decay rate can be expressed in terms of a superposition of exponential functions.

Theory of Activated Radiationless Processes: Orientation Relaxation of Polar Molecules

A first-principles theoretical expression for the rate of a thermally activated process is derived. The treatment is specialized to the orientation relaxation of dipolar molecules, which is viewed as a radiationless transition between electronic states corresponding to the dipole in discrete orientations. The dipolar electronic states are calculated in the Born-Oppenheimer approximation and the associated adiabatic potential-energy surfaces are taken to be displaced, undistorted harmonic potentials. Transitions between the different electronic states arise through the nonadiabatic kinetic-energy operator associated with the librational degree of freedom of the reorienting dipole. The explicit expression for the transition rate is calculated to first order by evaluating the integral over the time-correlation function of the Kubo representation of the rate constant in the strong-coupling limit using the method of steepest descent. It is shown that the transition rate is actually a sum of five contributions arising from phonon scattering processes in which 0, ±1, ±2 quantum changes take place in the librational degree of freedom of the dipole. When kT is large compared with a quantum of librational energy, the expression for the transition rate simplifies to the functional form of the Arrhenius equation in which the pre-exponential factor and the activation energy are given in terms of specific molecular properties. The theory is applied to a quantitative treatment of the relaxation of dipolar impurities in ionic crystals. The dielectric behavior of polar organic molecules in liquids is also qualitatively examined, and the explicit dependence of the relaxation time on the molecular dimensions in a homologous series of compounds is obtained. Even though the theory is specialized to dipolar relaxation, the basic expressions are generally applicable to any thermally activated process involving the migration of ions or atoms, e.g., ionic conductivity, mobility, viscous flow, and diffusion.

Calculation of cross sections for the depolarization of 2P states in alkali atoms

Optical pumping experiments have yielded very large disorientation cross sections (40–100 Å2) for collisions between oriented 2P1/2 atoms of potassium, rubidium, cesium and thalium, and helium, neon, argon, krypton, and xenon atoms in their ground states, in contrast to the extraordinarily small cross section (< 10−5 Å2) for the depolarization of 2S1/2 atoms, as found by Gallagher and by Anderson and Ramsey. Franz, Leutert, and Shuey pointed out that, within the adiabatic model, the transition ψ(j = 1/2, m = 1/2) → ψ(j = 1/2, m = −1/2) is strongly forbidden in conformity with Kramer's theorem according to which it is impossible to split the two components ψ(j = 1/2, m = ± 1/2) in an electric field. In the present investigation it has been shown that the inclusion of an angular nonadiabatic operator (i.e. the operator responsible for Coriolis mixing of adiabatic electronic molecular states) makes possible such transitions. Calculations are presented of cross sections for the resulting depolarization induced in collisions between potassium, rubidium, and cesium, and inert gas atoms.