Final Quantum State Research Articles

Black hole thermodynamics without a black hole?

In the present paper we consider, using our earlier results, the process of quantum gravitational collapse and argue that there exists the final quantum state when the collapse stops. This state, which can be called the “no-memory state”, reminds the final “no-hair state” of the classical gravitational collapse. Translating the “no-memory state” into classical language we construct the classical analogue of quantum black hole and show that such a model has a topological temperature which equals exactly the Hawking's temperature. Assuming for the entropy the Bekenstein–Hawking value we develop the local thermodynamics for our model and show that the entropy is naturally quantized with the equidistant spectrum S+ γ 0 N. Our model allows, in principle, to calculate the value of γ 0. In the simplest case, considered here, we obtain γ 0=ln2.

A classical ensemble model of three-body collisions in the point contact approximation and application to alignment effects in near-resonant energy transfer collisions of He atoms with Rydberg Ca atoms

A classical ensemble model of three-body energy transfer in the point contact approximation is presented. This model yields cross sections for transitions between initial and final states defined by energy, magnitude of angular momentum, and projection of angular momentum along an axis of spatial quantization corresponding to the quantum numbers of the initial and final stationary states, n,l,m and n′,l′,m′. Using a cross section that is differential in the final-state quantum numbers, the spatial constraints imposed by conservation of energy and angular momentum can be investigated even for comparatively small quantum numbers. When applied to the Ca(17d)+He→Ca(18p)+He energy transfer processes, the model sheds light on recently discovered alignment phenomena in collisions of rare-gas atoms with initially aligned Rydberg atoms. Materials for the implementation of this model are available from the authors via the Internet.

On the scaling of semiclassical initial value methods

The semiclassical initial value method of Walton and Manolopoulos, the cellularized frozen Gaussian approximation for the calculation of bound–bound Franck–Condon spectra, has been applied to a series of model problems with up to ten coupled degrees of freedom. The number of classical trajectories required to converge these spectra is found to increase exponentially with the number of degrees of freedom in the model problems. On comparison with earlier applications of the method to the threshold photodetachment spectra of the ArnI− (n=2–6) anions, it appears that the number of trajectories required to converge a Franck–Condon spectrum semiclassically is directly proportional to the number of final quantum states which contribute to the spectrum.

Impact parameter related final n-level splitting observed in aligned ion-Rydberg collisions

The classical trajectory Monte Carlo method has been used to calculate the final product principal quantum state -distributions in electron capture collisions involving a proton incident on a Rydberg hydrogen atom in an state. The generalized eccentricity, defined by orienting the classical eccentricity of the electron's orbit relative to the incident ion, was varied to show how the final state -levels depended on this quantity over the range of reduced collision speeds -2.4. Plots of the final product -distributions at low reduced velocities show a resonance peak near at all generalized eccentricities. At speeds of -2.2, two peaks arise in the final product -distributions from collisions with circular targets. In these cases, one peak is centred on the resonance point of , while the second peak migrates through higher -levels as increases and is believed to possibly be a new collision mechanism. This high -level peak reaches a maximum around before disappearing completely from the final product -distributions by , leaving only the resonant peak near .

The development of semiclassical dynamical methods and their application to vibrational relaxation in condensed-phase systems

A semiclassical surface-hopping propagator for problems involving nonadiabatic transitions is discussed. The propagator is employed in expressions for the probability of transitions between quantum states of molecules in condensed phases. This approach is implemented for the evaluation of the rate of vibrational transitions in liquids, dense gases, and clusters. Results for the rates of relaxation of excited vibrational states of a molecule in a simple solvent are discussed. The use of computationally simplifying short-time approximations for the solvent dynamics are considered. These approximations are tested using calculations on simple model systems. It is found that these simplifying approximations work well as long as the energy difference between the initial and final quantum states is not small. Calculations are also performed for the probability of resonant transfer of vibrational excitation energy between molecules in clusters using a mixed quantum-classical calculational procedure. It is found that quantum coherence effects are observed for several picoseconds in the probability for resonant transfer in these systems. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 897–907, 1998

Coherence Control of Photocurrents in Semiconductors

It has not been widely appreciated that the phase of an optical beam can be used as a parameter to control the properties of matter. However, if two or more phase-related beams connect the same initial and final quantum states of a system, interference between the different quantum mechanical pathways can influence the final configuration. When harmonically-related optical beams generate carriers in semiconductors the relative phase of the two beams can be used to generate and control the directionality of an electrical current in the absence of any external bias. We briefly review recent activity in coherently controlled photocurrents for quantum well and bulk semiconductors and indicate how the effects can also be understood in terms of nonlinear optics.

Three-dimensional analytical infinite order sudden quantum theory for triatomic indirect photodissociation processes

Our previously developed analytical infinite order sudden (IOS) quantum theory of triatomic photodissociation is extended to describe indirect photodissociation processes through a real or virtual intermediate state. The theory uses the IOS approximation for the dynamics in the final dissociative channels and an Airy function approximation for the continuum states. These approximations enable us to evaluate the multi-dimensional non-separable transition amplitudes analytically (as one-dimensional quadratures), despite the different natural coordinates for the initial bound, the intermediate resonant, and the final dissociative states. The fragment internal energy distributions are described as a function of the initial and final quantum states and the photon excitation energy. The theory readily permits the evaluation of rotational distributions for high values of the total angular momentum J in the initial bound molecular state, a feature that would be very difficult with close-coupled methods. In paper II we apply the theory to describe the photofragment yield spectrum of NOCl in the region of the T1(13A″)←S0(11A′) transition.

Quantum decoherence: a consistent histories treatment of condensed-phase non-adiabatic quantum molecular dynamics

We address the issue of quantum decoherence in mixed quantum classical simulations. We demonstrate that restricting the bath paths to a single stationary path which connects an initial quantum state to a final quantum state affects a coarse graining of the quantum subspace which leads to a macroscopic loss of quantum coherence. The coarse graining can be described in terms of reduction mappings of the density matrix of the reduced quantum system + stationary bath path. Application of the present model to various prototypical condensed-phase chemical problems reveals that non-adiabaticity is extremely sensitive to the decoherence timescale. Furthermore, we derive how to obtain quantum coherence timescales from realistic mixed quantum classical simulations and use this information to compute the non-radiative lifetimes for an excess electron in H 2O and D 2O. We demonstrate that subtle differences in the quantum coherence times provide a rationalization for a long-standing puzzle regarding the lack of experimentally observed isotopic dependence of the non-radiative lifetime of a photoexcited electron in H 2O and D 2O.

Mindful of Quantum Possibilities

It is sometimes asserted that standard quantum dynamics (without collapse) is incapable of accounting for definite 'events' occurring in the measurement process. But doesn't the emergence of the definite, final quantum state of the composite object + apparatus system constitute an event of sorts? To be sure, but it cannot be whole story. For the physical event of this quantum kind, now involving Alice's brain as a result of her looking, or otherwise appropriately interacting with such a system (see Lockwood [1996], equation (4)), does not seem to correspond to the sensations or perceptions she knows she has in these circumstances. The issue of psycho-physical parallelism is at the heart of the problem of measurement in quantum mechanics (QM). That no analogous problem appears in classical physics has to do with the following observation by Bell:

Photodissociation dynamics of à state ammonia molecules. I. State dependent μ-v correlations in the NH2(ND2) products

The H(D) Rydberg atom photofragment translational spectroscopy technique has been applied to a further detailed investigation of the photodissociation dynamics of NH3 and ND3 molecules following excitation to the lowest two (v2=0 and 1) vibrational levels of the first excited (à 1A2″) singlet electronic state. Analysis of the respective total kinetic energy release spectra, recorded at a number of scattering angles Θ [where Θ is the angle between the ε vector of the photolysis photon and the time-of-flight (TOF) axis], enables quantification of a striking, quantum state dependent, μ-v correlation in the NH2(ND2) products. The spatial distribution of the total flux of H(D) atom photofragments is rather isotropic (βlab∼0). However, more careful analysis of the way in which the TOF spectra of the H(D) atom photofragments vary with Θ reveals that each H+NH2(D+ND2) product channel has a different ‘‘partial’’ anisotropy parameter, βlab(v2,N), associated with it: The H(D) atom ejected by those molecules that dissociate to yield NH2(ND2) fragments with little rotational excitation largely appear in the plane of the excited molecule (i.e., perpendicular to the transition moment and the C3 axis of the parent, with β tending towards −1). Conversely, the H(D) atoms formed in association with the most highly rotationally excited partner NH2(ND2) fragments tend to recoil almost parallel to this C3 axis (i.e., β→+2). Such behavior is rationalized in the context of the known potential energy surfaces of the à and X̃ states of ammonia using a classical, energy and angular momentum conserving impact parameter model in which we assume that all of the product angular momentum is established at the ‘‘point’’ of the conical intersection in the H–NH2(D–ND2) dissociation coordinate. We conclude by reemphasizing the level of care needed in interpreting experimentally measured β parameters in situations where there is averaging over either the initial (parent) or final (product) quantum states.

FISSION OF NUCLEI AND METAL CLUSTERS

The fission process is very revealing in the way it illustrates the interplay between average (i.e., bulk) properties of the fissioning medium and specific quantum-size effects. In the nuclear quantum liquid, the charge (i.e., proton) density is everywhere confined to be about one-half of the total nucleon density, and the polarizability is extremely small. In metals, on the other hand, the net charge-to-mass ratio is virtually a free parameter and the excess charge resides on the surface, where it is easily polarized by external fields. Because of this, there is a very wide scope for fission studies with metal clusters. So far, such fission experiments have relied on thermally activated fission in competition with the evaporation of neutral atoms. The high polarizability and the sensitivity to initial- and final-state quantum effects is brought to light in this way. On the other hand, fission of large and highly charged clusters, which should be truly symmetric and proceed through a relatively compact transition configuration, remains to be explored.

Quantum corrections to instanton calculations in the Abelian Higgs model

In the (1+1)-dimensional Abelian Higgs model we calculate the final state quantum corrections to the fermion number violating cross-section in the background of the instanton. The arising determinants are treated in the Schwinger proper time formalism using some refined approximation techniques which are controlled in several ways and are also applied to the well known case of the quantum double well for comparison.

Wrong theory—Right experiment: The significance of the Stern-Gerlach experiments

Hybrid entanglement occurs between discrete and continuous variables, resulting in a considerable difficulty for its quantification. However, some advancements have been made, one of them is the discretization of the continuous variable as a tool to quantify it. Here, in this paper, the applicability of discrete entanglement measures to the final quantum state of the Stern-Gerlach Experiment is discussed in order to quantify its hybrid entanglement. Additionally, the possibility of using an equivalent discrete state is compared to the employment of the partial trace in order to consider the discrete component only, we show that the entanglement entropy distinctively represents the discrete part. Hence, the known entanglement capabilities of the SGE allow us to support the use of both techniques. Therefore, these measures give a detailed description of the entanglement creation in this famous experiment.

Molecule–corrugated surface collisions: Converged close coupling wave packet and quasiclassical trajectory calculations for N2 scattering from corrugated lattices

The close coupling wave packet (CCWP) and quasiclassical trajectory methods are used to study rotationally inelastic scattering of N2 from static, corrugated surfaces. The collision energy in these calculations ranges from 10 to 100 meV; 18 711 quantum states are included in the highest energy calculations to ensure convergence. The scattered molecules are analyzed with respect to the polarization of the final angular momentum vector and the amount of energy transferred into rotational motion and translational motion parallel to the surface. Comparisons of quantum and quasiclassical results show that quantum effects are important even with the relatively large mass of N2 and the high scattering energies used and can be seen even after summing over many final quantum states. A test of a factorization relation derived from the coordinate-representation sudden (CRS) approximation gives qualitative agreement with the exact quantum results.

Area in phase space as determiner of transition probability: Bohr-Sommerfeld bands, Wigner ripples, and Fresnel zones

We consider an oscillator subjected to a sudden change in equilibrium position or in effective spring constant, or both—to a “squeeze” in the language of quantum optics. We analyze the probability of transition from a given initial state to a final state, in its dependence on final-state quantum number. We make use of five sources of insight: Bohr-Sommerfeld quantization via bands in phase space, area of overlap between before-squeeze band and after-squeeze band, interference in phase space, Wigner function as quantum update of B-S band and near-zone Fresnel diffraction as mockup Wigner function.

Multichannel quantum theory for propagation of second order transition amplitudes

We study the Green’s function representation of second order transition amplitudes for the transition from an initial to a final quantum state that occurs because both are weakly coupled to a manifold of intermediate states. These processes apply to Raman scattering, two-photon absorption, fluoresecence from dissociating molecules, electron stimulated desorption, etc., and the transition amplitudes are called generalized Raman amplitudes. The generalized Raman transition amplitudes are expressed in terms of matrix elements of a multichannel Green’s function whose determination requires the simultaneous generation of the regular and irregular solutions of the multichannel Schrödinger equation for the intermediate state manifold. However, the numerical propagation of the generalized Raman transition amplitudes through classically forbidden regions requires, in effect, the simultaneous propagation (in the same direction) of both the regular and irregular solutions of the intermediate manifold Schrödinger equation, and use of standard multichannel scattering methods lead to numerical instabilities. We introduce new methods for maintaining both the stability and linear independence of the regular and irregular multichannel intermediate manifold eigenfunctions as they are one-way propagated along a reaction coordinate with standard quantum scattering methods. The methods may be used with systems having asymptotically open or closed channels or both in the intermediate state manifold. First order transition amplitudes, such as state selected photodissociation amplitudes to fragment states of the intermediate state manifold, emerge as a by-product of our algorithm, and the computation of the second order generalized Raman amplitudes scales roughly as double the computation time required for the first order amplitudes.

Infrared predissociation of the Ar–HD van der Waals molecule

The theory of photodissociation and predissociation processes is briefly discussed and the results of accurate quantum calculations for the infrared predissociation of the Ar–HD van der Waals molecule are presented. The absorption lineshapes for infrared radiation in the range 3866–3906 cm–1 have been computed for transitions originating in all 11 bound states of the van der Waals complex. A selected few of these lineshapes are presented and discussed in detail. Every one of the 29 absorption processes in the frequency range studied leads to the eventual dissociation of the complex. The final quantum state distribution of the HD products has been computed for all the transitions. Comparisons are made between observed and computed linewidths for those cases where the former are available. Comparison is also made of the present theoretical results with those of other theories. The system provides an excellent testing ground for theories of photodissociation processes.

Understanding Molecular Dynamics Quantum-State by Quantum-State

It is now possible to resolve completely the initial and final quantum states in chemical processes. Spectra of reactive intermediates, of highly vibrationally excited molecules, and even of molecules in the process of falling apart have been recorded. This information has led to greater understanding of the molecular structure and dynamics of small gas-phase molecules. Many of the concepts and spectroscopic techniques that have been developed will be valuable throughout chemistry.

The (n,l) distributions in electron capture reactions for C3+, N4+and O5+ions colliding with He

Distributions of captured electrons in the reaction Aq++He to A(q-1)+(n,l)+He+ over the final-state quantum numbers n and l are measured using a beam spectroscopy method at the energy of 1.0q keV. Projectile ions Aq+ are Li-like species of carbon (q=3), nitrogen (q=4) and oxygen (q=5).

Picosecond spectroscopy and solvation clusters. The dynamics of localizing electrons in polar fluids

New spectroscopic evidence concerning the dynamics of electron-induced solvation clusters in polar liquids is presented and integrated with previous picosecond data, in order to outline the roles molecular dynamics and structure can play both in initiating electron localization at subpicosecond times and in governing the solvation dynamics to form e/sup -//sub s/ in the picosecond domain. Particulr emphasis is placed on the picosecond time-resolved absorption spectroscopy of electrons in a wide range of alcohols and alcohol-alkane systems at 300/sup 0/K as a framework for the cluster model of electron solvation. While the configurationally relaxed final quantum state of e/sup -//sub s/ appears identical for e/sup -//sub s/ generated by different techniques, it is possible that the time evolution of the solvation cluster and the dynamics of electron populations between localized and continuum states could be influenced by the initial state of the system. Selected examples are discussed for alcohols, amines, and water, and comparisons are made for picosecond observations from different visible and IR spectroscopic techniques, NMR, and complementary nanosecond electron mobility data to demonstrate the overall consistency of a model in which only the dynamical, microscopic properties of the liquid determine these solvation events.