as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus decoherence is caused by the interaction in which the environment in effect monitors certain observables of the system, destroying coherence between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly nonlocal ''Schrodinger-cat states.'' The classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit. Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation. Only the preferred pointer observable of the apparatus can store information that has predictive power. When the measured quantum system is microscopic and isolated, this restriction on the predictive utility of its correlations with the macroscopic apparatus results in the effective ''collapse of the wave packet.'' The existential interpretation implied by einselection regards observers as open quantum systems, distinguished only by their ability to acquire, store, and process information. Spreading of the correlations with the effectively classical pointer states throughout the environment allows one to understand ''classical reality'' as a property based on the relatively objective existence of the einselected states. Effectively classical pointer states can be ''found out'' without being re-prepared, e.g, by intercepting the information already present in the environment. The redundancy of the records of pointer states in the environment (which can be thought of as their ''fitness'' in the Darwinian sense) is a measure of their classicality. A new symmetry appears in this setting. Environment-assisted invariance or envariance sheds new light on the nature of ignorance of the state of the system due to quantum correlations with the environment and leads to Born's rules and to reduced density matrices, ultimately justifying basic principles of the program of decoherence and einselection.

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Decoherence, einselection, and the quantum origins of the classical

In the last decade, ab initio simulations and especially Car-Parrinello molecular dynamics have significantly contributed to the improvement of our understanding of both the physical and chemical properties of water, ice, and hydrogen-bonded systems in general. At the heart of this family of in silico techniques lies the crucial idea of computing the many-body interactions by solving the electronic structure problem "on the fly" as the simulation proceeds, which circumvents the need for pre-parameterized potential models. In particular, the field of proton transfer in hydrogen-bonded networks greatly benefits from these technical advances. Here, several systems of seemingly quite different nature and of increasing complexity, such as Grotthuss diffusion in water, excited-state proton-transfer in solution, phase transitions in ice, and protonated water networks in the membrane protein bacteriorhodopsin, are discussed in the realms of a unifying viewpoint.

Proton transfer 200 years after von Grotthuss: insights from ab initio simulations.

Numerous studies have identified large quantum mechanical effects in the dynamics of liquid water. In this paper, we suggest that these effects may have been overestimated due to the use of rigid water models and flexible models in which the intramolecular interactions were described using simple harmonic functions. To demonstrate this, we introduce a new simple point charge model for liquid water, q-TIP4P/F, in which the O-H stretches are described by Morse-type functions. We have parametrized this model to give the correct liquid structure, diffusion coefficient, and infrared absorption frequencies in quantum (path integral-based) simulations. The model also reproduces the experimental temperature variation of the liquid density and affords reasonable agreement with the experimental melting temperature of hexagonal ice at atmospheric pressure. By comparing classical and quantum simulations of the liquid, we find that quantum mechanical fluctuations increase the rates of translational diffusion and orientational relaxation in our model by a factor of around 1.15. This effect is much smaller than that observed in all previous simulations of empirical water models, which have found a quantum effect of at least 1.4 regardless of the quantum simulation method or the water model employed. The small quantum effect in our model is a result of two competing phenomena. Intermolecular zero point energy and tunneling effects destabilize the hydrogen-bonding network, leading to a less viscous liquid with a larger diffusion coefficient. However, this is offset by intramolecular zero point motion, which changes the average water monomer geometry resulting in a larger dipole moment, stronger intermolecular interactions, and a slower diffusion. We end by suggesting, on the basis of simulations of other potential energy models, that the small quantum effect we find in the diffusion coefficient is associated with the ability of our model to produce a single broad O-H stretching band in the infrared absorption spectrum.

Competing quantum effects in the dynamics of a flexible water model

Nuclear quantum effects influence the structure and dynamics of hydrogen-bonded systems, such as water, which impacts their observed properties with widely varying magnitudes. This review highlights the recent significant developments in the experiment, theory, and simulation of nuclear quantum effects in water. Novel experimental techniques, such as deep inelastic neutron scattering, now provide a detailed view of the role of nuclear quantum effects in water's properties. These have been combined with theoretical developments such as the introduction of the principle of competing quantum effects that allows the subtle interplay of water's quantum effects and their manifestation in experimental observables to be explained. We discuss how this principle has recently been used to explain the apparent dichotomy in water's isotope effects, which can range from very large to almost nonexistent depending on the property and conditions. We then review the latest major developments in simulation algorithms and theory that have enabled the efficient inclusion of nuclear quantum effects in molecular simulations, permitting their combination with on-the-fly evaluation of the potential energy surface using electronic structure theory. Finally, we identify current challenges and future opportunities in this area of research.

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Nuclear Quantum Effects in Water and Aqueous Systems: Experiment, Theory, and Current Challenges

Nonlinear electron dynamics in metal clusters

The atomic momentum distribution of lithium-7 in natural Li has been determined as a function of temperature from 20 to 300 K. The experiments were undertaken within the impulse approximation using the electronvolt spectrometer at ISIS. Final state effects were present above the statistical accuracy of our data and were accounted for by symmetrizing the neutron Compton profiles. The mean atomic kinetic energy of the Li nucleus was obtained directly from our measurements and was found to be approximately 10% higher than that predicted by a harmonic model incorporating a density of states derived from previous phonon measurements. A fit of the data to the Debye model gave a Debye temperature of 419+or-3 K.

https://iopscience.iop.org/article/10.1088/0953-8984/6/22/018/pdf

The kinetic energy of lithium-7 above and below the martensitic transformation

The VESUVIO spectrometer at the ISIS pulsed neutron source performs inelastic neutron scattering at high-energy and wave vector transfers, employing gold and uranium resonant foils. A factor of two improvement in the instrumental resolution has been achieved by making use of the double filter difference method. Experimental results are presented for measurements on polycrystalline Pb, which indicate that accurate measurements of single-particle momentum distribution n(p) in quantum fluids are now possible at eV energy transfers.

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VESUVIO—the double difference inverse geometry spectrometer at ISIS

Concentration dependence of the kinetic energy in 3He-4He mixtures.

The momentum distribution in KD2PO4 (DKDP) has been measured using neutron Compton scattering above and below the weakly first-order paraelectric–ferroelectric phase transition (T=229 K). There is very little difference between the two distributions, and no sign of the coherence over two locations for the proton observed in the paraelectric phase, as in KH2PO4 (KDP). We conclude that the tunnel splitting must be much less than 20 meV. The width of the distribution indicates that the effective potential for DKDP is significantly softer than that for KDP. As electronic structure calculations indicate that the stiffness of the potential increases with the size of the coherent region locally undergoing soft mode fluctuations, we conclude that there is a mass-dependent quantum coherence length in both systems.

https://iopscience.iop.org/article/10.1088/1367-2630/10/1/013016/pdf

Deuteron momentum distribution in KD2PO4

We have measured the double differential cross section of liquid hydrogen using deep inelastic neutron scattering in an intermediate region of momentum and energy transfer where the crossover between the molecular and atomic regimes is expected. The range of the momentum transfer, computed on the basis of the atomic recoil, is between 24.6 and 36.2 ${\mathrm{\AA{}}}^{\ensuremath{-}1},$ i.e., beyond the limit where intermolecular interactions are effective and therefore the incoherent scattering approximation applies. The data cannot be reproduced either using a molecular or an atomic model. We find that a satisfactory fit to the data is obtained by a linear combination of the two models. The relative weight of the molecular model turns out a decreasing function of the energy transfer.

J. Mayers

Papers

The kinetic energy of lithium-7 above and below the martensitic transformation

VESUVIO—the double difference inverse geometry spectrometer at ISIS

Concentration dependence of the kinetic energy in 3He-4He mixtures.

Deuteron momentum distribution in KD2PO4

Deep inelastic neutron scattering on liquid hydrogen in the crossover region between the molecular and atomic regimes