Unification of the quantum and classical theories of methyl NMR.

The existing low and high temperature theories of methyl NMR are not linked because two conditions imposed on state functions in the low temperature theory are not compatible with the classical rotations on which the high temperature theory is based. The conditions do not occur in a geometrical theory of quantum phenomena in which particles and waves have separate roles. When applied to methyl dynamics, this theory covers the whole temperature range.     

NMR lineshape equations for hindered methyl group: a comparison of the semi-classical and quantum mechanical models

The semiclassical and quantum mechanical NMR lineshape equations for a hindered methyl group are compared. In both the approaches, the stochastic dynamics can be interpreted in terms of a progressive symmetrization of the spin density matrix. However, the respective ways of achieving the same limiting symmetry can be remarkably different. From numerical lineshape simulations it is inferred that in the regime of intermediate exchange, where the conventional theory predicts occurrence of a single Lorentzian, the actual spectrum can have nontrivial features. This observation may open new perspectives in the search for nonclassical effects in the stochastic behavior of methyl groups in liquid-phase NMR.     

Stochastic theory for classical and quantum mechanical systems

We formulate from first principles a theory of stochastic processes in configuration space. The fundamental equations of the theory are an equation of motion which generalizes Newton's second law and an equation which expresses the condition of conservation of matter. Two types of stochastic motion are possible, both described by the same general equations, but leading in one case to classical Brownian motion behavior and in the other to quantum mechanical behavior. The Schrödinger equation, which is derived here with no further assumption, is thus shown to describe a specific stochastic process. It is explicitly shown that only in the quantum mechanical process does the superposition of probability amplitudes give rise to interference phenomena; moreover, the presence of dissipative forces in the Brownian motion equations invalidates the superposition principle. At no point are any special assumptions made concerning the physical nature of the underlying stochastic medium, although some suggestions are discussed in the last section.     

2H NMR and X-ray diffraction studies of methyl rotation in crystals of ortho-methyldibenzocycloalkanones

We have used (2)H NMR lineshape analyses and single crystal X-ray diffraction (XRD) to investigate the effects of molecular structure and crystalline environment on the rotational dynamics of methyl groups in four aromatic cycloalkanones. These include two methyl-substituted anthrones, one anthraquinone and one dibenzosuberone, which are known to undergo excited state H-atom tunneling from the ortho-methyl group to the carbonyl oxygen. With experiments conducted between 100 and 300K, samples 1,4-dimethylanthrone (DMAT) and 1,4-dimethylanthraquinone (DMAQ) were shown to enter the intermediate exchange regime (k(rot) approximately <10(7)s(-1)) at ca. 120K while samples of 1,4,10,10-tetramethylanthrone (TMAT) and 1,4-dimethyldibenzosuberone (DMDBS) remained in the fast exchange regime even at ca. 100K. Single crystal XRD analyses suggest that high intramolecular hindrance is avoided by molecular distortions, and that intermolecular contacts play an important role.     

Notes on the classical and the nonrelativistic limits in quantum mechanics

A method is presented which can be used to discuss both the classical and also the nonrelativistic limit of quantum mechanics. A one-to-one correspondence may be established between the asymptotic convergence of the resolvent and that of the timedependent solution. In so far as the question of dynamics is concerned we investigate the relation between families of nonrelativistic Hamiltonians and the corresponding Dirac-Hamiltonians when c± or when c±0. The nonrelativistic free theory formally shows the same pattern when ±0 (the classical limit) or when ±. The investigation finally shows how the asymptotic convergence of the relativistic theory can take place under some fairly general conditions of the radiation field.     

On the classical support of quantum mechanical wavefunctions

The nature of the classical support of quantum-mechanical wave-functions is examined in the limit ? → 0. We prove that a sequence of states can only localize to those regions of phase space supporting an invariant measure.     

A procedure for obtaining quantum mechanical transformation of diagonalization from the classical

Using as an example two coupled harmonic oscillators, a transformation to normal coordinates is made using the classical-type simultaneous diagonalization of quadratic forms, and this is then used to develop a procedure for constructing the corresponding quantum mechanical transformation to normal coordinates. The total classical transformation is nonunitary, whereas the quantum mechanical is unitary as it has to be in order to satisfy Von Neumann's theorem. Since the classical transformation has definite steps and is a very straightforward procedure, this could be a very useful procedure for constructing the quantum mechanical transformation in many models, and/or an alternative method for many models.     

Performance comparison between classical and quantum control for a simple quantum system

Brańczyk et al. pointed out that the quantum control scheme is superior to the classical control scheme for a simple quantum system using simulation [A.M. Brańczyk, P.E.M.F. Mendonca, A. Gilchrist, A.C. Doherty, S.D. Barlett, Quantum control theory of a single qubit, Physical Review A 75 (2007) 012329 or arXiv e-print quant-ph/0608037]. Here we rigorously prove the result. Furthermore we will show that any quantum operation does not universally “correct” the dephasing noise.     

Interaction between classical and quantum systems and the measurement of quantum observables

Quantum mechanics presumes classical measuring instruments with which they interact. The problem of measurement interaction between classical and quantum systems is posed and solved. The restriction to compatible measurements comes about naturally as the condition for the integrity of the classical system. A technical device is the perspective on classical mechanics as quantum mechanics with essentially hidden dynamical variables. Work supported in part by U.S. Atomic Energy Commission, ERDA.     

On the relation between classical and quantum observables

For systems with a finite number of degrees of freedom, the relation between classical and quantum observables is analysed. In particular, a precise statement of the correspondence limit is obtained.     

On the connection between quantum and classical descriptions

The review paper presents generalization of d??Alembert??s variational principle: the dynamics of a quantum system for an external observer is defined by the exact equilibrium of all acting in the system forces, including the random quantum force ?j, ??. Spatial attention is dedicated to the systems with (hidden) symmetries. It is shown how the symmetry reduces the number of quantum degrees of freedom down to the independent ones. The sin-Gordon model is considered as an example of such field theory with symmetry. It is shown why the particles S-matrix is trivial in that model.     

Development of the analogy between classical and quantum mechanics

A quantum-mechanical generalisation of Carathéodory’s theorem in classical dynamics is established. Several related properties of classical canonical transformations are also generalised to the quantum case.     

On the relation between classical and quantum statistical mechanics

Classical and quantum statistical mechanics are compared in the high temperature limit =1/kT0. While this limit is rather trivial for spin systems, we obtain some rigorous results which suggest (and sometimes prove) different asymptotics for continuous systems, depending on the behaviour of the two-body potential for small distances: the difference between suitable classical and quantum variables vanishes as ² for smooth potentials and as for potentials with hard cores.Supported in part by FAPESP. Permanent address: Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo, Brazil     

Dissociative adsorption of H2: Time-dependent quantum studies

In this short review we consider some selected results for the dissociation of hydrogen on metal surfaces. In particular we focus our attention on the effects that surface corrugation have on the dissociation and also how rotations and vibrations couple in the interaction region. Results from time dependent quantum wavepacket calculations have been particularly helpful in forming our ideas of how diatomics dissociate. We describe this method along with two examples of propagation schemes. The power of limited dimensional models to rationalize experimental observations is clearly demonstrated.     

Spinors in the Lorentz group and their implications for quantum mechanics

We investigate what the precise meaning is of a spinor in the rotation and Lorentz groups. We find that spinors correspond to a special coding of a group element. This is achieved by coding the whole reference frame into a special isotropic or “zero-length” vector. The precise form of that special vector in the Lorentz group is lacking in the literature, and this leads to some confusion, as the point that the coding can be complete has been missed. We then apply these ideas to quantum mechanics and find that the Dirac equation can be derived by just trying to describe a rotating electron. PACS 02.20.-a; 03.65.-w; 03.65.Fd     

Optical nuclear polarization for sensitivity enhancement of2H NMR single-crystal studies

A gain in detection sensitivity of more than three orders of magnitude is achieved in high-resolution solid-state²H nuclear magnetic resonance of monocrystalline fluorene-d₁₀ by applying optical nuclear polarization via excited triplet states of acridine-h₉ guest molecules. The sensitivity gain is utilized to measure the angular dependence (rotation pattern) of the²H nuclear magnetic resonance lines. In this way the principal values and orientations of all²H quadrupolar tensors are determined. Except for the methylene deuterons, all tensors belonging to the same molecule have one principal axis in common, namely the axis perpendicular to the molecular plane, showing that in the crystal lattice the fluorene molecule is in a planar configuration.     

2H T2rho relaxation dynamics and double-quantum filtered NMR studies

In this study 2H T2rho DQF NMR spectra of water in MCM-41 were measured. The T2rho double-quantum filtered (DQF) NMR signal is generated by applying a radio frequency (RF) field for various durations and then observed after a monitor RF pulse. It was found that the transfer between different quantum coherences by the couplings during long-duration RF fields (i.e., soft pulses) and that residual quadrupolar interaction dominates the signal decay. Knowledge of coherence transfer during long-RF pulses has special significance for the development of sophisticated multi-quantum NMR experiments especially multi-quantum MRI applications.