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Indispensable role of quantum theory in the brain dynamics.

Recently, Tegmark pointed out that the superposition of ion states involved in the superposition of firing and resting states of a neuron quickly decohere. It undoubtedly indicates that neural networks cannot work as quantum computers, or computers taking advantage of coherent states. Does it also mean that the brain can be modeled as a neural network obeying classical physics? Here we show that it does not mean that the brain can be modeled as a neural network obeying classical physics. A brand new perspective in research of neural networks from quantum theoretical aspect is presented.

Animals↗

[From Einstein's Quantum Theory to modern laser therapy. The history of lasers in dermatology and aesthetic medicine].

Laser technology has considerably expanded therapeutic modalities in dermatology and aesthetic medicine. In addition, lasers have broadened the spectrum of diagnostic and therapeutic options in many other medical fields. Dermatologists, especially Dr. Leon Goldman, played an important role in the evolution and use of medical lasers. There was a long way from the concept of stimulated emission as the fundamental idea of laser technology by Albert Einstein in 1917 to the practical use of the laser today. We review the development of laser technology from the early days through the latest advances.

Animals↗

On the value of clinical information. Is there a bridge between quantum theory and medical diagnosis?

This paper discusses the problems in assigning a precise value to an item (or group of items) of clinical information. Historical viewpoints are reviewed; the paper illustrates how determinist descriptive thinking has been overtaken by concepts of uncertainty and probability. Four equations are proposed outlining the factors which affect the value of clinical information. The validation of these equations and their implications is discussed. Parallels are drawn between the situation in theoretical physics a century ago and medical diagnostics today; and the central theme of uncertainty in both is emphasised. Finally, the need for further radical thinking is stressed.

Clinical Medicine↗

Do the neighboring residues in a polypeptide affect the electron distribution of an amino acid significantly? A quantitative study using the quantum theory of atoms in molecules (QTAIM).

Geometries, as well as bond and atomic properties obtained with the atoms-in-molecules theory applied on B3LYP/6-31++G//B3LYP/6-31G charge densities, of the N-formyl amides of the nine tripeptides obtained by combining glycine, alanine, and serine around a central glycine residue were analyzed to check how the properties of the central residue are modified by other amino acids bonded to it. All of the molecules were optimized from an alpha-helix conformation that was also displayed by the optimized structure. Significant variations of the geometry (especially remarkable for dihedral angles) and atomic properties of the central glycine residue are observed when it is attached to a serine residue whose side chain is involved in a hydrogen bond.

Amino Acids↗

Quantum theory of dissociative chemisorption on metal surfaces.

Recent theoretical progress in gas-surface reaction dynamics, a field relevant to heterogeneous catalysis, is described. One of the most fundamental reactions, the dissociative chemisorption of H2 on metal surfaces, can now be treated accurately using quantum mechanics. Density functional theory is used to compute the molecule-surface interaction, and the motion of the hydrogen atoms is simulated using quantum dynamics, modeling all six molecular degrees of freedom. Theory is in good quantitative agreement with molecular beam experiments, offering useful interpretations, and allowing reliable predictions. The success of the approach calls for extensions to larger systems, such as dissociative chemisorption of polyatomic molecules.

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Limit cycles in quantum theories.

Renormalization group limit cycles and more chaotic behavior may be commonplace for quantum Hamiltonians requiring renormalization, in contrast to experience based on classical models with critical behavior, where fixed points are far more common. We discuss the simplest quantum model Hamiltonian identified so far that exhibits a renormalization group with both limit cycle and chaotic behavior. The model is a discrete Hermitian matrix with two coupling constants, both governed by a nonperturbative renormalization group equation that involves changes in only one of these couplings and is soluble analytically.

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Quantum theory of chiral interactions in cholesteric liquid crystals.

The effective chiral interaction between molecules arising from long-range quantum interactions between fluctuating charge moments is analyzed in terms of a simple model of chiral molecules. This model is based on the approximations that (a) the dominant excited states of a molecule form a band whose width is small compared to the average energy of excitation above the ground state and (b) biaxial orientational correlation between adjacent molecules can be neglected. Previous treatments of quantum chiral interactions have been based on a multipole expansion of the effective interaction energy within second-order perturbation theory. We consider a system consisting of elongated molecules and, although we invoke the expansion in terms of coordinates transverse to the long axis of constituent molecules, we treat the longitudinal coordinate exactly. Such an approximation is plausible for molecules in real liquid crystals. The macroscopic cholesteric wave vector Q (Q=2 pi/P, where P is the pitch) is obtained via Q=h/K(2), where K2 is the Frank elastic constant for twist and h is the torque field which we calculate from the effective chiral interaction kappa(IJ)a(I)xa(J) x R(IJ), where the unit vector a(I) specifies the orientation of molecule I and R(IJ) is the displacement of molecule I relative to molecule J. We identify two distinct physical limits depending on whether one or both of the interacting molecules are excited in the virtual state. When both molecules are excited, we regain the R(-8)(IJ) dependence of kappa(IJ) on intermolecular separation found previously by Van der Meer et al. [J. Chem. Phys. 65, 3935 (1976)]. The two-molecule, unlike the one-molecule term, can be interpreted in terms of a superposition of pairwise interactions between individual atoms (or local chiral centers) on the two molecules. Contributions to kappa(IJ) when one molecule is excited in the virtual state are of order R(-7)(IJ) for helical molecules which are assumed not to have a global dipole moment, but whose atoms possess a dipole moment. It is shown that for a helical molecule Q can have either the same or the opposite sign as the chiral pitch of an individual molecule, depending on the details of the anisotropy of the atomic polarizability. The one-molecule mechanism can become important when the local atomic dipoles become sizable, although biaxial correlations (ignored here) should then be taken into account. Our results suggest how the architecture of molecular dipole moments might be adjusted to significantly influence the macroscopic pitch.

Journal Article↗

Bose-Einstein condensates beyond mean field theory: quantum backreaction as decoherence.

We propose an experiment to measure the slow log(N) convergence to mean field theory (MFT) around a dynamical instability. Using a density matrix formalism instead of the standard macroscopic wave function approach, we derive equations of motion which go beyond MFT and provide accurate predictions for the quantum break time. The leading quantum corrections appear as decoherence of the reduced single-particle quantum state.

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Quantum theory of attosecond XUV pulse measurement by laser dressed photoionization.

The first reported measurements of single attosecond pulses use laser dressed single-photon extreme ultraviolet (XUV) ionization of gas atoms. The determination of XUV pulse duration from the electron spectrum is based on a classical theory. Although classical models are known to give a qualitatively correct description of strong laser atom interaction, the validity must be scrutinized by a quantum-mechanical analysis. We establish a theoretical framework for the accurate temporal characterization of attosecond XUV pulses. Our analysis reveals an improved scheme that allows for direct experimental discrimination between single and multiple attosecond pulses.

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Connection between the regular approximation and the normalized elimination of the small component in relativistic quantum theory.

The regular approximation to the normalized elimination of the small component (NESC) in the modified Dirac equation has been developed and presented in matrix form. The matrix form of the infinite-order regular approximation (IORA) expressions, obtained in [Filatov and Cremer, J. Chem. Phys. 118, 6741 (2003)] using the resolution of the identity, is the exact matrix representation and corresponds to the zeroth-order regular approximation to NESC (NESC-ZORA). Because IORA (=NESC-ZORA) is a variationally stable method, it was used as a suitable starting point for the development of the second-order regular approximation to NESC (NESC-SORA). As shown for hydrogenlike ions, NESC-SORA energies are closer to the exact Dirac energies than the energies from the fifth-order Douglas-Kroll approximation, which is much more computationally demanding than NESC-SORA. For the application of IORA (=NESC-ZORA) and NESC-SORA to many-electron systems, the number of the two-electron integrals that need to be evaluated (identical to the number of the two-electron integrals of a full Dirac-Hartree-Fock calculation) was drastically reduced by using the resolution of the identity technique. An approximation was derived, which requires only the two-electron integrals of a nonrelativistic calculation. The accuracy of this approach was demonstrated for heliumlike ions. The total energy based on the approximate integrals deviates from the energy calculated with the exact integrals by less than 5 x 10(-9) hartree units. NESC-ZORA and NESC-SORA can easily be implemented in any nonrelativistic quantum chemical program. Their application is comparable in cost with that of nonrelativistic methods. The methods can be run with density functional theory and any wave function method. NESC-SORA has the advantage that it does not imply a picture change.

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Two-electron integrations in the quantum theory of atoms in molecules with correlated wave functions.

A recent method proposed to compute two-electron integrals over arbitrary regions of space [Martin Pendas, A. et al., J Chem Phys 2004, 120, 4581] is extended to deal with correlated wave functions. To that end, we use a monadic factorization of the second-order reduced density matrix originally proposed by E. R. Davidson [Chem Phys Lett 1995, 246, 209] that achieves a full separation of the interelectronic components into one-electron terms. The final computational effort is equivalent to that found in the integration of a one determinant wave function with as many orbitals as occupied functions in the correlated expansion. Similar strategies to extract the exchange and self-interaction contributions from the two-electron repulsion are also discussed, and several numerical results obtained in a few test systems are summarized.

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