Geometric Phase, Curvature, and Extrapotentials in Constrained Quantum Systems

We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian depends on quantities which are external to the constraint manifold, such as the external curvature of the constraint manifold, the (Riemannian) curvature of the ambient space, and the constraining potential. In particular, we find the remarkable fact that the twisting of the constraining potential appears as a gauge potential in the constrained Hamiltonian. This gauge potential is an example of geometric phase, closely related to that originally discussed by Berry. The constrained Hamiltonian also contains an effective potential depending on the external curvature of the constraint manifold, the curvature of the ambient space, and the twisting of the constraining potential. The general nature of our analysis allows applications to a wide variety of problems, such as rigid molecules, the evolution of molecular systems along reaction paths, and quantum strip waveguides.Comment: 27 pages with 1 figure, submitted to Phys. Rev.

Ubiquitin in the immune system

Ubiquitination is a post‐translational modification process that has been implicated in the regulation of innate and adaptive immune responses. There is increasing evidence that both ubiquitination and its reversal, deubiquitination, play crucial roles not only during the development of the immune system but also in the orchestration of an immune response by ensuring the proper functioning of the different cell types that constitute the immune system. Here, we provide an overview of the latest discoveries in this field and discuss how they impact our understanding of the ubiquitin system in host defence mechanisms as well as self‐tolerance

Inflammation and breast cancer. Inflammatory component of mammary carcinogenesis in ErbB2 transgenic mice

This review addresses genes differentially expressed in the mammary gland transcriptome during the progression of mammary carcinogenesis in BALB/c mice that are transgenic for the rat neu (ERBB2, or HER-2/neu) oncogene (BALB-neuT664V-E mice). The Ingenuity knowledge database was used to characterize four functional association networks whose hub genes are directly linked to inflammation (specifically, the genes encoding IL-1β, tumour necrosis factor, interferon-γ, and monocyte chemoattractant protein-1/CC chemokine ligand-2) and are increasingly expressed during such progression. In silico meta-analysis in a human breast cancer dataset suggests that proinflammatory activation in the mammary glands of these mice reflects a general pattern of human breast cancer

N-body Quantum-mechanical Hamiltonians - Extrapotential Terms

After a brief review of the basic algebraic ingredients needed to express the quantum-mechanical Hamiltonian of an /b N/-body system in terms of curvilinear coordinates and quasi-momentum operators, the effect of changing the normalization convention is thoroughly investigated, with special emphasis on the occurrence of a nondifferential term in the expression of the kinetic energy operator, the so-called `extrapotential' term. Four examples are presented, concerning various parametrizations and various referentials, for acetylene-like molecules.Anglai

Vibrational spectra of the acetylene-like molecules by using the potential energy surface of strey and mills

By using the potential energy surface of Strey and Mills and the kinetic energy operator expressed in terms of valence coordinates, rewritten in order to calculate analytically the angular part of the Hamiltonian matrix elements, the low-lying vibrational levels of the acetylene-like molecules are derived variationally

Too exhausted to go to bed: Implicit theories about willpower and stress predict bedtime procrastination

While most people are aware of the importance of sleep for their health, well‐being, and performance, bedtime procrastination is a pervasive phenomenon that can be conceptualized as a case of self‐control failure (Kroese et al., Frontiers in Psychology, 5, 2014, 1). Two daily diary studies (N1 = 185, N2 = 137) investigated beliefs about willpower and stress as interactive predictors of bedtime procrastination. Beliefs about willpower capture whether people think of their willpower as limited resource that gets easily depleted (limited theory) or as something that remains regardless of previous acts of self‐control (non‐limited theory). Results show that after a stressful day, people with a limited versus non‐limited theory procrastinate more on going to bed, while there is no difference in bedtime procrastination on less stressful days. Thus, ironically, limited theorists who should be more concerned with recovering their resources after a stressful day sleep less the following night

A Comment On Recent Proposals for the Calculation of Vibration-rotation Energies in More-than-3 Atom Molecules

In a recent paper (Molec. Phys. 1991, 73, 1183), Bramley et al. analysed the physical and mathematical context in which the vibrational rotational Hamiltonian operator for a molecule is expressed in terms of Euler angles for the rotation and internal curvilinear coordinates for the vibration. In the case of a generic tetra-atomic molecule, they derived a few rules which determine the choice of the basis functions, in order (i) to ensure continuity and single-valuedness of the eigenfunctions and (ii) to cancel out the singularities (infinite integrals) that unavoidably crop up in the matrix representation of the vibration-rotation kinetic energy operator. In another recent paper (Phys. Rev. A, 1992, 45, 6217), Chapuisat and lung considered the vibration-rotation of a polyatomic molecule as resulting from the rotational-vibrational motion of coupled relative vectors; with the help of a standard representation for the angular motion of each vector viewed in the moving frame resulting from the first two Euler rotations, i.e. for the whole molecule a direct product of spherical harmonics, they have shown that it is possible to get rid of the singularities and to derive, after completing the third Euler rotation, analytical expressions of the kinetic energy operator matrix elements in the usual bending-torsion-rotation basis. In implementing this approach, the rules derived for tetra-atomics by Bramley et al. are confirmed and are next generalized to the case of the N-atom molecule. The restrictions to the direct product representation which must be explicitly taken into account are established on the basis of a purely physical analysis of the coupled vector motion