E. C. G. Sudarshan and Symmetry in Classical Dynamics, Optics and Quantum Mechanics

We review work initiated and inspired by Sudarshan in relativistic dynamics, beam optics, partial coherence theory, Wigner distribution methods, multimode quantum optical squeezing, and geometric phases. The 1963 No Interaction Theorem using Dirac's instant form and particle World Line Conditions is recalled. Later attempts to overcome this result exploiting constrained Hamiltonian theory, reformulation of the World Line Conditions and extending Dirac's formalism, are reviewed. Dirac's front form leads to a formulation of Fourier Optics for the Maxwell field, determining the actions of First Order Systems (corresponding to matrices of Sp(2,R) and Sp(4,R)) on polarization in a consistent manner. These groups also help characterize properties and propagation of partially coherent Gaussian Schell Model beams, leading to invariant quality parameters and the new Twist phase. The higher dimensional groups Sp(2n,R) appear in the theory of Wigner distributions and in quantum optics. Elegant criteria for a Gaussian phase space function to be a Wigner distribution, expressions for multimode uncertainty principles and squeezing are described. In geometric phase theory we highlight the use of invariance properties that lead to a kinematical formulation and the important role of Bargmann invariants. Special features of these phases arising from unitary Lie group representations, and a new formulation based on the idea of Null Phase Curves, are presented.

Crystal structures of fluorinated aryl biscarbonates and a biscarbamate: a counterpoise between weak intermolecular interactions and molecular symmetry

Conformational features and supramolecular structural organization in three aryl biscarbonates and an aryl biscarbamate with rigid acetylenic unit providing variable spacer lengths have been probed to gain insights into the packing features associated with molecular symmetry and the intermolecular interactions involving `organic' fluorine. Four structures but-2-yne-1,4-diyl bis(2,3,4,5,6-pentafluorophenylcarbonate), 1; but-2-yne-1,4-diyl bis(4-fluorophenylcarbonate), 2; but-2-yne-1,4-diyl bis(2,3,4,5,6-pentafluorophenylcarbamate), 3 and hexa-2,4-diyne-1,6-diyl bis(2,3,4,5,6-pentafluorophenylcarbonate), 4 have been analyzed in this context. Compound 1 adopts a non-centrosymmetric ``twisted'' (syn) conformation, whereas 2, 3 and 4 acquire a centrosymmetric ``extended'' (anti) conformation. Weak intermolecular interactions and in particular those involving fluorine are found to dictate this conformational variation in the crystal structure of 1. A single-crystal neutron diffraction study at 90 K was performed on 1 to obtain further insights into these interactions involving `organic' fluorine.

Symmetry Properties of the Large-Deviation Function of the Velocity of a Self-Propelled Polar Particle

A geometrically polar granular rod confined in 2D geometry, subjected to a sinusoidal vertical oscillation, undergoes noisy self-propulsion in a direction determined by its polarity. When surrounded by a medium of crystalline spherical beads, it displays substantial negative fluctuations in its velocity. We find that the large-deviation function (LDF) for the normalized velocity is strongly non-Gaussian with a kink at zero velocity, and that the antisymmetric part of the LDF is linear, resembling the fluctuation relation known for entropy production, even when the velocity distribution is clearly non-Gaussian. We extract an analogue of the phase-space contraction rate and find that it compares well with an independent estimate based on the persistence of forward and reverse velocities.

Combining Bayes Classification and Point Group Symmetry under Boolean Framework for Enhanced Protein Quaternary Structure Inference

Our ability to infer the protein quaternary structure automatically from atom and lattice information is inadequate, especially for weak complexes, and heteromeric quaternary structures. Several approaches exist, but they have limited performance. Here, we present a new scheme to infer protein quaternary structure from lattice and protein information, with all-around coverage for strong, weak and very weak affinity homomeric and heteromeric complexes. The scheme combines naive Bayes classifier and point group symmetry under Boolean framework to detect quaternary structures in crystal lattice. It consistently produces >= 90% coverage across diverse benchmarking data sets, including a notably superior 95% coverage for recognition heteromeric complexes, compared with 53% on the same data set by current state-of-the-art method. The detailed study of a limited number of prediction-failed cases offers interesting insights into the intriguing nature of protein contacts in lattice. The findings have implications for accurate inference of quaternary states of proteins, especially weak affinity complexes.

Symmetry-breaking transition in a two-level system coupled to an Ohmic bath: A squeezed-state approach

Displaced squeezed states are proposed as variational ground states for phonons (Bose fields) coupled to two-level systems (spin systems). We have investigated the zero-temperature phase diagram for the localization-delocalization transition of a tunneling particle interacting with an Ohmic heat bath. Our results are compared with known existing approximate treatments. A modified phase diagram using the displaced squeezed state is presented.

Levitation Effect: Role of Symmetry and Dependence of Diffusivity on the Bond Length of Homonuclear and Heteronuclear Diatomic Species

Molecular dynamics investigation of model diatomic species confined to the alpha-cages of zeolite NaY is reported. The dependence of self-diffusivity on the bond length of the diatomic species has been investigated. Three different sets of runs have been carried out. In the first set, the two atoms of the diatomic molecule interact with the zeolite atoms with equal strength (example, O-2, the symmetric case). In the second and third sets which correspond to asymmetric cases, the two atoms of the diatomic molecule interact with unequal strengths (example, CO). The result for the symmetric case exhibits a well-defined maximum in self-diffusivity for an intermediate bond length. In contrast to this, the intermediate asymmetry leads to a less pronounced maximum. For the large asymmetric case, the maximum is completely absent. These findings are analyzed by computing a number of related properties. These results provide a direct confirmation at the microscopic level of the suggestion by Derouane that the supermobility observed experimentally by Kemball has its origin in the mutual cancellation of forces. The maximum in diffusivity from molecular dynamics is seen at the value predicted by the levitation effect. Further, these findings suggest a role for symmetry in the existence of a diffusivity maximum as a function of diameter of the diffusant often referred to as the levitation effect. The nature of the required symmetry for the existence of anomalous diffusivity is interaction symmetry which is different from that normally encountered in crystallography.

Cyclization of enediyne radical cations through chemical, photochemical, and electrochemical oxidation: The role of state symmetry

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Strength Symmetry Index: A measure of seizure adequacy in ECT

Seizure electroencephalography (EEG) was recorded from two channels-right (Rt) and left (Lt)-during bilateral electroconvulsive therapy (ECT) (n = 12) and unilateral ECT (n = 12). The EEG was also acquired into a microcomputer and was analyzed without knowledge of the clinical details. EEG recordings of both ECT procedures yielded seizures of comparable duration. The Strength Symmetry Index (SSI) was computed from the early- and midseizure phases using the fractal dimension of the EEG. The seizures of unilateral ECT were characterized by significantly smaller SSI in both phases. More unilateral than bilateral ECT seizures had a smaller than median SSI in both phases. The seizures also differed on other measures as reported in the literature. The findings indicate that SSI may be a potential measure of seizure adequacy that remains to be validated in future research.

Symmetry-breaking transitions in equilibrium shapes of coherent precipitates: Effect of elastic anisotropy and inhomogeneity

We examine the symmetry-breaking transitions in equilibrium shapes of coherent precipitates in two-dimensional (2-D) systems under a plane-strain condition with the principal misfit strain components epsilon(xx)*. and epsilon(yy)*. For systems with cubic elastic moduli, we first show all the shape transitions associated with different values of t = epsilon(yy)*/epsilon(xx)*. We also characterize each of these transitions, by studying its dependence on elastic anisotropy and inhomogeneity. For systems with dilatational misfit (t = 1) and those with pure shear misfit (t = -1), the transition is from an equiaxed shape to an elongated shape, resulting in a break in rotational symmetry. For systems with nondilatational misfit (-1 < t < 1; t not equal 0), the transition involves a break in mirror symmetries normal to the x- and y-axes. The transition is continuous in all cases, except when 0 < t < 1. For systems which allow an invariant line (-1 less than or equal to t < 0), the critical size increases with an increase in the particle stiffness. However, for systems which do not allow an invariant line (0 < t less than or equal to 1), the critical size first decreases, reaches a minimum, and then starts increasing with increasing particle stiffness; moreover, the transition is also forbidden when the particle stiffness is greater than a critical value.

Symmetry in Scalar Field Topology

Study of symmetric or repeating patterns in scalar fields is important in scientific data analysis because it gives deep insights into the properties of the underlying phenomenon. Though geometric symmetry has been well studied within areas like shape processing, identifying symmetry in scalar fields has remained largely unexplored due to the high computational cost of the associated algorithms. We propose a computationally efficient algorithm for detecting symmetric patterns in a scalar field distribution by analysing the topology of level sets of the scalar field. Our algorithm computes the contour tree of a given scalar field and identifies subtrees that are similar. We define a robust similarity measure for comparing subtrees of the contour tree and use it to group similar subtrees together. Regions of the domain corresponding to subtrees that belong to a common group are extracted and reported to be symmetric. Identifying symmetry in scalar fields finds applications in visualization, data exploration, and feature detection. We describe two applications in detail: symmetry-aware transfer function design and symmetry-aware isosurface extraction.

Symmetry of one-dimensional dynamical systems in terms of transfer matrix parameters

The concept of symmetry for passive, one-dimensional dynamical systems is well understood in terms of the impedance matrix, or alternatively, the mobility matrix. In the past two decades, however, it has been established that the transfer matrix method is ideally suited for the analysis and synthesis of such systems. In this paper an investigatiob is described of what symmetry means in terms of the transfer matrix parameters of an passive element or a set of elements. One-dimensional flexural systems with 4 × 4 transfer matrices as well as acoustical and mechanical systems characterized by 2 × 2 transfer matrices are considered. It is shown that the transfer matrix of a symmetrical system, defined with respect to symmetrically oriented state variables, is involutory, and that a physically symmetrical system may not necessarily be functionally or dynamically symmetrical.

Full spin and spatial symmetry adapted technique for correlated electronic hamiltonians: Application to an icosahedral cluster

One of the long standing problems in quantum chemistry had been the inability to exploit full spatial and spin symmetry of an electronic Hamiltonian belonging to a non-Abelian point group. Here, we present a general technique which can utilize all the symmetries of an electronic (magnetic) Hamiltonian to obtain its full eigenvalue spectrum. This is a hybrid method based on Valence Bond basis and the basis of constant z-component of the total spin. This technique is applicable to systems with any point group symmetry and is easy to implement on a computer. We illustrate the power of the method by applying it to a model icosahedral half-filled electronic system. This model spans a huge Hilbert space (dimension 1,778,966) and in the largest non-Abelian point group. The C60 molecule has this symmetry and hence our calculation throw light on the higher energy excited states of the bucky ball. This method can also be utilized to study finite temperature properties of strongly correlated systems within an exact diagonalization approach. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

Symmetry-dependent phonon renormalization in monolayer MoS2 transistor

A strong electron-phonon interaction which limits the electronic mobility of semiconductors can also have significant effects on phonon frequencies. The latter is the key to the use of Raman spectroscopy for nondestructive characterization of doping in graphene-based devices. Using in situ Raman scattering from a single-layer MoS2 electrochemically top-gated field-effect transistor (FET), we show softening and broadening of the A(1g) phonon with electron doping, whereas the other Raman-active E-2g(1) mode remains essentially inert. Confirming these results with first-principles density functional theory based calculations, we use group theoretical arguments to explain why the A(1g) mode specifically exhibits a strong sensitivity to electron doping. Our work opens up the use of Raman spectroscopy in probing the level of doping in single-layer MoS2-based FETs, which have a high on-off ratio and are of technological significance.