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At least 1,711 records · Page 95
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DOE OSTI2013

The oscillator model for the Lie superalgebra sh(2|2) and Charlier polynomials

We investigate an algebraic model for the quantum oscillator based upon the Lie superalgebra sh(2|2), known as the Heisenberg–Weyl superalgebra or “the algebra of supersymmetric quantum mechanics,” and its Fock representation. The model offers some freedom in the choice of a position and a momentum operator, leading to a free model parameter γ. Using the technique of Jacobi matrices, we determine the spectrum of the position operator, and show that its wavefunctions are related to Charlier polynomials C{sub n} with parameter γ{sup 2}. Some properties of these wavefunctions are discussed, as well as some other properties of the current oscillator model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

Cluster synchronization induced by one-node clusters in networks with asymmetric negative couplings

This paper deals with the problem of cluster synchronization in networks with asymmetric negative couplings. By decomposing the coupling matrix into three matrices, and employing Lyapunov function method, sufficient conditions are derived for cluster synchronization. The conditions show that the couplings of multi-node clusters from one-node clusters have beneficial effects on cluster synchronization. Based on the effects of the one-node clusters, an effective and universal control scheme is put forward for the first time. The obtained results may help us better understand the relation between cluster synchronization and cluster structures of the networks. The validity of the control scheme is confirmed through two numerical simulations, in a network with no cluster structure and in a scale-free network.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Generalized complement operators and applications in some semirings

Generalized complement operators on the semiring of all Boolean matrices as semilattice homomorphisms are considered. Some applications in solving equations on the set Bn of all binary relations are developed. In particular the structure of B3 is investigated by computer methods. Specific properties of the subsemigroup generated by all irregular relations in B3 are found. Stochastic experiments on the monoid Bn were made. The frequency of irregular elements as well as those of solvable equations depending on n is examined.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

First order deformations of the Fourier matrix

The N × N complex Hadamard matrices form a real algebraic manifold C{sub N}. The singularity at a point H ∈ C{sub N} is described by a filtration of cones T{sub H}{sup ×}C{sub N}⊂T{sub H}{sup ∘}C{sub N}⊂T{sub H}C{sub N}⊂T{sup ~}{sub H}C{sub N}, coming from the trivial, affine, smooth, and first order deformations. We study here these cones in the case where H = F{sub N} is the Fourier matrix, (w{sup ij}) with w = e{sup 2πi/N}, our main result being a simple description of T{sup ~}{sub H}C{sub N}. As a consequence, the rationality conjecture dim{sub R}(T{sup ~}{sub H}C{sub N})=dim{sub Q}(T{sup ~}{sub H}C{sub N}∩M{sub N}(Q)) holds at H = F{sub N}.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Monomer-dimer problem on random planar honeycomb lattice

We consider the monomer-dimer (MD) problem on a random planar honeycomb lattice model, namely, the random multiple chain. This is a lattice system with non-periodic boundary condition, whose generating process is inspired by the growth of single walled zigzag carbon nanotubes. By applying algebraic and combinatorial techniques we establish a calculating expression of the MD partition function for bipartite graphs, which corresponds to the permanent of a matrix. Further, by using the transfer matrix argument we show that the computing problem of the permanent of high order matrix can be converted into some lower order matrices for this family of lattices, based on which we derive an explicit recurrence formula for evaluating the MD partition function of multiple chains and random multiple chains. Finally, we analyze the expectation of the number of monomer-dimer arrangements on a random multiple chain and the asymptotic behavior of the annealed MD entropy when the multiple chain becomes infinite in width and length, respectively.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Sphere-plate Casimir interaction in (D + 1)-dimensional spacetime

In this paper, we derive the formula for the Casimir interaction energy between a sphere and a plate in (D + 1)-dimensional Minkowski spacetime. It is assumed that the scalar field satisfies the Dirichlet or Neumann boundary conditions on the sphere and the plate. As in the D = 3 case, the formula is of TGTG type. One of our main contributions is deriving the translation matrices which express the change of bases between plane waves and spherical waves for general D. Using orthogonality of Gegenbauer polynomials, it turns out that the final TGTG formula for the Casimir interaction energy can be simplified to one that is similar to the D = 3 case. To illustrate the application of the formula, both large separation and small separation asymptotic behaviors of the Casimir interaction energy are computed. The large separation leading term is proportional to L{sup −D+1} if the sphere is imposed with Dirichlet boundary condition, and to L{sup −D−1} if the sphere is imposed with Neumann boundary condition, where L is distance from the center of the sphere to the plane. For the small separation asymptotic behavior, it is shown that the leading term is equal to the one obtained using proximity force approximation. The next-to-leading order term is also computed using perturbation method. It is shown that when the space dimension D is larger than 5, the next-to-leading order has sign opposite to the leading order term. Moreover, the ratio of the next-to-leading order term to the leading order term is linear in D, indicating a larger correction at higher dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Low-temperature random matrix theory at the soft edge

“Low temperature” random matrix theory is the study of random eigenvalues as energy is removed. In standard notation, β is identified with inverse temperature, and low temperatures are achieved through the limit β → ∞. In this paper, we derive statistics for low-temperature random matrices at the “soft edge,” which describes the extreme eigenvalues for many random matrix distributions. Specifically, new asymptotics are found for the expected value and standard deviation of the general-β Tracy-Widom distribution. The new techniques utilize beta ensembles, stochastic differential operators, and Riccati diffusions. The asymptotics fit known high-temperature statistics curiously well and contribute to the larger program of general-β random matrix theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

The Ginibre evolution in the large-N limit

We analyse statistics of the real eigenvalues of gl(N, R)-valued Brownian motion (the Ginibre evolution) in the limit of large N. In particular, we calculate the limiting two-time correlation function of spin variables associated with real eigenvalues of the Ginibre evolution. We also show how the formalism of spin variables can be used to compute the fixed time correlation functions of real eigenvalues discovered originally by Forrester and Nagao [“Eigenvalue statistics of the real Ginibre ensemble,” Phys. Rev. Lett. 99(5), 050603 (2007)] and Borodin and Sinclair [“The Ginibre ensemble of real random matrices and its scaling limits,” Commun. Math. Phys. 291(1), 177–224 (2009)].

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Beam envelope calculations in general linear coupled lattices

The envelope equations and Twiss parameters (β and α) provide important bases for uncoupled linear beam dynamics. For sophisticated beam manipulations, however, coupling elements between two transverse planes are intentionally introduced. The recently developed generalized Courant-Snyder theory offers an effective way of describing the linear beam dynamics in such coupled systems with a remarkably similar mathematical structure to the original Courant-Snyder theory. In this work, we present numerical solutions to the symmetrized matrix envelope equation for β which removes the gauge freedom in the matrix envelope equation for w. Furthermore, we construct the transfer and beam matrices in terms of the generalized Twiss parameters, which enables calculation of the beam envelopes in arbitrary linear coupled systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Comparison of the kinetics of different Markov models for ligand binding under varying conditions

We recently derived a Markov model for macromolecular ligand binding dynamics from few physical assumptions and showed that its stationary distribution is the grand canonical ensemble [J. W. R. Martini, M. Habeck, and M. Schlather, J. Math. Chem. 52, 665 (2014)]. The transition probabilities of the proposed Markov process define a particular Glauber dynamics and have some similarity to the Metropolis-Hastings algorithm. Here, we illustrate that this model is the stochastic analog of (pseudo) rate equations and the corresponding system of differential equations. Moreover, it can be viewed as a limiting case of general stochastic simulations of chemical kinetics. Thus, the model links stochastic and deterministic approaches as well as kinetics and equilibrium described by the grand canonical ensemble. We demonstrate that the family of transition matrices of our model, parameterized by temperature and ligand activity, generates ligand binding kinetics that respond to changes in these parameters in a qualitatively similar way as experimentally observed kinetics. In contrast, neither the Metropolis-Hastings algorithm nor the Glauber heat bath reflects changes in the external conditions correctly. Both converge rapidly to the stationary distribution, which is advantageous when the major interest is in the equilibrium state, but fail to describe the kinetics of ligand binding realistically. To simulate cellular processes that involve the reversible stochastic binding of multiple factors, our pseudo rate equation model should therefore be preferred to the Metropolis-Hastings algorithm and the Glauber heat bath, if the stationary distribution is not of only interest.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Förster resonance energy transfer, absorption and emission spectra in multichromophoric systems. I. Full cumulant expansions and system-bath entanglement

We study the Förster resonant energy transfer rate, absorption and emission spectra in multichromophoric systems. The multichromophoric Förster theory (MCFT) is determined from an overlap integral of generalized matrices related to the donor’s emission and acceptor’s absorption spectra, which are obtained via a full 2nd-order cumulant expansion technique developed in this work. We calculate the spectra and MCFT rate for both localized and delocalized systems, and calibrate the analytical 2nd-order cumulant expansion with the exact stochastic path integral method. We present three essential findings: (i) The role of the initial entanglement between the donor and its bath is found to be crucial in both the emission spectrum and the MCFT rate. (ii) The absorption spectra obtained by the cumulant expansion method are nearly identical to the exact spectra for both localized and delocalized systems, even when the system-bath coupling is far from the perturbative regime. (iii) For the emission spectra, the cumulant expansion can give reliable results for localized systems, but fail to provide reliable spectra of the high-lying excited states of a delocalized system, when the system-bath coupling is large and the thermal energy is small. This paper also provides a simple golden-rule derivation of the MCFT, reviews existing methods, and motivates further developments in the subsequent papers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Magnetocrystalline anisotropy of 4d/5d transition metals on a Co(0001) surface: A first-principles study

Magnetism and magnetocrystalline anisotropy (MCA) of 4d and 5d transition metal monolayers have been investigated in the presence of a Co(0001) substrate using first-principles electronic structure calculations. Magnetization of Co-group elements undergoes a transition from an in-plane to perpendicular MCA on Co(0001), whose energies (E{sub MCA}) are +0.75 meV/cell and +3.67 meV/cell for Rh/Co(0001) and Ir/Co(0001), respectively. On the other hand, the Fe-group Ru/Co(0001) and Os/Co(0001) exhibit the in-plane MCA with antiparallel spin moments to that of the Co substrate. From band analysis, enhancement of MCA in the Ir/Co(0001) is mainly due to the Ir atom by 〈m=0| l{sub x} |m=±1〉 matrix in the ↑↓-channel, where negative MCA found in Os/Co(0001) is due to Co with dominant contribution from 〈m=0| l{sub x} |m=±1〉 and 〈m=±2| l{sub x} |m=±1〉 matrices in the ↓↓- and ↑↓-channel, respectively. The significant enhancement of E{sub MCA} in Rh/ and Ir/ Co(0001) is ascribed to larger spin-orbit coupling of 4d and 5d orbitals, mainly by coupling between m = 0 and m = ±1 states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

On the derivation of the semiclassical approximation to the quantum propagator

In order to rigorously derive the amplitude factor of the semiclassical approximation to the quantum propagator, we extend an existing method originally devised to evaluate Gaussian path-integral expressions. Using a result which relates the determinant of symmetric block-tridiagonal matrices to the determinants of their blocks, two difference equations are obtained. The first one allows to establish the connection of the amplitude factor to Jacobi’s accessory equations in the continuous-time limit, while the second one leads to an additional factor which, however, contributes to the final result only in exceptional cases. In order to demonstrate the wide applicability of these difference equations, we treat explicitly the case where the time-sliced Lagrangian is written in generalized coordinates, for which a general derivation has so far been unavailable.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Continuity of the maximum-entropy inference: Convex geometry and numerical ranges approach

We study the continuity of an abstract generalization of the maximum-entropy inference—a maximizer. It is defined as a right-inverse of a linear map restricted to a convex body which uniquely maximizes on each fiber of the linear map a continuous function on the convex body. Using convex geometry we prove, amongst others, the existence of discontinuities of the maximizer at limits of extremal points not being extremal points themselves and apply the result to quantum correlations. Further, we use numerical range methods in the case of quantum inference which refers to two observables. One result is a complete characterization of points of discontinuity for 3 × 3 matrices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Microscopic theory of cooperative spin crossover: Interaction of molecular modes with phonons

In this article, we present a new microscopic theoretical approach to the description of spin crossover in molecular crystals. The spin crossover crystals under consideration are composed of molecular fragments formed by the spin-crossover metal ion and its nearest ligand surrounding and exhibiting well defined localized (molecular) vibrations. As distinguished from the previous models of this phenomenon, the developed approach takes into account the interaction of spin-crossover ions not only with the phonons but also a strong coupling of the electronic shells with molecular modes. This leads to an effective coupling of the local modes with phonons which is shown to be responsible for the cooperative spin transition accompanied by the structural reorganization. The transition is characterized by the two order parameters representing the mean values of the products of electronic diagonal matrices and the coordinates of the local modes for the high- and low-spin states of the spin crossover complex. Finally, we demonstrate that the approach provides a reasonable explanation of the observed spin transition in the [Fe(ptz){sub 6}](BF{sub 4}){sub 2} crystal. The theory well reproduces the observed abrupt low-spin → high-spin transition and the temperature dependence of the high-spin fraction in a wide temperature range as well as the pronounced hysteresis loop. At the same time within the limiting approximations adopted in the developed model, the evaluated high-spin fraction vs. T shows that the cooperative spin-lattice transition proves to be incomplete in the sense that the high-spin fraction does not reach its maximum value at high temperature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Algebraic techniques for diagonalization of a split quaternion matrix in split quaternionic mechanics

In the study of the relation between complexified classical and non-Hermitian quantum mechanics, physicists found that there are links to quaternionic and split quaternionic mechanics, and this leads to the possibility of employing algebraic techniques of split quaternions to tackle some problems in complexified classical and quantum mechanics. This paper, by means of real representation of a split quaternion matrix, studies the problem of diagonalization of a split quaternion matrix and gives algebraic techniques for diagonalization of split quaternion matrices in split quaternionic mechanics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

W-band EPR studies of high-spin nitrenes with large spin-orbit contribution to zero-field splitting

First W-band 94 GHz EPR spectra of randomly oriented triplet, quintet, and septet nitrenes formed during the photolysis of 1,3,5-triazido-2,4,6-tribromobenzene in cryogenic matrices are reported. In comparison with conventional X-band 9 GHz electron paramagnetic resonance (EPR) spectroscopy, W-band EPR spectroscopy allows the detection and complete spectroscopic characterization of all paramagnetic species formed at different stages of the photolysis of aromatic polyazides. This type of spectroscopy is of paramount importance for experimental determination of the sign of the zero-field splitting (ZFS) parameters of high-spin molecules with large spin-orbit contribution to the ZFS, caused by the effect of heavy atoms. The study shows that triplet 1,3-diazido-2,4,6-tribromo-5-nitrenobenzene (T1) has D{sub T} = 1.369 cm{sup −1}, E{sub T} = 0.093 cm{sup −1}, and g = 2.0033, quintet 1-azido-2,4,6-tribromo-3,5-dinitrenobenzene (Q1) shows D{sub Q} = − 0.306 cm{sup −1}, E{sub Q} = 0.0137 cm{sup −1}, and g = 2.0070, and septet 2,4,6-tribromo-1,3,5-trinitrenobenzene (S1) has D{sub S} = − 0.203 cm{sup −1}, E{sub S} = 0, and g = 2.0073. The experimental ZFS parameters agree well with the results of density functional theory calculations at the PBE/Ahlrichs-DZ level of theory, showing that such calculations adequately describe the magnetic properties of bromine-containing high-spin nitrenes. Both experimental and theoretical data indicate that, in contrast to all known to date quintet dinitrenes, dinitrene Q1 has the negative sign of magnetic anisotropy due to the “heavy atom effect.” This dinitrene along with septet trinitrene S1 possess the largest negative value of D among all known quintet and septet organic polyradicals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗