Erratum: Reexamination of the helium fine structure [Phys. Rev. A 79, 062516 (2009)]
Krzysztof Pachucki and Vladimir A. Yerokhin
Abstract not available. [Phys. Rev. A 81, 039903 ] published .
Numerical approach to the Schrodinger equation in momentum space
William A. Karr, Christopher R. Jamell, and Yogesh N. Joglekar
The treatment of the time-independent Schrodinger equation in real space is an indispensable part of introductory quantum mechanics. In contrast, the Schrodinger equation in momentum space is an integral equation that is not readily amenable to an analytical solution and is rarely taught. We present ... [Am. J. Phys. 78, 407 (2010)] published Thu Mar 11, 2010.
Fixed trace beta-Hermite ensembles: Asymptotic eigenvalue density and the edge of the density
Da-Sheng Zhou, Dang-Zheng Liu, and Tao Qian
In the present paper, fixed trace beta-Hermite ensembles generalizing the fixed trace Gaussian ensembles are considered. For all beta, we prove the Wigner semicircle law for these ensembles by using two different methods: one is the moment equivalence method with the help of the matrix model for gen ... [J. Math. Phys. 51, 033301 (2010)] published Thu Mar 11, 2010.
Exact moment scaling from multiplicative noise
Giacomo Bormetti and Danilo Delpini
For a general class of diffusion processes with multiplicative noise, describing a variety of physical as well as financial phenomena, mostly typical of complex systems, we obtain the analytical solution for the moments at all times. We allow for a nontrivial time dependence of the microscopic dynam ... [Phys. Rev. E 81, 032102 ] published .
Nonequilibrium stationary state of a truncated stochastic nonlinear Schrodinger equation: Formulation and mean-field approximation
Philippe Mounaix, Pierre Collet, and Joel L. Lebowitz
We investigate the stationary state of a model system evolving according to a modified focusing truncated nonlinear Schrodinger equation used to describe the envelope of Langmuir waves in a plasma. We restrict the system to have a finite number of normal modes each of which is in contact with a Lang ... [Phys. Rev. E 81, 031109 ] published .
Reverse Engineering: Statistical Threshold for New Selective Sampling Morphological Descriptor
E. Vezzetti
During the digitization process of a physical object, the operator has to choose an acquisition pitch. Currently, 3D scanners employ constant pitches. For this reason the grid dimension choice normally represents a compromise between the scanner performances and specific applications, and the resolu ... [J. Comput. Inf. Sci. Eng. 10, 011008 (2010)] published Wed Mar 10, 2010.
Estimating generalized Lyapunov exponents for products of random matrices
J. Vanneste
We discuss several techniques for the evaluation of the generalized Lyapunov exponents which characterize the growth of products of random matrices in the large-deviation regime. A Monte Carlo algorithm that performs importance sampling using a simple random resampling step is proposed as a general- ... [Phys. Rev. E 81, 036701 ] published .
Finite nuclear mass corrections to electric and magnetic interactions in diatomic molecules
Krzysztof Pachucki
In order to interpret precise measurements of molecular properties, finite nuclear mass corrections to the Born-Oppenheimer approximation have to be accounted for. It is demonstrated that they can be obtained systematically using nonadiabatic perturbation theory. The formulas for the leading correct ... [Phys. Rev. A 81, 032505 ] published .
Gauge invariance and reciprocity in quantum mechanics
P. T. Leung (梁培德) and K. Young (楊綱凱)
Reciprocity in wave propagation usually refers to the symmetry of the Green's function under the interchange of the source and the observer coordinates, but this condition is not gauge invariant in quantum mechanics, a problem that is particularly significant in the presence of a vector potential. S ... [Phys. Rev. A 81, 032107 ] published .
Discrete and continuous invariance in phyllotactic tilings
Patrick D. Shipman
Phyllotaxis refers to the arrangement of primordia (the first stage in the development of a structure such as a leaf) on plants and phyllotactic planforms refer to the shapes of the primordia in a phyllotactic arrangement. This paper focuses on invariances in phyllotactic planforms as the van Iterso ... [Phys. Rev. E 81, 031905 ] published .
Final-state spectrum of He after beta decay of tritium anions T
Alexander Stark and Alejandro Saenz
The final-state spectrum of beta decaying tritium anions T was calculated. The wave functions describing the initial T ground state and the final He states were obtained by the full configuration-interaction method. The transition probability was calculated within the sudden approximation. The trans ... [Phys. Rev. A 81, 032501 ] published .
A fractional calculus of variations for multiple integrals with application to vibrating string
Ricardo Almeida, Agnieszka B. Malinowska, and Delfim F. M. Torres
We introduce a fractional theory of the calculus of variations for multiple integrals. Our approach uses the recent notions of RiemannLiouville fractional derivatives and integrals in the sense of Jumarie. The main results provide fractional versions of the theorems of Green and Gauss, fractional Eu ... [J. Math. Phys. 51, 033503 (2010)] published Fri Mar 5, 2010.
Compact and flexible basis functions for quantum Monte Carlo calculations
F. R. Petruzielo, Julien Toulouse, and C. J. Umrigar
Molecular calculations in quantum Monte Carlo frequently employ a mixed basis consisting of contracted and primitive Gaussian functions. While standard basis sets of varying size and accuracy are available in the literature, we demonstrate that reoptimizing the primitive function exponents within qu ... [J. Chem. Phys. 132, 094109 (2010)] published Fri Mar 5, 2010.
Optimal Stopping Rules For Some Blackjack Type Problems
Andrzej Z. Grzybowski
The paper deals with a class of optimal stopping problems having some features of blackjack type games. A decision maker observes sequentially the values of a finite sequence of non-negative random variables. After each observation he decides whether to stop or to continue. If he decides to stop, he ... [AIP Conf. Proc. 1220, 91 (2010)] published Fri Mar 5, 2010.
A Multigrid Block Krylov Subspace Spectral Method for Variable-Coefficient Elliptic PDE
James V. Lambers
Krylov subspace spectral (KSS) methods have been demonstrated to be effective tools for solving time-dependent variable-coefficient PDE. They employ techniques developed by Golub and Meurant for computing elements of functions of matrices to approximate each Fourier coefficient of the solution using ... [AIP Conf. Proc. 1220, 134 (2010)] published Fri Mar 5, 2010.
Integrability of the KruskalZabusky Discrete Equation by Multiscale Expansion
Decio Levi and Christian Scimiterna
In 1965 Kruskal and Zabusky in a very famous article in Physical Review Letters introduced the notion of soliton to describe the interaction of solitary waves solutions of the Korteweg de Vries equation (KdV). To do so they introduced a discrete approximation to the KdV, the KruskalZabusky equation ... [AIP Conf. Proc. 1212, 66 (2010)] published Fri Mar 5, 2010.
Integral transformation and Darboux transformation of Heun's differential equation
Kouichi Takemura
We review Darboux-Crum transformation of Heun's differential equation. By rewriting an integral transformation of Heun's differential equation into a form of elliptic functions, we see that the integral representation is a generalization of Darboux-Crum transformation. We also consider conservation ... [AIP Conf. Proc. 1212, 58 (2010)] published Fri Mar 5, 2010.
Singular solutions of nonlinear systems and patterns associated with them
Mikhail Kovalyov
We discuss properties of and patterns exhibited by singular solutions of integrable systems. ... [AIP Conf. Proc. 1212, 43 (2010)] published Fri Mar 5, 2010.
Virasoro and W-constraints for the q-KP hierarchy
Kelei Tian, Jingsong He, and Yi Cheng
Based on the Adler-Shiota-van Moerbeke (ASvM) formula, the Virasoro constraints and W-constraints for the p-reduced q-deformed Kadomtsev-Petviashvili (q-KP) hierarchy are established. ... [AIP Conf. Proc. 1212, 35 (2010)] published Fri Mar 5, 2010.
Multi-component matrix loop algebras and their applications to integrable systems
Zhu Li
Firstly, a multi-component matrix Loop algebra A and its expanding Loop algebra A are constructed. Then using A, an isospectral problem is established; and by virtue of the Tu scheme, a multi-component integrable system is obtained, which is Liouville integrable. Further, the Hamiltonian structure o ... [AIP Conf. Proc. 1212, 286 (2010)] published Fri Mar 5, 2010.
On the Exp-function method for constructing travelling wave solutions of nonlinear equations
Lijun Zhang and Xuwen Huo
The Exp-function method or some similar direct methods have been applied by many researchers to the construction of new solutions to nonlinear differential equations. In this paper, we demonstrate that some of those so-called new solutions can always be transformed into a uniform formula, which can ... [AIP Conf. Proc. 1212, 280 (2010)] published Fri Mar 5, 2010.
Oriented Matroids -- Combinatorial Structures Underlying Loop Quantum Gravity. (arXiv:1003.2348v1 [gr-qc])
ePrint arXiv http://arXiv.org/
Nonabelian parafermions and their dimensions. (arXiv:1003.2342v1 [hep-th])
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Mathematical aspects of intertwining operators: the role of Riesz bases. (arXiv:1003.2288v1 [math-ph])
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Ultradistributions and The Fractionary Schr\"{o}dinger Equation. (arXiv:1003.2356v1 [math-ph])
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Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient flows. (arXiv:0812.1269v2 [math-ph] UPDATED)
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The saga of the Ising susceptibility. (arXiv:1003.0751v2 [math-ph] UPDATED)
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On the soliton dynamics under slowly varying medium for Nonlinear Schr\"odinger equations. (arXiv:1002.1295v2 [math.AP] UPDATED)
ePrint arXiv http://arXiv.org/
Dynamical Invariants for Variable Quadratic Hamiltonians. (arXiv:1002.0144v6 [math-ph] UPDATED)
ePrint arXiv http://arXiv.org/
Equivalence of the generalized and complex Kohn variational methods. (arXiv:1001.1181v2 [quant-ph] UPDATED)
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A new approach to derive Pfaffian structures for random matrix ensembles. (arXiv:0912.0658v3 [math-ph] UPDATED)
ePrint arXiv http://arXiv.org/
Fluctuations of the nodal length of random spherical harmonics. (arXiv:0907.1648v2 [math.PR] UPDATED)
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