The Experts below are selected from a list of 15711 Experts worldwide ranked by ideXlab platform
Alex Ayet - One of the best experts on this subject based on the ideXlab platform.
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the single particle density matrix of a quantum bright soliton from the Coordinate bethe ansatz
2017Co-Authors: Alex Ayet, Joachim BrandAbstract:We present a novel approach for computing reduced density matrices for superpositions of eigenstates of a Bethe-ansatz solvable model by direct integration of the wave function in Coordinate Representation. A diagrammatic approach is developed to keep track of relevant terms and identify symmetries, which helps to reduce the number of terms that have to be evaluated numerically. As a first application we compute with modest numerical resources the single-particle density matrix and its eigenvalues including the condensate fraction for a quantum bright soliton with up to N = 10 bosons. The latter are constructed as superpositions of string-type Bethe-ansatz eigenstates of nonrelativistic bosons in one spatial dimension with attractive contact interaction. Upon delocalising the superposition in momentum space we find that the condensate fraction reaches maximum values larger than 97% with weak particle-number dependence in the range of particles studied. The presented approach is suitable for studying time-dependent problems and generalises to higher-order correlation functions.
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the single particle density matrix of a quantum bright soliton from the Coordinate bethe ansatz
2015Co-Authors: Alex Ayet, Joachim BrandAbstract:We present a novel approach for computing reduced density matrices for superpositions of eigenstates of a Bethe-ansatz solvable model by direct integration of the wave function in Coordinate Representation. A diagrammatic approach is developed to keep track of relevant terms and identify symmetries, which helps to reduce the number of terms that have to be evaluated numerically. As a first application we compute with modest numerical resources the single-particle density matrix and its eigenvalues including the condensate fraction for a quantum bright soliton with up to $N=10$ bosons. The latter are constructed as superpositions of string-type Bethe-ansatz eigenstates of nonrelativistic bosons in one spatial dimension with attractive contact interaction. Upon delocalising the superposition in momentum space we find that the condensate fraction reaches maximum values larger than 97\% in the range of particles studied. The presented approach is suitable for studying time-dependent problems and generalises to higher-order correlation functions.
R H Tipping - One of the best experts on this subject based on the ideXlab platform.
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irreducible correlation functions of the s matrix in the Coordinate Representation application in calculating lorentzian half widths and shifts
2006Co-Authors: R H Tipping, C BouletAbstract:By introducing the Coordinate Representation, the derivation of the perturbation expansion of the Liouville S matrix is formulated in terms of classically behaved autocorrelation functions. Because these functions are characterized by a pair of irreducible tensors, their number is limited to a few. They represent how the overlaps of the potential components change with a time displacement, and under normal conditions, their magnitudes decrease by several orders of magnitude when the displacement reaches several picoseconds. The correlation functions contain all dynamical information of the collision processes necessary in calculating half-widths and shifts and can be easily derived with high accuracy. Their well-behaved profiles, especially the rapid decrease of the magnitude, enables one to transform easily the dynamical information contained in them from the time domain to the frequency domain. More specifically, because these correlation functions are well time limited, their continuous Fourier transf...
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water vapor millimeter wave foreign continuum a lanczos calculation in the Coordinate Representation
2002Co-Authors: R H TippingAbstract:The water vapor foreign-continuum absorption has been calculated theoretically from first principles for the millimeter wave spectral region as a function of frequency f and temperature T. The calculations are made using the Lanczos algorithm by writing the resolvent operator (ω−L)−1 as continued fractions. In order to guarantee the quick convergence of the continued fractions, the line space of H2O is divided into two subspaces: one consists of the positive resonance lines and the other the negative ones. By ignoring the coupling between them, (ω−L)−1 is expressed as a sum of two continued fractions. The parameters appearing in each of the fractions are functions of the matrix elements of powers of the Liouville operator L between the starting vectors spanning the corresponding subspaces. In the present work, we have taken into account all powers of L up to 5. With the Coordinate Representation in which the orientations of the H2O–N2 collision pair are chosen as the basis functions in Hilbert space, the ...
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the density matrix of h2o n2 in the Coordinate Representation a monte carlo calculation of the far wing line shape
2000Co-Authors: R H TippingAbstract:The far-wing line shape theory within the binary collision and quasistatic framework has been developed using the Coordinate Representation. Within this formalism, the main computational task is the evaluation of multidimensional integrals whose variables are the orientational angles needed to specify the initial and final positions of the system during transition processes. Using standard methods, one is able to evaluate the seven-dimensional integrations required for linear molecular systems, or the seven-dimensional integrations for more complicated asymmetric-top (or symmetric-top) molecular systems whose interaction potential contains cyclic Coordinates. In order to obviate this latter restriction on the form of the interaction potential, a Monte Carlo method is used to evaluate the nine-dimensional integrations required for systems consisting of one asymmetric-top (or symmetric-top) and one linear molecule, such as H2O–N2. Combined with techniques developed previously to deal with sophisticated pote...
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the averaged density matrix in the Coordinate Representation application to the calculation of the far wing line shapes for h2o
1999Co-Authors: R H TippingAbstract:The far-wing line shape theory within the binary collision and quasistatic framework developed previously for linear molecules using the Coordinate Representation has been generalized to symmetric- and asymmetric-top molecular systems. However, due to more variables needed to specify the orientation of these complicated molecules, one has to evaluate multidimensional integrals with higher dimensionality and this would be intractable for practical calculations. In cases where the anisotropic interaction contains cyclic Coordinates, one can carry out the integration of the density matrix over these Coordinates analytically and obtain the “averaged” density matrix. This reduces the dimensionality of the multidimensional integrals and thus dramatically reduces the computational time necessary to obtain converged results. In addition, a new interpolation method that enables one to treat more realistic potential models has been formulated. Using these results, calculations for the band-average far-wing line sha...
Joachim Brand - One of the best experts on this subject based on the ideXlab platform.
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the single particle density matrix of a quantum bright soliton from the Coordinate bethe ansatz
2017Co-Authors: Alex Ayet, Joachim BrandAbstract:We present a novel approach for computing reduced density matrices for superpositions of eigenstates of a Bethe-ansatz solvable model by direct integration of the wave function in Coordinate Representation. A diagrammatic approach is developed to keep track of relevant terms and identify symmetries, which helps to reduce the number of terms that have to be evaluated numerically. As a first application we compute with modest numerical resources the single-particle density matrix and its eigenvalues including the condensate fraction for a quantum bright soliton with up to N = 10 bosons. The latter are constructed as superpositions of string-type Bethe-ansatz eigenstates of nonrelativistic bosons in one spatial dimension with attractive contact interaction. Upon delocalising the superposition in momentum space we find that the condensate fraction reaches maximum values larger than 97% with weak particle-number dependence in the range of particles studied. The presented approach is suitable for studying time-dependent problems and generalises to higher-order correlation functions.
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the single particle density matrix of a quantum bright soliton from the Coordinate bethe ansatz
2015Co-Authors: Alex Ayet, Joachim BrandAbstract:We present a novel approach for computing reduced density matrices for superpositions of eigenstates of a Bethe-ansatz solvable model by direct integration of the wave function in Coordinate Representation. A diagrammatic approach is developed to keep track of relevant terms and identify symmetries, which helps to reduce the number of terms that have to be evaluated numerically. As a first application we compute with modest numerical resources the single-particle density matrix and its eigenvalues including the condensate fraction for a quantum bright soliton with up to $N=10$ bosons. The latter are constructed as superpositions of string-type Bethe-ansatz eigenstates of nonrelativistic bosons in one spatial dimension with attractive contact interaction. Upon delocalising the superposition in momentum space we find that the condensate fraction reaches maximum values larger than 97\% in the range of particles studied. The presented approach is suitable for studying time-dependent problems and generalises to higher-order correlation functions.
Mikael Vejdemojohansson - One of the best experts on this subject based on the ideXlab platform.
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generalized penalty for circular Coordinate Representation
2020Co-Authors: Hengrui Luo, Alice Patania, Jisu Kim, Mikael VejdemojohanssonAbstract:Topological Data Analysis (TDA) provides novel approaches that allow us to analyze the geometrical shapes and topological structures of a dataset. As one important application, TDA can be used for data visualization and dimension reduction. We follow the framework of circular Coordinate Representation, which allows us to perform dimension reduction and visualization for high-dimensional datasets on a torus using persistent cohomology. In this paper, we propose a method to adapt the circular Coordinate framework to take into account sparsity in high-dimensional applications. We use a generalized penalty function instead of an $L_{2}$ penalty in the traditional circular Coordinate algorithm. We provide simulation experiments and real data analysis to support our claim that circular Coordinates with generalized penalty will accommodate the sparsity in high-dimensional datasets under different sampling schemes while preserving the topological structures.
Hengrui Luo - One of the best experts on this subject based on the ideXlab platform.
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generalized penalty for circular Coordinate Representation
2020Co-Authors: Hengrui Luo, Alice Patania, Jisu Kim, Mikael VejdemojohanssonAbstract:Topological Data Analysis (TDA) provides novel approaches that allow us to analyze the geometrical shapes and topological structures of a dataset. As one important application, TDA can be used for data visualization and dimension reduction. We follow the framework of circular Coordinate Representation, which allows us to perform dimension reduction and visualization for high-dimensional datasets on a torus using persistent cohomology. In this paper, we propose a method to adapt the circular Coordinate framework to take into account sparsity in high-dimensional applications. We use a generalized penalty function instead of an $L_{2}$ penalty in the traditional circular Coordinate algorithm. We provide simulation experiments and real data analysis to support our claim that circular Coordinates with generalized penalty will accommodate the sparsity in high-dimensional datasets under different sampling schemes while preserving the topological structures.