Search results for "Ansatz"
showing 10 items of 113 documents
Dipole soliton solution for the homogeneous high-order nonlinear Schrödinger equation with cubic–quintic–septic non-Kerr terms
2015
Abstract We consider a high-order nonlinear Schrodinger equation with third- and fourth-order dispersions, cubic–quintic–septic nonlinearities, self-steepening, and instantaneous Raman response. This equation models describes ultra-short optical pulse propagation in highly-nonlinear media. The ansatz solution of Choudhuri and Porsezian (in Ref. [16]) is adapted to investigate solutions composed of the product of bright and dark solitary waves. Parametric conditions for the existence of the derived soliton solutions are given and their stabilities are numerically discussed. These exact solutions provide insight into balance mechanisms between several high-order nonlinearities of different na…
From supersymmetric to non-supersymmetric black holes
2012
Methods similar to those used for obtaining supersymmetric black hole solutions can be employed to find also non-supersymmetric solutions. We briefly review some of them, with the emphasis on the non-extremal deformation ansatz of [1].
The band structure of double excited states for a linear chain
2000
Abstract The energy band structure in the case of double excited states of finite spin systems (s= 1 2 ) has been investigated. A geometrical construction based on the Bethe Ansatz method for determining eigenstates has been proposed. The formula for energy spectrum in the center and at the border of Brillouin zone has been obtained. Classification of energy bands has been elaborated on and approximated dispersion law for bounded states given. Some problems with application of the Bethe Ansatz in the case of finite system has been pointed out.
The inhomogeneous phase of dense skyrmion matter
2019
It was predicted qualitatively in ref.[1] that skyrmion matter at low density is stable in an inhomogeneous phase where skyrmions condensate into lumps while the remaining space is mostly empty. The aim of this paper is to proof quantitatively this prediction. In order to construct an inhomogeneous medium we distort the original FCC crystal to produce a phase of planar structures made of skyrmions. We implement mathematically these planar structures by means of the 't Hooft instanton solution using the Atiyah-Manton ansatz. The results of our calculation of the average density and energy confirm the prediction suggesting that the phase diagram of the dense skyrmion matter is a lot more comp…
Linear-response theory for Mukherjee's multireference coupled-cluster method: Static and dynamic polarizabilities
2012
The formalism of response theory is applied to derive expressions for static and dynamic polarizabilities within the state-specific multireference coupled-cluster theory suggested by Mukherjee and co-workers (Mk-MRCC) [J. Chem. Phys. 110, 6171 (1998)]. We show that the redundancy problem inherent to Mk-MRCC theory gives rise to spurious poles in the Mk-MRCC response functions, which hampers the reliable calculation of dynamic polarizabilities. Furthermore, we demonstrate that in the case of a symmetry-breaking perturbation a working response theory is obtained only if certain internal excitations are included in the responses of the cluster amplitudes. Exemplary calculations within the sing…
Insights into the orbital invariance problem in state-specific multireference coupled cluster theory.
2010
In this communication we report the results of our studies on the orbital invariance properties of the state-specific multireference coupled cluster approach suggested by Mukherjee and co-workers (Mk-MRCC). In particular, we have gathered numerical evidence to show that even when the linear excitation manifold is modified in order to span the same space for each reference, the resulting method is not orbital invariant. In order to test this conjecture we have proposed a new truncation scheme (Mk-MRCCSDtq) which, in addition to full single and double excitations, contains partial triple and quadruple excitations. For a reference space generated by all possible combinations of two electrons i…
Spin-restricted coupled-cluster theory with triple excitations
2002
Working equations for a spin-restricted coupled-cluster (SR-CC) ansatz with full inclusion of triple excitations are presented. The equations have been derived using a new formulation of the SR-CC theory that is equivalent to the original one but much easier processed and also provides a new interpretation of the underlying concepts of the SR-CC approach. Test calculations with a preliminary SR-CC singles, doubles, triples (SR-CCSDT) implementation indicate that spin-restriction has a rather small effect on the computed energies and that the effects are—as expected—less pronounced than in the case of the CC singles, doubles approximation. The corresponding partially spin-adapted scheme turn…
Explicitly correlated connected triple excitations in coupled-cluster theory.
2009
A way to incorporate explicit electron correlation into connected triple excitations in coupled-cluster theory is proposed. The new ansatz is applied to the coupled-cluster singles and doubles model with noniterative triple excitations [CCSD(T)] and does not introduce any further sets of equations to be solved. A first implementation using automated generation and string-based evaluation of the explicit expressions is reported. The results demonstrate that the ansatz significantly enhances the basis set convergence of the noniterative triple excitation correction and thus improves upon previous approaches to explicitly correlated CCSD(T).
Explicitly correlated coupled-cluster theory using cusp conditions. I. Perturbation analysis of coupled-cluster singles and doubles (CCSD-F12)
2010
Geminal functions based on Slater-type correlation factors and fixed expansion coefficients, determined by cusp conditions, have in recent years been forwarded as an efficient and numerically stable method for introducing explicit electron correlation into coupled-cluster theory. In this work, we analyze the equations of explicitly correlated coupled-cluster singles and doubles (CCSD-F12) theory and introduce an ordering scheme based on perturbation theory which can be used to characterize and understand the various approximations found in the literature. Numerical results for a test set of 29 molecules support our analysis and give additional insight. In particular, our results help ration…
Explicitly correlated coupled-cluster theory using cusp conditions. II. Treatment of connected triple excitations.
2010
The coupled-cluster singles and doubles method augmented with single Slater-type correlation factors (CCSD-F12) determined by the cusp conditions (also denoted as SP ansatz) yields results close to the basis set limit with only small overhead compared to conventional CCSD. Quantitative calculations on many-electron systems, however, require to include the effect of connected triple excitations at least. In this contribution, the recently proposed [A. Köhn, J. Chem. Phys. 130, 131101 (2009)] extended SP ansatz and its application to the noniterative triples correction CCSD(T) is reviewed. The approach allows to include explicit correlation into connected triple excitations without introducin…