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Alexander Ulyanenkov - One of the best experts on this subject based on the ideXlab platform.

  • Non-perturbative Description of Quantum Systems
    Lecture Notes in Physics, 2015
    Co-Authors: Ilya Feranchuk, Alexey Ivanov, Alexander Ulyanenkov
    Abstract:

    This book introduces systematically the operator method for the solution of the Schrödinger equation. This method permits to describe the states of quantum systems in the entire range of parameters of Hamiltonian with a predefined accuracy. The operator method is unique compared with other non-perturbative methods due to its ability to deliver in Zeroth Approximation the uniformly suitable estimate for both ground and excited states of quantum system. The method has been generalized for the application to quantum statistics and quantum field theory.  In this book, the numerous applications of operator method for various physical systems are demonstrated. Simple models are used to illustrate the basic principles of the method which are further used for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures

Ilya Feranchuk - One of the best experts on this subject based on the ideXlab platform.

  • Non-perturbative Description of Quantum Systems
    Lecture Notes in Physics, 2015
    Co-Authors: Ilya Feranchuk, Alexey Ivanov, Alexander Ulyanenkov
    Abstract:

    This book introduces systematically the operator method for the solution of the Schrödinger equation. This method permits to describe the states of quantum systems in the entire range of parameters of Hamiltonian with a predefined accuracy. The operator method is unique compared with other non-perturbative methods due to its ability to deliver in Zeroth Approximation the uniformly suitable estimate for both ground and excited states of quantum system. The method has been generalized for the application to quantum statistics and quantum field theory.  In this book, the numerous applications of operator method for various physical systems are demonstrated. Simple models are used to illustrate the basic principles of the method which are further used for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures

Qi Guo - One of the best experts on this subject based on the ideXlab platform.

  • A perturbed (1 + 2)-dimensional soliton solution in nematic liquid crystals
    Journal of Optics A: Pure and Applied Optics, 2008
    Co-Authors: Hongyan Ren, Shigen Ouyang, Qi Guo, Longgui Cao
    Abstract:

    With the perturbation method, we present a (1 + 2)-dimensional ((1 + 2)D) soliton solution in the second Approximation in nematic liquid crystals (NLCs). Numerical simulations confirm the analytical soliton solution in the strongly nonlocal case, and show that the soliton solution in the second Approximation is more accurate than that in the Zeroth Approximation. It is found that, in an NLC, the critical power of a soliton accords with the result of numerical simulation, and the critical power of a strongly nonlocal soliton is in direct proportion to (wm/w) 2 ,w herewm is a characteristic length of the material response, and w is the soliton width.

  • Perturbative analysis of generally nonlocal spatial optical solitons.
    Physical Review E, 2006
    Co-Authors: Shigen Ouyang, Qi Guo
    Abstract:

    In analogy to a perturbed harmonic oscillator, we calculate the fundamental and some other higher order soliton solutions of the nonlocal nonlinear Sch\"odinger equation (NNLSE) in the second Approximation in the generally nonlocal case. Comparing with numerical simulations we show that soliton solutions in the second Approximation can describe the generally nonlocal soliton states of the NNLSE more exactly than that in the Zeroth Approximation. We show that for the nonlocal case of an exponential-decay type nonlocal response the Gaussian-function-like soliton solutions cannot describe the nonlocal soliton states exactly even in the strongly nonlocal case. The properties of such nonlocal solitons are investigated. In the strongly nonlocal limit, the soliton's power and phase constant are both in inverse proportion to the fourth power of its beam width for the nonlocal case of a Gaussian function type nonlocal response, and are both in inverse proportion to the third power of its beam width for the nonlocal case of an exponential-decay type nonlocal response.

Juan Antonio González - One of the best experts on this subject based on the ideXlab platform.

  • application of the Zeroth Approximation of the disquac model to cyclohexane n alkane mixtures using different combinatorial entropy terms
    Fluid Phase Equilibria, 1995
    Co-Authors: Juan Antonio González, José Carlos Cobos, Carlos Casanova, Garcia I De La Fuente, Ahmed Aitkaci
    Abstract:

    Abstract Literature data on molar excess functions, Gibbs energy GE, enthalpy HE, and heat capacity CpE, on activity coefficients γi∞, and partial molar excess enthalpies HiE,∞, at infinite dilution and on solid-liquid equilibria, SLE, of the cyclohexane + n-alkane mixtures are examined on the basis of the Zeroth Approximation of the DISQUAC group contribution model. The model provides a quite satisfactory description of the thermodynamic properties for the mixtures under study, although the symmetry of the calculated excess functions differs from the experimental one for systems containing long-chain n-alkanes. This may be due to the so-called Patterson effect. The influence of different combinatorial entropy terms (Flory-Huggins, Stavermann-Guggenheim or Kikic equations) on the prediction of thermodynamic properties such as GE, lnγi∞ and SLE is also examined. HE, CPE or HiE,∞ are represented by an interactional term only. The results calculated using the Flory-Huggins term are slightly better than those obtained applying the Stavermann-Guggenheim equation. Results based on the Kikic expression are poorer than those given by Flory-Huggins, particularly at high concentration of cyclohexane in systems containing the longer n-alkanes. So, the Kikic equation leads to poorer results for lnγ2∞ for these systems. SLE predictions are determined mainly by the physical constants of the pure compounds. So, essentially they do not depend on the combinatorial term used. A comparison between the Zeroth Approximation of DISQUAC and the modified UNIFAC model (Lyngby version) is also presented. Such comparison shows that both methods lead to similar results; although the latter gives poorer predictions on the temperature dependence of the excess functions than the former. On the other hand, the number of interaction parameters needed in modified UNIFAC is larger than when the Zeroth Approximation of DISQUAC is applied and, more important, they change with the number of carbon atoms of the n-alkane in a rather erratic way for the first members of the series. This makes the predictive task of UNIFAC more difficult.

  • Application of the Zeroth Approximation of the DISQUAC model to cyclohexane + n-alkane mixtures using different combinatorial entropy terms
    Fluid Phase Equilibria, 1995
    Co-Authors: Juan Antonio González, I. García De La Fuente, José Carlos Cobos, Carlos Casanova, A. Ait-kaci
    Abstract:

    Abstract Literature data on molar excess functions, Gibbs energy GE, enthalpy HE, and heat capacity CpE, on activity coefficients γi∞, and partial molar excess enthalpies HiE,∞, at infinite dilution and on solid-liquid equilibria, SLE, of the cyclohexane + n-alkane mixtures are examined on the basis of the Zeroth Approximation of the DISQUAC group contribution model. The model provides a quite satisfactory description of the thermodynamic properties for the mixtures under study, although the symmetry of the calculated excess functions differs from the experimental one for systems containing long-chain n-alkanes. This may be due to the so-called Patterson effect. The influence of different combinatorial entropy terms (Flory-Huggins, Stavermann-Guggenheim or Kikic equations) on the prediction of thermodynamic properties such as GE, lnγi∞ and SLE is also examined. HE, CPE or HiE,∞ are represented by an interactional term only. The results calculated using the Flory-Huggins term are slightly better than those obtained applying the Stavermann-Guggenheim equation. Results based on the Kikic expression are poorer than those given by Flory-Huggins, particularly at high concentration of cyclohexane in systems containing the longer n-alkanes. So, the Kikic equation leads to poorer results for lnγ2∞ for these systems. SLE predictions are determined mainly by the physical constants of the pure compounds. So, essentially they do not depend on the combinatorial term used. A comparison between the Zeroth Approximation of DISQUAC and the modified UNIFAC model (Lyngby version) is also presented. Such comparison shows that both methods lead to similar results; although the latter gives poorer predictions on the temperature dependence of the excess functions than the former. On the other hand, the number of interaction parameters needed in modified UNIFAC is larger than when the Zeroth Approximation of DISQUAC is applied and, more important, they change with the number of carbon atoms of the n-alkane in a rather erratic way for the first members of the series. This makes the predictive task of UNIFAC more difficult.

Alexey Ivanov - One of the best experts on this subject based on the ideXlab platform.

  • Non-perturbative Description of Quantum Systems
    Lecture Notes in Physics, 2015
    Co-Authors: Ilya Feranchuk, Alexey Ivanov, Alexander Ulyanenkov
    Abstract:

    This book introduces systematically the operator method for the solution of the Schrödinger equation. This method permits to describe the states of quantum systems in the entire range of parameters of Hamiltonian with a predefined accuracy. The operator method is unique compared with other non-perturbative methods due to its ability to deliver in Zeroth Approximation the uniformly suitable estimate for both ground and excited states of quantum system. The method has been generalized for the application to quantum statistics and quantum field theory.  In this book, the numerous applications of operator method for various physical systems are demonstrated. Simple models are used to illustrate the basic principles of the method which are further used for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures