Erratum: Rayleigh-Schrödinger perturbation theory based on Gaussian wave functional approach [Phys. Rev. D<b>64</b>, 025006 (2001)]

Lu, Wen-Fa; Kim, Chul Koo; Yee, Jae Hyung; Nahm, Kyun

doi:10.1103/physrevd.66.069901

Cited by 9 publications

(17 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[2](iv,v), and yields the result in Ref. [6] [2](ii,iii) if one chooses to use the same constraint on ϕ as in Ref. [2](ii).…”

Section: Introductionmentioning

confidence: 59%

“…(3) in Ref. [6], is dependent on x. Then, for the above vacuum, the annihilation and creation operators can respectively be constructed as…”

Section: A Free Field Theory With An External Sourcementioning

confidence: 99%

“…They were used to give the loop or Gaussian EP and propose those schemes in Refs. [2,6]. Yet another equivalent definition of the EP is given through the vacuum energy functional of an external source obtained by solving the relevant functional Schrödinger equation [5].…”

Section: Optimized Rayleigh-schrödinger Expansion For the Effectmentioning

confidence: 99%

See 2 more Smart Citations

Optimized Rayleigh–Schrödinger expansion of the effective potential

2002

Self Cite

View full text Add to dashboard Cite

An optimized Rayleigh-Schrödinger expansion scheme of solving the functional Schrödinger equation with an external source is proposed to calculate the effective potential beyond the Gaussian approximation. For a scalar field theory whose potential function has a Fourier representation in a sense of tempered distributions, we obtain the effective potential up to the second order, and show that the first-order result is just the Gaussian effective potential. Its application to the λφ 4 field theory yields the same post-Gaussian effective potential as obtained in the functional integral formalism.

show abstract

“…[2](iv,v), and yields the result in Ref. [6] [2](ii,iii) if one chooses to use the same constraint on ϕ as in Ref. [2](ii).…”

Section: Introductionmentioning

confidence: 59%

“…(3) in Ref. [6], is dependent on x. Then, for the above vacuum, the annihilation and creation operators can respectively be constructed as…”

Section: A Free Field Theory With An External Sourcementioning

confidence: 99%

See 1 more Smart Citation

Optimized Rayleigh–Schrödinger expansion of the effective potential

2002

Self Cite

View full text Add to dashboard Cite

show abstract

“…Some other perturbation methods appeared in 1970's and 1980's, such as the non-parameter expansion method [10], and the linear δ expansion method (LDE) [11,12,13,14,15,16,17], have the same idea as implied in the OPT. These methods, especially the LDE, have found successful applications in many physical contexts during the past three decades.…”

mentioning

confidence: 99%

Nonsensitive Nonlinear Homotopy Approach

Gao

Tang

Sen-Yue

2009

Chinese Phys. Lett.

View full text Add to dashboard Cite

Generally, natural scientific problems are so complicated that one has to establish some effective perturbation or nonperturbation theories with respect to some associated ideal models. In this Letter, a new theory that combines perturbation and nonperturbation is constructed. An artificial nonlinear homotopy parameter plays the role of a perturbation parameter, while other artificial nonlinear parameters, of which the original problems are independent, introduced in the nonlinear homotopy models are nonperturbatively determined by means of a principle minimal sensitivity. The method is demonstrated through several quantum anharmonic oscillators and a non-hermitian parity-time symmetric Hamiltonian system. In fact, the framework of the theory is rather general that can be applied to a broad range of natural phenomena. Possible applications to condensed matter physics, matter wave systems, and nonlinear optics are briefly discussed.PACS numbers: 02.90.+p, 42.65.Tg In general, natural scientific problems cannot be exactly described by some analytical expressions. What scientists usually do is just first to establish some ideal models, and then to consider additional effects by use of some perturbation and nonperturbation theories.Perturbation theories (PTs) [1, 2] already have quite a long and interesting history in physics. They have been used to explore physical systems that can not be solved exactly but with a small parameter. Though great challenges are coming from the blooming numerical calculation methods, PTs are still showing their great power in solving various problems. For instance, perturbation theories have been used to study the spectrum of non-hermitian parity-time (PT ) symmetric Hamiltonian [3], the structure of trapped Bose-Einstein condensates (BECs) with long-range anisotropic dipolar interactions [4], and the interacting fermions in two-dimensions [5]. Besides, the fundamental ideas of PTs have been utilized to study some models in quantum computation theory (QCT). Techniques based on PTs have also been applied to engineer interesting Hamiltonians, whereby the outstanding perturbation theory gadgets (PTGs) technique was developed [6,7]. A short but incisive review of the history of PT and its new development in quantum manybody theory, quantum computation and quantum complexity theory has been given recently by M. M. Wolf [8].On the other hand, nonperturbation theories (NPTs) have been established to solve real scientific problems with the lack of a small parameter that acts as a perturbation parameter. In this case, some parameters will be artificially introduced as some formal perturbation parameters and/or nonperturbation parameters. Usually, one of these artificial perturbation parameters have to be set finite, say, the unit one, while others will be determined in some nonperturbative ways such as some types of optimized approaches.Considering the fact that physical quantities should be independent of any particular perturbation and/or nonperturbation method used to calculate them, Ste...

show abstract

“…Further improvements beyond the Gaussian approxiamtion have been investigated mostly in two directions. One is to try it with non-Gaussian wavefunctionals [16,17], and the other is to perform appropriate expansions based on Gaussian trial wavefunctional [18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Rayleigh-Schr�dinger-Goldstone variational perturbation theory for many Fermion systems

You

Kim

2005

Eur. Phys. J. B

Self Cite

View full text Add to dashboard Cite

Abstract. We present a Rayleigh-Schrödinger-Goldstone perturbation formalism for many fermion systems. Based on this formalism, variational perturbation scheme which goes beyond the Gaussian approximation is developed. In order to go beyond the Gaussian approximation, we identify a parent Hamiltonian which has an effective Gaussian vacuum as a variational solution and carry out further perturbation with respect to the renormalized interaction using Goldstone's expansion. Perturbation rules for the ground state wavefunctional and energy are found. Useful commuting relations between operators and the Gaussian wavefunctional are also found, which could reduce the calculational efforts substantially. As examples, we calculate the first order correction to the Gaussian wavefunctional and the second order correction to the ground state of an electron gas system with the Yukawa-type interaction. Rayleigh-Schrödinger-Goldstone variational perturbation theory for many fermion systems2

show abstract

Erratum: Rayleigh-Schrödinger perturbation theory based on Gaussian wave functional approach [Phys. Rev. D64, 025006 (2001)]

Abstract: A Rayleigh-Schrödinger perturbation theory based on the Gaussian wavefunctional is constructed. The method can be used for calculating the energies of both the vacuum and the excited states. A model calculation is carried out for the vacuum state of the λφ 4 field theory.

Cited by 9 publications

References 20 publications

Optimized Rayleigh–Schrödinger expansion of the effective potential

Optimized Rayleigh–Schrödinger expansion of the effective potential

Nonsensitive Nonlinear Homotopy Approach

Rayleigh-Schr�dinger-Goldstone variational perturbation theory for many Fermion systems

Contact Info

Product

Resources

About