Variational approach to N -body interactions in finite volume

Guo, Peng; Döring, Michael; Szczepaniak, Adam P.

doi:10.1103/PhysRevD.98.094502

Title: Variational approach to $N$ -body interactions in finite volume

Abstract

Here, we explore variational approach to the finite-volume $N$ -body problem. The general formalism for $N$ non-relativistic spinless particles interacting with periodic pair-wise potentials yields $N$ -body secular equations. The solutions depend on the infinite-volume $N$ -body wave functions. Given that the infinite-volume $N$ -body dynamics may be solved by the standard Faddeev approach, the variational $N$ -body formalism can provide a convenient numerical framework for finding discrete energy spectra in periodic lattice structures.

Authors:: Guo, Peng; Döring, Michael; Szczepaniak, Adam P.

Publication Date:: Thu Nov 08 00:00:00 EST 2018

Research Org.:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP)

OSTI Identifier:: 1481326

Alternate Identifier(s):: OSTI ID: 1481736

Report Number(s):: JLAB-THY-18-2837; DOE/OR/23177-4556; arXiv:1810.01261
Journal ID: ISSN 2470-0010; PRVDAQ; 094502

Grant/Contract Number:: AC05-06OR23177; FG02-87ER40365; PHY-1748958; PHY-1415459; PHY-1452055

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 98 Journal Issue: 9; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Guo, Peng, Döring, Michael, and Szczepaniak, Adam P. Variational approach to N -body interactions in finite volume.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevD.98.094502.

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                    Guo, Peng, Döring, Michael, & Szczepaniak, Adam P. Variational approach to N -body interactions in finite volume.  United States.  https://doi.org/10.1103/PhysRevD.98.094502

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                    Guo, Peng, Döring, Michael, and Szczepaniak, Adam P. Thu .  
"Variational approach to N -body interactions in finite volume".  United States.  https://doi.org/10.1103/PhysRevD.98.094502.

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@article{osti_1481326,

  title        = {Variational approach to N -body interactions in finite volume},

  author       = {Guo, Peng and Döring, Michael and Szczepaniak, Adam P.},

  abstractNote = {Here, we explore variational approach to the finite-volume N-body problem. The general formalism for N non-relativistic spinless particles interacting with periodic pair-wise potentials yields N-body secular equations. The solutions depend on the infinite-volume N-body wave functions. Given that the infinite-volume N-body dynamics may be solved by the standard Faddeev approach, the variational N-body formalism can provide a convenient numerical framework for finding discrete energy spectra in periodic lattice structures.},

  doi          = {10.1103/PhysRevD.98.094502},

  journal      = {Physical Review D},

  number       = 9,

  volume       = 98,

  place        = {United States},

  year         = {Thu Nov 08 00:00:00 EST 2018},

  month        = {Thu Nov 08 00:00:00 EST 2018}

}

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Works referencing / citing this record:

Lattice model of heavy-light three-body system
journal, February 2020

Guo, Peng; Döring, Michael
Physical Review D, Vol. 101, Issue 3
DOI: 10.1103/physrevd.101.034501

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Title: Variational approach to N -body interactions in finite volume

Abstract

Citation Formats

Three-particle quantization condition in a finite volume: 1. The role of the three-particle force journal, September 2017

Connecting physical resonant amplitudes and lattice QCD journal, June 2016

Three-body final state interaction in η→ 3π updated journal, August 2017

Spectrum of Three-Body Bound States in a Finite Volume journal, March 2015

Coupled-channel scattering in 1 + 1 dimensional lattice model journal, July 2013

Principles of the Theory of Solids book, January 1972

Coupled-channel scattering on a torus journal, July 2013

Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles journal, April 2017

Signatures of few-body resonances in finite volume journal, September 2018

Analytic continuation of the Pasquier inversion representation of the Khuri-Treiman equation journal, April 2015

n -boson energies at finite volume and three-boson interactions journal, October 2007

Solution of the Schrödinger Equation in Periodic Lattices with an Application to Metallic Lithium journal, June 1954

Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV journal, April 2011

Three-boson problem at low energy and implications for dilute Bose-Einstein condensates journal, July 2008

Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data journal, October 2017

Variational Methods in Nuclear Collision Problems journal, December 1948

A coupled-channel formalism for three-body final state interaction journal, March 2016

Chiral extrapolations of the ρ ( 770 ) meson in N f = 2 + 1 lattice QCD simulations journal, August 2017

Highly Excited and Exotic Meson Spectrum from Dynamical Lattice QCD journal, December 2009

Relativistic, model-independent, three-particle quantization condition journal, December 2014

Erratum: Spectrum of Three-Body Bound States in a Finite Volume [Phys. Rev. Lett. 114 , 091602 (2015)] journal, August 2016

Three particles in a finite volume journal, May 2012

A solvable three-body model in finite volume journal, November 2017

Three-particle scattering amplitudes from a finite volume formalism journal, May 2013

Coupled π π , K K ¯ scattering in P -wave and the ρ resonance from lattice QCD journal, November 2015

QCD with two light dynamical chirally improved quarks: Baryons journal, April 2013

Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude journal, December 2015

Pion-nucleon scattering in the Roper channel from lattice QCD journal, January 2017

Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD journal, July 2018

Three particles in a finite volume: The breakdown of spherical symmetry journal, July 2012

Multipion states in lattice QCD and the charged-pion condensate journal, July 2008

Dispersive analysis of ω→3π and ϕ→3π decays journal, May 2012

Excited state baryon spectroscopy from lattice QCD journal, October 2011

Three-body unitarity in the finite volume journal, December 2017

Pion-Pion Scattering and K ± → 3 π Decay journal, August 1960

Khuri-Treiman Representation and Perturbation Theory journal, December 1963

Numerical approach for finite volume three-body interaction journal, January 2018

Two- and three-body interactions in $$\varphi ^4$$ φ 4 theory from lattice simulations journal, October 2018

Three-Body Unitarity and Khuri-Treiman Amplitudes journal, December 1966

Extraction of isoscalar π π phase shifts from lattice QCD journal, July 2018

Numerical study of the relativistic three-body quantization condition in the isotropic approximation journal, July 2018

Dispersive approaches for three-particle final state interaction journal, October 2015

Two-particle states on a torus and their relation to the scattering matrix journal, May 1991

Three-body spectrum in a finite volume: The role of cubic symmetry journal, June 2018

Final-state interactions among three particles journal, January 1965

Energy of n identical bosons in a finite volume at O ( L − 7 ) journal, March 2008

Dispersive analysis of ω / ϕ → 3 π , π γ * journal, May 2015

Threshold expansion of the three-particle quantization condition journal, May 2016

Three-body unitarity with isobars revisited journal, September 2017

From deep inelastic scattering to heavy-flavor semileptonic decays: Total rates into multihadron final states from lattice QCD journal, November 2017

Dispersion Theory of Three-Body Production and Decay Processes journal, February 1967

Three-body final state interaction in η → 3 π journal, September 2015

Volume dependence of N -body bound states journal, April 2018

Multipion Systems in Lattice QCD and the Three-Pion Interaction journal, February 2008

Lattice model of heavy-light three-body system journal, February 2020

Title: Variational approach to $N$ -body interactions in finite volume

Three-particle quantization condition in a finite volume: 1. The role of the three-particle force
journal, September 2017

Connecting physical resonant amplitudes and lattice QCD
journal, June 2016

Three-body final state interaction in η→ 3π updated
journal, August 2017

Spectrum of Three-Body Bound States in a Finite Volume
journal, March 2015

Coupled-channel scattering in $1 + 1$ dimensional lattice model
journal, July 2013

Principles of the Theory of Solids
book, January 1972

Coupled-channel scattering on a torus
journal, July 2013

Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles
journal, April 2017

Signatures of few-body resonances in finite volume
journal, September 2018

Analytic continuation of the Pasquier inversion representation of the Khuri-Treiman equation
journal, April 2015

$n$ -boson energies at finite volume and three-boson interactions
journal, October 2007

Solution of the Schrödinger Equation in Periodic Lattices with an Application to Metallic Lithium
journal, June 1954

Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV
journal, April 2011

Three-boson problem at low energy and implications for dilute Bose-Einstein condensates
journal, July 2008

Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data
journal, October 2017

Variational Methods in Nuclear Collision Problems
journal, December 1948

A coupled-channel formalism for three-body final state interaction
journal, March 2016

Chiral extrapolations of the $ρ (770)$ meson in $N_{f} = 2 + 1$ lattice QCD simulations
journal, August 2017

Highly Excited and Exotic Meson Spectrum from Dynamical Lattice QCD
journal, December 2009

Relativistic, model-independent, three-particle quantization condition
journal, December 2014

Erratum: Spectrum of Three-Body Bound States in a Finite Volume [Phys. Rev. Lett. 114 , 091602 (2015)]
journal, August 2016

Three particles in a finite volume
journal, May 2012

A solvable three-body model in finite volume
journal, November 2017

Three-particle scattering amplitudes from a finite volume formalism
journal, May 2013

Coupled $π π$ , $K \bar{K}$ scattering in $P$ -wave and the $ρ$ resonance from lattice QCD
journal, November 2015

QCD with two light dynamical chirally improved quarks: Baryons
journal, April 2013

Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
journal, December 2015

Pion-nucleon scattering in the Roper channel from lattice QCD
journal, January 2017

Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD
journal, July 2018

Three particles in a finite volume: The breakdown of spherical symmetry
journal, July 2012

Multipion states in lattice QCD and the charged-pion condensate
journal, July 2008

Dispersive analysis of ω→3π and ϕ→3π decays
journal, May 2012

Excited state baryon spectroscopy from lattice QCD
journal, October 2011

Three-body unitarity in the finite volume
journal, December 2017

Pion-Pion Scattering and $K^{\pm} \to 3 π$ Decay
journal, August 1960

Khuri-Treiman Representation and Perturbation Theory
journal, December 1963

Numerical approach for finite volume three-body interaction
journal, January 2018

Two- and three-body interactions in $$\varphi ^4$$ φ 4 theory from lattice simulations
journal, October 2018

Three-Body Unitarity and Khuri-Treiman Amplitudes
journal, December 1966

Extraction of isoscalar $π π$ phase shifts from lattice QCD
journal, July 2018

Numerical study of the relativistic three-body quantization condition in the isotropic approximation
journal, July 2018

Dispersive approaches for three-particle final state interaction
journal, October 2015

Two-particle states on a torus and their relation to the scattering matrix
journal, May 1991

Three-body spectrum in a finite volume: The role of cubic symmetry
journal, June 2018

Final-state interactions among three particles
journal, January 1965

Energy of $n$ identical bosons in a finite volume at $O (L^{- 7})$
journal, March 2008

Dispersive analysis of $ω / ϕ \to 3 π, π γ^{*}$
journal, May 2015

Threshold expansion of the three-particle quantization condition
journal, May 2016

Three-body unitarity with isobars revisited
journal, September 2017

From deep inelastic scattering to heavy-flavor semileptonic decays: Total rates into multihadron final states from lattice QCD
journal, November 2017

Dispersion Theory of Three-Body Production and Decay Processes
journal, February 1967

Three-body final state interaction in $η \to 3 π$
journal, September 2015

Volume dependence of N -body bound states
journal, April 2018

Multipion Systems in Lattice QCD and the Three-Pion Interaction
journal, February 2008

Lattice model of heavy-light three-body system
journal, February 2020