# 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:

- California State Univ., Bakersfield, CA (United States); Univ. of California, Santa Barbara, CA (United States)
- The George Washington Univ., Washington, DC (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Indiana Univ., Bloomington, IN (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- 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

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

- Resource Type:
- Journal Article: Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 98; Journal Issue: 9; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- 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.

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

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

```
@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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Publisher's Version of Record at 10.1103/PhysRevD.98.094502

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