Transseries for the ground state density and generalized Bloch equation: Double-well potential case

Shuryak, E.; Turbiner, A. V.

doi:10.1103/PhysRevD.98.105007

Title: Transseries for the ground state density and generalized Bloch equation: Double-well potential case

Abstract

Based on the generalized Bloch equation, the transseries expansion for the phase (exponent) of the ground state density for double-well potential is constructed. It is shown that the leading and next-to-leading terms in semiclassical expansion are still defined by the flucton trajectory (its classical action) and quadratic fluctuations (the determinant), respectively, while the next-to-next-to-leading term (at large distances) is of nonperturbative nature. It comes from the fact that all flucton classical trajectories modified by multi-instanton, instanton–anti-instanton additions lead to the same classical action behavior at large distances. This correction is proportional to sum of all leading instanton contributions to energy gap.

Authors:: Shuryak, E.; Turbiner, A. V.

Publication Date:: Fri Nov 16 00:00:00 EST 2018

Research Org.:: Stony Brook Univ., NY (United States); State Univ. of New York (SUNY), Albany, NY (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1482424

Alternate Identifier(s):: OSTI ID: 1610122

Grant/Contract Number:: FG02-88ER40388

Resource Type:: Published Article

Journal Name:: Physical Review. D.

Additional Journal Information:: Journal Name: Physical Review. D. Journal Volume: 98 Journal Issue: 10; 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; astronomy & astrophysics; physics; nonperturbative effects in field theory; path integrals; perturbation theory

Citation Formats


                    Shuryak, E., and Turbiner, A. V. Transseries for the ground state density and generalized Bloch equation: Double-well potential case.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevD.98.105007.

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                    Shuryak, E., & Turbiner, A. V. Transseries for the ground state density and generalized Bloch equation: Double-well potential case.  United States.  https://doi.org/10.1103/PhysRevD.98.105007

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                    Shuryak, E., and Turbiner, A. V. Fri .  
"Transseries for the ground state density and generalized Bloch equation: Double-well potential case".  United States.  https://doi.org/10.1103/PhysRevD.98.105007.

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@article{osti_1482424,

  title        = {Transseries for the ground state density and generalized Bloch equation: Double-well potential case},

  author       = {Shuryak, E. and Turbiner, A. V.},

  abstractNote = {Based on the generalized Bloch equation, the transseries expansion for the phase (exponent) of the ground state density for double-well potential is constructed. It is shown that the leading and next-to-leading terms in semiclassical expansion are still defined by the flucton trajectory (its classical action) and quadratic fluctuations (the determinant), respectively, while the next-to-next-to-leading term (at large distances) is of nonperturbative nature. It comes from the fact that all flucton classical trajectories modified by multi-instanton, instanton–anti-instanton additions lead to the same classical action behavior at large distances. This correction is proportional to sum of all leading instanton contributions to energy gap.},

  doi          = {10.1103/PhysRevD.98.105007},

  journal      = {Physical Review. D.},

  number       = 10,

  volume       = 98,

  place        = {United States},

  year         = {Fri Nov 16 00:00:00 EST 2018},

  month        = {Fri Nov 16 00:00:00 EST 2018}

}

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Cited by: 6 works

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Figures / Tables:

FIG. 1: The flucton path (left) and flucton-plus-instanton path (right) both pass from some generic point x₀ and relax to one or two degenerate minima, to ensure the finiteness of the action.

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Works referenced in this record:

Multi-instantons and exact results II: specific cases, higher-order effects, and numerical calculations
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Zinn-Justin, Jean; Jentschura, Ulrich D.
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Escobar-Ruiz, M. A.; Shuryak, E.; Turbiner, A. V.
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The eigenvalue spectrum in quantum mechanics and the nonlinearization procedure
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Multi-instanton contributions in quantum mechanics
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Escobar-Ruiz, M. A.; Shuryak, E.; Turbiner, A. V.
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Three-loop correction to the instanton density. I. The quartic double well potential
journal, July 2015

Escobar-Ruiz, M. A.; Shuryak, E.; Turbiner, A. V.
Physical Review D, Vol. 92, Issue 2
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Uniform WKB, multi-instantons, and resurgent trans-series
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Dunne, Gerald V.; Ünsal, Mithat
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journal, August 2017

Escobar-Ruiz, M. A.; Shuryak, E.; Turbiner, A. V.
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Two-loop correction to the instanton density for the double well potential
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Quantum and thermal fluctuations in quantum mechanics and field theories from a new version of semiclassical theory
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Escobar-Ruiz, M. A.; Shuryak, E.; Turbiner, A. V.
Physical Review D, Vol. 93, Issue 10
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Figures / Tables found in this record:

FIG. 1 (p. 2)

Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

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Similar Records

Title: Transseries for the ground state density and generalized Bloch equation: Double-well potential case

Abstract

Citation Formats

Figures / Tables:

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