A new picture of quantum tunneling in the real-time path integral from Lefschetz thimble calculations
Abstract It is well known that quantum tunneling can be described by instantons in the imaginary-time path integral formalism. However, its description in the real-time path integral formalism has been elusive. Here we establish a statement that quantum tunneling can be characterized in general by t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-09-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP09(2023)110 |
| _version_ | 1797371250713034752 |
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| author | Jun Nishimura Katsuta Sakai Atis Yosprakob |
| author_facet | Jun Nishimura Katsuta Sakai Atis Yosprakob |
| author_sort | Jun Nishimura |
| collection | DOAJ |
| description | Abstract It is well known that quantum tunneling can be described by instantons in the imaginary-time path integral formalism. However, its description in the real-time path integral formalism has been elusive. Here we establish a statement that quantum tunneling can be characterized in general by the contribution of complex saddle points, which can be identified by using the Picard-Lefschetz theory. We demonstrate this explicitly by performing Monte Carlo simulations of simple quantum mechanical systems, overcoming the sign problem by the generalized Lefschetz thimble method. We confirm numerically that the contribution of complex saddle points manifests itself in a complex “weak value” of the Hermitian coordinate operator x ̂ $$ \hat{x} $$ evaluated at time t, which is a physical quantity that can be measured by experiments in principle. We also discuss the transition to classical dynamics based on our picture. |
| first_indexed | 2024-03-08T18:17:12Z |
| format | Article |
| id | doaj.art-fbbd2471ff1b48d3beb00abc353871a0 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-08T18:17:12Z |
| publishDate | 2023-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-fbbd2471ff1b48d3beb00abc353871a02023-12-31T12:06:44ZengSpringerOpenJournal of High Energy Physics1029-84792023-09-012023913410.1007/JHEP09(2023)110A new picture of quantum tunneling in the real-time path integral from Lefschetz thimble calculationsJun Nishimura0Katsuta Sakai1Atis Yosprakob2KEK Theory Center, Institute of Particle and Nuclear Studies, High Energy Accelerator Research OrganizationKEK Theory Center, Institute of Particle and Nuclear Studies, High Energy Accelerator Research OrganizationKEK Theory Center, Institute of Particle and Nuclear Studies, High Energy Accelerator Research OrganizationAbstract It is well known that quantum tunneling can be described by instantons in the imaginary-time path integral formalism. However, its description in the real-time path integral formalism has been elusive. Here we establish a statement that quantum tunneling can be characterized in general by the contribution of complex saddle points, which can be identified by using the Picard-Lefschetz theory. We demonstrate this explicitly by performing Monte Carlo simulations of simple quantum mechanical systems, overcoming the sign problem by the generalized Lefschetz thimble method. We confirm numerically that the contribution of complex saddle points manifests itself in a complex “weak value” of the Hermitian coordinate operator x ̂ $$ \hat{x} $$ evaluated at time t, which is a physical quantity that can be measured by experiments in principle. We also discuss the transition to classical dynamics based on our picture.https://doi.org/10.1007/JHEP09(2023)110Nonperturbative EffectsSolitons Monopoles and InstantonsAlgorithms and Theoretical Developments |
| spellingShingle | Jun Nishimura Katsuta Sakai Atis Yosprakob A new picture of quantum tunneling in the real-time path integral from Lefschetz thimble calculations Journal of High Energy Physics Nonperturbative Effects Solitons Monopoles and Instantons Algorithms and Theoretical Developments |
| title | A new picture of quantum tunneling in the real-time path integral from Lefschetz thimble calculations |
| title_full | A new picture of quantum tunneling in the real-time path integral from Lefschetz thimble calculations |
| title_fullStr | A new picture of quantum tunneling in the real-time path integral from Lefschetz thimble calculations |
| title_full_unstemmed | A new picture of quantum tunneling in the real-time path integral from Lefschetz thimble calculations |
| title_short | A new picture of quantum tunneling in the real-time path integral from Lefschetz thimble calculations |
| title_sort | new picture of quantum tunneling in the real time path integral from lefschetz thimble calculations |
| topic | Nonperturbative Effects Solitons Monopoles and Instantons Algorithms and Theoretical Developments |
| url | https://doi.org/10.1007/JHEP09(2023)110 |
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