Open Quantum Dynamics: Memory Effects and Superactivation of Backflow of Information
We investigate the divisibility properties of the tensor products <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="sans-serif">Λ</mi><mi>t</mi&...
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MDPI AG
2023-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/1/37 |
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| author | Fabio Benatti Giovanni Nichele |
| author_facet | Fabio Benatti Giovanni Nichele |
| author_sort | Fabio Benatti |
| collection | DOAJ |
| description | We investigate the divisibility properties of the tensor products <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="sans-serif">Λ</mi><mi>t</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup><mo>⊗</mo><msubsup><mi mathvariant="sans-serif">Λ</mi><mi>t</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msubsup></mrow></semantics></math></inline-formula> of open quantum dynamics <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi mathvariant="sans-serif">Λ</mi><mi>t</mi><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></msubsup></semantics></math></inline-formula> with time-dependent generators. These dynamical maps emerge from a compound open system <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>S</mi><mn>1</mn></msub><mo>+</mo><msub><mi>S</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> that interacts with its own environment in such a way that memory effects remain when the environment is traced away. This study is motivated by the following intriguing effect: one can have Backflow of Information (BFI) from the environment to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>S</mi><mn>1</mn></msub><mo>+</mo><msub><mi>S</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> without the same phenomenon occurring for either <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mn>1</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mn>2</mn></msub></semantics></math></inline-formula>. We shall refer to this effect as the Superactivation of BFI (SBFI). |
| first_indexed | 2024-03-08T15:02:14Z |
| format | Article |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T15:02:14Z |
| publishDate | 2023-12-01 |
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| spelling | doaj.art-3f2326636e024e3685445dd3010da0d22024-01-10T15:03:22ZengMDPI AGMathematics2227-73902023-12-011213710.3390/math12010037Open Quantum Dynamics: Memory Effects and Superactivation of Backflow of InformationFabio Benatti0Giovanni Nichele1Department of Physics, University of Trieste, Strada Costiera 11, I-34151 Trieste, ItalyDepartment of Physics, University of Trieste, Strada Costiera 11, I-34151 Trieste, ItalyWe investigate the divisibility properties of the tensor products <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="sans-serif">Λ</mi><mi>t</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup><mo>⊗</mo><msubsup><mi mathvariant="sans-serif">Λ</mi><mi>t</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msubsup></mrow></semantics></math></inline-formula> of open quantum dynamics <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi mathvariant="sans-serif">Λ</mi><mi>t</mi><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></msubsup></semantics></math></inline-formula> with time-dependent generators. These dynamical maps emerge from a compound open system <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>S</mi><mn>1</mn></msub><mo>+</mo><msub><mi>S</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> that interacts with its own environment in such a way that memory effects remain when the environment is traced away. This study is motivated by the following intriguing effect: one can have Backflow of Information (BFI) from the environment to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>S</mi><mn>1</mn></msub><mo>+</mo><msub><mi>S</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> without the same phenomenon occurring for either <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mn>1</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mn>2</mn></msub></semantics></math></inline-formula>. We shall refer to this effect as the Superactivation of BFI (SBFI).https://www.mdpi.com/2227-7390/12/1/37non-MarkovianityBackflow of InformationP-divisibility |
| spellingShingle | Fabio Benatti Giovanni Nichele Open Quantum Dynamics: Memory Effects and Superactivation of Backflow of Information Mathematics non-Markovianity Backflow of Information P-divisibility |
| title | Open Quantum Dynamics: Memory Effects and Superactivation of Backflow of Information |
| title_full | Open Quantum Dynamics: Memory Effects and Superactivation of Backflow of Information |
| title_fullStr | Open Quantum Dynamics: Memory Effects and Superactivation of Backflow of Information |
| title_full_unstemmed | Open Quantum Dynamics: Memory Effects and Superactivation of Backflow of Information |
| title_short | Open Quantum Dynamics: Memory Effects and Superactivation of Backflow of Information |
| title_sort | open quantum dynamics memory effects and superactivation of backflow of information |
| topic | non-Markovianity Backflow of Information P-divisibility |
| url | https://www.mdpi.com/2227-7390/12/1/37 |
| work_keys_str_mv | AT fabiobenatti openquantumdynamicsmemoryeffectsandsuperactivationofbackflowofinformation AT giovanninichele openquantumdynamicsmemoryeffectsandsuperactivationofbackflowofinformation |