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Flament E, Impens F, Guéry-Odelin D. Emulating Non-Hermitian Dynamics in a Finite Non-Dissipative Quantum System. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1256. [PMID: 37761555 PMCID: PMC10528010 DOI: 10.3390/e25091256] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2023] [Revised: 08/18/2023] [Accepted: 08/21/2023] [Indexed: 09/29/2023]
Abstract
We discuss the emulation of non-Hermitian dynamics during a given time window using a low-dimensional quantum system coupled to a finite set of equidistant discrete states acting as an effective continuum. We first emulate the decay of an unstable state and map the quasi-continuum parameters, enabling the precise approximation of non-Hermitian dynamics. The limitations of this model, including in particular short- and long-time deviations, are extensively discussed. We then consider a driven two-level system and establish criteria for non-Hermitian dynamics emulation with a finite quasi-continuum. We quantitatively analyze the signatures of the finiteness of the effective continuum, addressing the possible emergence of non-Markovian behavior during the time interval considered. Finally, we investigate the emulation of dissipative dynamics using a finite quasi-continuum with a tailored density of states. We show through the example of a two-level system that such a continuum can reproduce non-Hermitian dynamics more efficiently than the usual equidistant quasi-continuum model.
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Affiliation(s)
- Eloi Flament
- Laboratoire Collisions, Agrégats, Réactivité, FeRMI, Université de Toulouse, CNRS, UPS, 118 Route de Narbonne, 31062 Toulouse, France;
| | - François Impens
- Instituto de Física, Universidade Federal do Rio de Janeiro, Rio de Janeiro 21941-972, RJ, Brazil;
| | - David Guéry-Odelin
- Laboratoire Collisions, Agrégats, Réactivité, FeRMI, Université de Toulouse, CNRS, UPS, 118 Route de Narbonne, 31062 Toulouse, France;
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Máthé L, Kovács-Krausz Z, Botiz I, Grosu I, El Anouz K, El Allati A, Zârbo LP. Phonon-Assisted Tunneling through Quantum Dot Systems Connected to Majorana Bound States. NANOMATERIALS (BASEL, SWITZERLAND) 2023; 13:1616. [PMID: 37242032 PMCID: PMC10222149 DOI: 10.3390/nano13101616] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2023] [Revised: 05/05/2023] [Accepted: 05/08/2023] [Indexed: 05/28/2023]
Abstract
We theoretically analyze phonon-assisted tunneling transport in a quantum dot side connected to a Majorana bound state in a topological superconducting nanowire. We investigate the behavior of the current through the dot, for a range of experimentally relevant parameters, in the presence of one long-wave optical phonon mode. We consider the current-gate voltage, the current-bias voltage and the current-dot-Majorana coupling characteristics under the influence of the electron-phonon coupling. In the absence of electron-phonon interaction, the Majorana bound states suppress the current when the gate voltage matches the Fermi level, but the increase in the bias voltage counteracts this effect. In the presence of electron-phonon coupling, the current behaves similarly as a function of the renormalized gate voltage. As an added feature at large bias voltages, it presents a dip or a plateau, depending on the size of the dot-Majorana coupling. Lastly, we show that the currents are most sensitive to, and depend non-trivially on the parameters of the Majorana circuit element, in the regime of low temperatures combined with low voltages. Our results provide insights into the complex physics of quantum dot devices used to probe Majorana bound states.
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Affiliation(s)
- Levente Máthé
- Center of Advanced Research and Technologies for Alternative Energies, National Institute for R & D of Isotopic and Molecular Technologies, 67-103 Donat, 400293 Cluj-Napoca, Romania;
- Faculty of Physics, Babeș-Bolyai University, 1 Kogălniceanu, 400084 Cluj-Napoca, Romania; (I.B.); (I.G.)
| | - Zoltán Kovács-Krausz
- Department of Physics, Institute of Physics, Budapest University of Technology and Economics, Műegyetem rkp. 3, H-1111 Budapest, Hungary;
| | - Ioan Botiz
- Faculty of Physics, Babeș-Bolyai University, 1 Kogălniceanu, 400084 Cluj-Napoca, Romania; (I.B.); (I.G.)
- Interdisciplinary Research Institute in Bio-Nano-Sciences, Babeș-Bolyai University, 42 Treboniu Laurian, 400271 Cluj-Napoca, Romania
| | - Ioan Grosu
- Faculty of Physics, Babeș-Bolyai University, 1 Kogălniceanu, 400084 Cluj-Napoca, Romania; (I.B.); (I.G.)
| | - Khadija El Anouz
- Laboratory of R & D in Engineering Sciences, Faculty of Sciences and Techniques Al-Hoceima, Abdelmalek Essaadi University, Tetouan 93000, Morocco; (K.E.A.); (A.E.A.)
| | - Abderrahim El Allati
- Laboratory of R & D in Engineering Sciences, Faculty of Sciences and Techniques Al-Hoceima, Abdelmalek Essaadi University, Tetouan 93000, Morocco; (K.E.A.); (A.E.A.)
| | - Liviu P. Zârbo
- Center of Advanced Research and Technologies for Alternative Energies, National Institute for R & D of Isotopic and Molecular Technologies, 67-103 Donat, 400293 Cluj-Napoca, Romania;
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