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Coherence in Open Quantum Systems

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: closed (15 December 2018) | Viewed by 19846

Special Issue Editors

Department of Applied Sciences and Mathematics, College of Arts and Sciences, Abu Dhabi University, Abu Dhabi, UAE
Interests: quantum optics; quantum information; open quantum systems; nonlinear dynamics; quantum mechanics
Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, Dresden, Germany
Interests: dynamics and description of realistic open quantum systems

Special Issue Information

Dear Colleagues,

Information on a quantum system can be obtained only when it is observed either by a special measurement device or in a natural manner, in an environment into which the system is embedded. Quantum systems are usually localized in space, meaning that they have a finite extension with a shape characteristic. The environment is, however, infinitely extended. The environment of the open quantum system can, generally, be parametrically varied and allows a parameter dependent study of the properties of quantum systems. Such studies are now performed theoretically, as well as experimentally, on very different open quantum systems. They allow us to obtain valuable information on quantum physics.

The aim of the present Special Issue is to discuss different theoretical, as well as experimental, results characteristic of open quantum systems. In order to underline their meaning, a few results that are characteristic of other systems (including classical systems and optics) will also be considered. Of special interest are, among others, the following topics: Singular points and their influence on the dynamics of open systems; eigenvalues and eigenfunctions of a non-Hermitian Hamilton operator describing an open quantum system; formation of aggregates in small systems; nonadiabatic processes in open quantum systems; transmission through quantum dots; and photosynthesis.

Prof. Dr. Hichem Eleuch
Prof. Dr. Ingrid Rotter
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Description of open quantum systems by a non-Hermitian Hamilton operator
  • Singular points in open quantum systems
  • Experimental counter-intuitive results in open quantum systems
  • Non-adiabatic processes in open quantum systems
  • Transmission through quantum dots
  • Formation of aggregates
  • Photosynthesis
  • Super- and sub-radiance in optics
  • Exceptional points in classical systems

Published Papers (5 papers)

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Research

14 pages, 1036 KiB  
Article
Time-Reversal Symmetry and Arrow of Time in Quantum Mechanics of Open Systems
by Naomichi Hatano and Gonzalo Ordonez
Entropy 2019, 21(4), 380; https://0-doi-org.brum.beds.ac.uk/10.3390/e21040380 - 08 Apr 2019
Cited by 6 | Viewed by 4350
Abstract
It is one of the most important and long-standing issues of physics to derive the irreversibility out of a time-reversal symmetric equation of motion. The present paper considers the breaking of the time-reversal symmetry in open quantum systems and the emergence of an [...] Read more.
It is one of the most important and long-standing issues of physics to derive the irreversibility out of a time-reversal symmetric equation of motion. The present paper considers the breaking of the time-reversal symmetry in open quantum systems and the emergence of an arrow of time. We claim that the time-reversal symmetric Schrödinger equation can have eigenstates that break the time-reversal symmetry if the system is open in the sense that it has at least a countably infinite number of states. Such eigenstates, namely the resonant and anti-resonant states, have complex eigenvalues. We show that, although these states are often called “unphysical”, they observe the probability conservation in a particular way. We also comment that the seemingly Hermitian Hamiltonian is non-Hermitian in the functional space of the resonant and anti-resonant states, and hence there is no contradiction in the fact that it has complex eigenvalues. We finally show how the existence of the states that break the time-reversal symmetry affects the quantum dynamics. The dynamics that starts from a time-reversal symmetric initial state is dominated by the resonant states for t > 0 ; this explains the phenomenon of the arrow of time, in which the decay excels the growth. The time-reversal symmetry holds in that the dynamic ending at a time-reversal symmetric final state is dominated by the anti-resonant states for t < 0 . Full article
(This article belongs to the Special Issue Coherence in Open Quantum Systems)
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16 pages, 1092 KiB  
Article
Locating the Sets of Exceptional Points in Dissipative Systems and the Self-Stability of Bicycles
by Oleg N. Kirillov
Entropy 2018, 20(7), 502; https://0-doi-org.brum.beds.ac.uk/10.3390/e20070502 - 01 Jul 2018
Cited by 2 | Viewed by 3820
Abstract
Sets in the parameter space corresponding to complex exceptional points (EP) have high codimension, and by this reason, they are difficult objects for numerical location. However, complex EPs play an important role in the problems of the stability of dissipative systems, where they [...] Read more.
Sets in the parameter space corresponding to complex exceptional points (EP) have high codimension, and by this reason, they are difficult objects for numerical location. However, complex EPs play an important role in the problems of the stability of dissipative systems, where they are frequently considered as precursors to instability. We propose to locate the set of complex EPs using the fact that the global minimum of the spectral abscissa of a polynomial is attained at the EP of the highest possible order. Applying this approach to the problem of self-stabilization of a bicycle, we find explicitly the EP sets that suggest scaling laws for the design of robust bikes that agree with the design of the known experimental machines. Full article
(This article belongs to the Special Issue Coherence in Open Quantum Systems)
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10 pages, 2202 KiB  
Article
Improving the Maximum Transmission Distance of Self-Referenced Continuous-Variable Quantum Key Distribution Using a Noiseless Linear Amplifier
by Yijun Wang, Xudong Wang, Duan Huang and Ying Guo
Entropy 2018, 20(6), 461; https://0-doi-org.brum.beds.ac.uk/10.3390/e20060461 - 14 Jun 2018
Cited by 2 | Viewed by 4125
Abstract
We show that a noiseless linear amplifier (NLA) can be placed properly at the receiver’s end to improve the performance of self-referenced (SR) continuous variable quantum key distribution (CV-QKD) when the reference pulses are weak. In SR CV-QKD, the imperfections of the amplitude [...] Read more.
We show that a noiseless linear amplifier (NLA) can be placed properly at the receiver’s end to improve the performance of self-referenced (SR) continuous variable quantum key distribution (CV-QKD) when the reference pulses are weak. In SR CV-QKD, the imperfections of the amplitude modulator limit the maximal amplitude of the reference pulses, while the performance of SR CV-QKD is positively related to the amplitude of the reference pulses. An NLA can compensate the impacts of large phase noise introduced by the weak reference pulses. Simulation results derived from collective attacks show that this scheme can improve the performance of SR CV-QKD with weak reference pulses, in terms of extending maximum transmission distance. An NLA with a gain of g can increase the maximum transmission distance by the equivalent of 20log10g dB of losses. Full article
(This article belongs to the Special Issue Coherence in Open Quantum Systems)
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8 pages, 203 KiB  
Article
Equilibrium States in Open Quantum Systems
by Ingrid Rotter
Entropy 2018, 20(6), 441; https://0-doi-org.brum.beds.ac.uk/10.3390/e20060441 - 06 Jun 2018
Cited by 7 | Viewed by 2854
Abstract
The aim of this paper is to study the question of whether or not equilibrium states exist in open quantum systems that are embedded in at least two environments and are described by a non-Hermitian Hamilton operator H . The eigenfunctions of [...] Read more.
The aim of this paper is to study the question of whether or not equilibrium states exist in open quantum systems that are embedded in at least two environments and are described by a non-Hermitian Hamilton operator H . The eigenfunctions of H contain the influence of exceptional points (EPs) and external mixing (EM) of the states via the environment. As a result, equilibrium states exist (far from EPs). They are different from those of the corresponding closed system. Their wavefunctions are orthogonal even though the Hamiltonian is non-Hermitian. Full article
(This article belongs to the Special Issue Coherence in Open Quantum Systems)
18 pages, 707 KiB  
Article
Liouvillian of the Open STIRAP Problem
by Thomas Mathisen and Jonas Larson
Entropy 2018, 20(1), 20; https://0-doi-org.brum.beds.ac.uk/10.3390/e20010020 - 03 Jan 2018
Cited by 11 | Viewed by 4222
Abstract
With the corresponding Liouvillian as a starting point, we demonstrate two seemingly new phenomena of the STIRAP problem when subjected to irreversible losses. It is argued that both of these can be understood from an underlying Zeno effect, and in particular both can [...] Read more.
With the corresponding Liouvillian as a starting point, we demonstrate two seemingly new phenomena of the STIRAP problem when subjected to irreversible losses. It is argued that both of these can be understood from an underlying Zeno effect, and in particular both can be viewed as if the environment assists the STIRAP population transfer. The first of these is found for relative strong dephasing, and, in the language of the Liouvillian, it is explained from the explicit form of the matrix generating the time-evolution; the coherence terms of the state decay off, which prohibits further population transfer. For pure dissipation, another Zeno effect is found, where the presence of a non-zero Liouvillian gap protects the system’s (adiabatic) state from non-adiabatic excitations. In contrast to full Zeno freezing of the evolution, which is often found in many problems without explicit time-dependence, here, the freezing takes place in the adiabatic basis such that the system still evolves but adiabatically. Full article
(This article belongs to the Special Issue Coherence in Open Quantum Systems)
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