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# Special Issue "Transport and Diffusion in Quantum Complex Systems"

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

Deadline for manuscript submissions: closed (30 November 2020).

## Special Issue Editors

Dr. Paolo Bordone
Website
Guest Editor
1. Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università degli Studi di Modena e Reggio Emilia, via Campi 213/A, I-41125 Modena, Italy
2. Centro S3, CNR-Istituto di Nanoscienze, I-41125 Modena, Italy
Interests: coherent and noisy quantum dynamics; quantum walks; quantum transport; electron quantum optics; complex quantum systems
Dr. Dario Tamascelli
Website
Guest Editor
Dipartimento di Fisica "Aldo Pontremoli", Università degli Studi di Milano, via Celoria 16, 20133 Milano (MI), Italy
Interests: open quantum systems; quantum metrology; quantum walks; quantum biology; simulation of complex quantum systems

## Special Issue Information

Dear Colleagues,

Our understanding of the transport of energy, mass, charge, or information in complex quantum systems plays a key role from both a fundamental and technological point of view. As such, it is triggering a large amount of theoretical and experimental research that aims to understand and exploit quantum coherent phenomena for the development of quantum devices that may outperform their classical counterparts.

Quantum interference is the origin of a number of peculiar effects, such as ballistic transport along lattices and resonant tunneling. On the other hand, the presence of unavoidable interactions with the surrounding environment typically leads to a loss of coherence and to the emergence of a diffusive behavior, closer to the classical scenario, that, in some cases, enhances the transport efficiency. The control of such phenomena, together with our understanding of the transition from microscopic to macroscopic or from single-particle to few- or many-particle systems, is of utmost importance for the successful build-out of quantum technologies, and constitutes the focus of this Special Issue.

Dr. Paolo Bordone
Dr. Dario Tamascelli
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.dlhwdz.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

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 1800 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

• coherent dynamics
• noisy quantum dynamics
• diffusive dynamics
• quantum transport
• quantum walks
• quantum networks
• energy transfer

## Published Papers (7 papers)

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# Research

Open AccessArticle
Transport Efficiency of Continuous-Time Quantum Walks on Graphs
Entropy 2021, 23(1), 85; https://doi.org/10.3390/e23010085 - 09 Jan 2021
Abstract
Continuous-time quantum walk describes the propagation of a quantum particle (or an excitation) evolving continuously in time on a graph. As such, it provides a natural framework for modeling transport processes, e.g., in light-harvesting systems. In particular, the transport properties strongly depend on [...] Read more.
Continuous-time quantum walk describes the propagation of a quantum particle (or an excitation) evolving continuously in time on a graph. As such, it provides a natural framework for modeling transport processes, e.g., in light-harvesting systems. In particular, the transport properties strongly depend on the initial state and specific features of the graph under investigation. In this paper, we address the role of graph topology, and investigate the transport properties of graphs with different regularity, symmetry, and connectivity. We neglect disorder and decoherence, and assume a single trap vertex that is accountable for the loss processes. In particular, for each graph, we analytically determine the subspace of states having maximum transport efficiency. Our results provide a set of benchmarks for environment-assisted quantum transport, and suggest that connectivity is a poor indicator for transport efficiency. Indeed, we observe some specific correlations between transport efficiency and connectivity for certain graphs, but, in general, they are uncorrelated. Full article
(This article belongs to the Special Issue Transport and Diffusion in Quantum Complex Systems)
Open AccessArticle
Matrix Product State Simulations of Non-Equilibrium Steady States and Transient Heat Flows in the Two-Bath Spin-Boson Model at Finite Temperatures
Entropy 2021, 23(1), 77; https://doi.org/10.3390/e23010077 - 06 Jan 2021
Abstract
Simulating the non-perturbative and non-Markovian dynamics of open quantum systems is a very challenging many body problem, due to the need to evolve both the system and its environments on an equal footing. Tensor network and matrix product states (MPS) have emerged as [...] Read more.
Simulating the non-perturbative and non-Markovian dynamics of open quantum systems is a very challenging many body problem, due to the need to evolve both the system and its environments on an equal footing. Tensor network and matrix product states (MPS) have emerged as powerful tools for open system models, but the numerical resources required to treat finite-temperature environments grow extremely rapidly and limit their applications. In this study we use time-dependent variational evolution of MPS to explore the striking theory of Tamascelli et al. (Phys. Rev. Lett. 2019, 123, 090402.) that shows how finite-temperature open dynamics can be obtained from zero temperature, i.e., pure wave function, simulations. Using this approach, we produce a benchmark dataset for the dynamics of the Ohmic spin-boson model across a wide range of coupling strengths and temperatures, and also present a detailed analysis of the numerical costs of simulating non-equilibrium steady states, such as those emerging from the non-perturbative coupling of a qubit to baths at different temperatures. Despite ever-growing resource requirements, we find that converged non-perturbative results can be obtained, and we discuss a number of recent ideas and numerical techniques that should allow wide application of MPS to complex open quantum systems. Full article
(This article belongs to the Special Issue Transport and Diffusion in Quantum Complex Systems)
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Open AccessArticle
Two-Excitation Routing via Linear Quantum Channels
Entropy 2021, 23(1), 51; https://doi.org/10.3390/e23010051 - 31 Dec 2020
Abstract
Routing quantum information among different nodes in a network is a fundamental prerequisite for a quantum internet. While single-qubit routing has been largely addressed, many-qubit routing protocols have not been intensively investigated so far. Building on a recently proposed many-excitation transfer protocol, we [...] Read more.
Routing quantum information among different nodes in a network is a fundamental prerequisite for a quantum internet. While single-qubit routing has been largely addressed, many-qubit routing protocols have not been intensively investigated so far. Building on a recently proposed many-excitation transfer protocol, we apply the perturbative transfer scheme to a two-excitation routing protocol on a network where multiple two-receivers block are coupled to a linear chain. We address both the case of switchable and permanent couplings between the receivers and the chain. We find that the protocol allows for efficient two-excitation routing on a fermionic network, although for a spin-$12$ network only a limited region of the network is suitable for high-quality routing. Full article
(This article belongs to the Special Issue Transport and Diffusion in Quantum Complex Systems)
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Open AccessArticle
Scattering as a Quantum Metrology Problem: A Quantum Walk Approach
Entropy 2020, 22(11), 1321; https://doi.org/10.3390/e22111321 - 19 Nov 2020
Abstract
We address the scattering of a quantum particle by a one-dimensional barrier potential over a set of discrete positions. We formalize the problem as a continuous-time quantum walk on a lattice with an impurity and use the quantum Fisher information as a means [...] Read more.
We address the scattering of a quantum particle by a one-dimensional barrier potential over a set of discrete positions. We formalize the problem as a continuous-time quantum walk on a lattice with an impurity and use the quantum Fisher information as a means to quantify the maximal possible accuracy in the estimation of the height of the barrier. We introduce suitable initial states of the walker and derive the reflection and transmission probabilities of the scattered state. We show that while the quantum Fisher information is affected by the width and central momentum of the initial wave packet, this dependency is weaker for the quantum signal-to-noise ratio. We also show that a dichotomic position measurement provides a nearly optimal detection scheme. Full article
(This article belongs to the Special Issue Transport and Diffusion in Quantum Complex Systems)
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Open AccessArticle
Excitation Dynamics in Chain-Mapped Environments
Entropy 2020, 22(11), 1320; https://doi.org/10.3390/e22111320 - 19 Nov 2020
Abstract
The chain mapping of structured environments is a most powerful tool for the simulation of open quantum system dynamics. Once the environmental bosonic or fermionic degrees of freedom are unitarily rearranged into a one dimensional structure, the full power of Density Matrix Renormalization [...] Read more.
The chain mapping of structured environments is a most powerful tool for the simulation of open quantum system dynamics. Once the environmental bosonic or fermionic degrees of freedom are unitarily rearranged into a one dimensional structure, the full power of Density Matrix Renormalization Group (DMRG) can be exploited. Beside resulting in efficient and numerically exact simulations of open quantum systems dynamics, chain mapping provides an unique perspective on the environment: the interaction between the system and the environment creates perturbations that travel along the one dimensional environment at a finite speed, thus providing a natural notion of light-, or causal-, cone. In this work we investigate the transport of excitations in a chain-mapped bosonic environment. In particular, we explore the relation between the environmental spectral density shape, parameters and temperature, and the dynamics of excitations along the corresponding linear chains of quantum harmonic oscillators. Our analysis unveils fundamental features of the environment evolution, such as localization, percolation and the onset of stationary currents. Full article
(This article belongs to the Special Issue Transport and Diffusion in Quantum Complex Systems)
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Open AccessFeature PaperArticle
Complex Systems in Phase Space
Entropy 2020, 22(10), 1103; https://doi.org/10.3390/e22101103 - 29 Sep 2020
Abstract
The continued reduction of semiconductor device feature sizes towards the single-digit nanometer regime involves a variety of quantum effects. Modeling quantum effects in phase space in terms of the Wigner transport equation has evolved to be a very effective approach to describe such [...] Read more.
The continued reduction of semiconductor device feature sizes towards the single-digit nanometer regime involves a variety of quantum effects. Modeling quantum effects in phase space in terms of the Wigner transport equation has evolved to be a very effective approach to describe such scaled down complex systems, accounting from full quantum processes to dissipation dominated transport regimes including transients. Here, we discuss the challanges, myths, and opportunities that arise in the study of these complex systems, and particularly the advantages of using phase space notions. The development of particle-based techniques for solving the transport equation and obtaining the Wigner function has led to efficient simulation approaches that couple well to the corresponding classical dynamics. One particular advantage is the ability to clearly illuminate the entanglement that can arise in the quantum system, thus allowing the direct observation of many quantum phenomena. Full article
(This article belongs to the Special Issue Transport and Diffusion in Quantum Complex Systems)
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Open AccessFeature PaperArticle
Entropy Dynamics of Phonon Quantum States Generated by Optical Excitation of a Two-Level System
Entropy 2020, 22(3), 286; https://doi.org/10.3390/e22030286 - 29 Feb 2020
Abstract
In quantum physics, two prototypical model systems stand out due to their wide range of applications. These are the two-level system (TLS) and the harmonic oscillator. The former is often an ideal model for confined charge or spin systems and the latter for [...] Read more.
In quantum physics, two prototypical model systems stand out due to their wide range of applications. These are the two-level system (TLS) and the harmonic oscillator. The former is often an ideal model for confined charge or spin systems and the latter for lattice vibrations, i.e., phonons. Here, we couple these two systems, which leads to numerous fascinating physical phenomena. Practically, we consider different optical excitations and decay scenarios of a TLS, focusing on the generated dynamics of a single phonon mode that couples to the TLS. Special emphasis is placed on the entropy of the different parts of the system, predominantly the phonons. While, without any decay, the entire system is always in a pure state, resulting in a vanishing entropy, the complex interplay between the single parts results in non-vanishing respective entanglement entropies and non-trivial dynamics of them. Taking a decay of the TLS into account leads to a non-vanishing entropy of the full system and additional aspects in its dynamics. We demonstrate that all aspects of the entropy’s behavior can be traced back to the purity of the states and are illustrated by phonon Wigner functions in phase space. Full article
(This article belongs to the Special Issue Transport and Diffusion in Quantum Complex Systems)
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