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19 pages, 13215 KiB

Open AccessArticle

Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with Non-Commuting Energy and Momentum Operators

by Matteo Villani, Guillermo Albareda, Carlos Destefani, Xavier Cartoixà and Xavier Oriols

Entropy 2021, 23(4), 408; https://doi.org/10.3390/e23040408 - 30 Mar 2021

Cited by 3 | Viewed by 1733

Abstract

Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by non-simulated degrees of freedom on the simulated [...] Read more.

Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by non-simulated degrees of freedom on the simulated ones as a transition between single-particle pure states. First, we show that Bohmian conditional wave functions (BCWFs) allow for a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of single-particle time-dependent pure states, either under Markovian or non-Markovian conditions. Second, we discuss the practical application of the method for modeling light–matter interaction phenomena in a resonant tunneling device, where a single photon interacts with a single electron. Third, we emphasize the importance of interpreting such a scattering mechanism as a transition between initial and final single-particle BCWF with well-defined central energies (rather than with well-defined central momenta). Full article

(This article belongs to the Special Issue Transport and Diffusion in Quantum Complex Systems)

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24 pages, 610 KiB

Open AccessArticle

Transport Efficiency of Continuous-Time Quantum Walks on Graphs

by Luca Razzoli, Matteo G. A. Paris and Paolo Bordone

Entropy 2021, 23(1), 85; https://doi.org/10.3390/e23010085 - 09 Jan 2021

Cited by 11 | Viewed by 1991

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)

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19 pages, 3205 KiB

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

by Angus J. Dunnett and Alex W. Chin

Entropy 2021, 23(1), 77; https://doi.org/10.3390/e23010077 - 06 Jan 2021

Cited by 9 | Viewed by 2613

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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10 pages, 829 KiB

Open AccessArticle

Two-Excitation Routing via Linear Quantum Channels

by Tony John George Apollaro and Wayne Jordan Chetcuti

Entropy 2021, 23(1), 51; https://doi.org/10.3390/e23010051 - 31 Dec 2020

Cited by 2 | Viewed by 1839

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-

\frac{1}{2}

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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13 pages, 2709 KiB

Open AccessArticle

Scattering as a Quantum Metrology Problem: A Quantum Walk Approach

by Francesco Zatelli, Claudia Benedetti and Matteo G. A. Paris

Entropy 2020, 22(11), 1321; https://doi.org/10.3390/e22111321 - 19 Nov 2020

Cited by 8 | Viewed by 2674

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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15 pages, 1077 KiB

Open AccessArticle

Excitation Dynamics in Chain-Mapped Environments

by Dario Tamascelli

Entropy 2020, 22(11), 1320; https://doi.org/10.3390/e22111320 - 19 Nov 2020

Cited by 8 | Viewed by 1812

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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19 pages, 3076 KiB

Open AccessFeature PaperArticle

Complex Systems in Phase Space

by David K. Ferry, Mihail Nedjalkov, Josef Weinbub, Mauro Ballicchia, Ian Welland and Siegfried Selberherr

Entropy 2020, 22(10), 1103; https://doi.org/10.3390/e22101103 - 29 Sep 2020

Cited by 5 | Viewed by 2150

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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19 pages, 2013 KiB

Open AccessFeature PaperArticle

Entropy Dynamics of Phonon Quantum States Generated by Optical Excitation of a Two-Level System

by Thilo Hahn, Daniel Wigger and Tilmann Kuhn

Entropy 2020, 22(3), 286; https://doi.org/10.3390/e22030286 - 29 Feb 2020

Cited by 3 | Viewed by 2845

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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