scholarly journals Excitation Dynamics in Chain-Mapped Environments

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1320
Author(s):  
Dario Tamascelli
Keyword(s):  
Degrees Of Freedom ◽  
Open Quantum Systems ◽  
Harmonic Oscillators ◽  
Dimensional Structure ◽  
One Dimensional ◽  
Open Quantum ◽  
Density Matrix Renormalization ◽  
Natural Notion ◽  
A Chain ◽  
The One

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.

scholarly journals Accurate Truncations of Chain Mapping Models for Open Quantum Systems

Nanomaterials ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 2104
Author(s):  
Mónica Sánchez-Barquilla ◽  
Johannes Feist
Keyword(s):  
Degrees Of Freedom ◽  
Nearest Neighbor ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum ◽  
Research Fields ◽  
A Chain ◽  
Chain Lengths ◽  
Mapping Models ◽  
Nearest Neighbor Coupling

The dynamics of open quantum systems are of great interest in many research fields, such as for the interaction of a quantum emitter with the electromagnetic modes of a nanophotonic structure. A powerful approach for treating such setups in the non-Markovian limit is given by the chain mapping where an arbitrary environment can be transformed to a chain of modes with only nearest-neighbor coupling. However, when long propagation times are desired, the required long chain lengths limit the utility of this approach. We study various approaches for truncating the chains at manageable lengths while still preserving an accurate description of the dynamics. We achieve this by introducing losses to the chain modes in such a way that the effective environment acting on the system remains unchanged, using a number of different strategies. Furthermore, we demonstrate that extending the chain mapping to allow next-nearest neighbor coupling permits the reproduction of an arbitrary environment, and adding longer-range interactions does not further increase the effective number of degrees of freedom in the environment.

ENTANGLEMENT IN THE ANISOTROPIC KONDO NECKLACE MODEL

2010 ◽  
Vol 24 (31) ◽  
pp. 6165-6174 ◽  
Author(s):  
J. J. MENDOZA-ARENAS ◽  
R. FRANCO ◽  
J. SILVA-VALENCIA
Keyword(s):  
Quantum Critical Point ◽  
Exact Diagonalization ◽  
Density Matrix Renormalization Group ◽  
Von Neumann ◽  
One Dimensional ◽  
Density Matrix Renormalization ◽  
Block Entropy ◽  
Ising Limit ◽  
A Chain ◽  
The One

We study the entanglement in the one-dimensional Kondo necklace model with exact diagonalization, calculating the concurrence as a function of the Kondo coupling J and an anisotropy η in the interaction between conduction spins, and we review some results previously obtained in the limiting cases η = 0 and 1. We observe that as J increases, localized and conduction spins get more entangled, while neighboring conduction spins diminish their concurrence; localized spins require a minimum concurrence between conduction spins to be entangled. The anisotropy η diminishes the entanglement for neighboring spins when it increases, driving the system to the Ising limit η = 1 where conduction spins are not entangled. We observe that the concurrence does not give information about the quantum phase transition in the anisotropic Kondo necklace model (between a Kondo singlet and an antiferromagnetic state), but calculating the von Neumann block entropy with the density matrix renormalization group in a chain of 100 sites for the Ising limit indicates that this quantity is useful for locating the quantum critical point.

scholarly journals Perturbation Analysis of Quantum Reset Models

2021 ◽  
Vol 183 (1) ◽  
Author(s):  
Géraldine Haack ◽  
Alain Joye
Keyword(s):  
Steady State ◽  
Perturbation Analysis ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Markov Semigroup ◽  
Coupling Constant ◽  
Coupling Term ◽  
Open Quantum ◽  
Effective Dynamics ◽  
A Chain

AbstractThis paper is devoted to the analysis of Lindblad operators of Quantum Reset Models, describing the effective dynamics of tri-partite quantum systems subject to stochastic resets. We consider a chain of three independent subsystems, coupled by a Hamiltonian term. The two subsystems at each end of the chain are driven, independently from each other, by a reset Lindbladian, while the center system is driven by a Hamiltonian. Under generic assumptions on the coupling term, we prove the existence of a unique steady state for the perturbed reset Lindbladian, analytic in the coupling constant. We further analyze the large times dynamics of the corresponding CPTP Markov semigroup that describes the approach to the steady state. We illustrate these results with concrete examples corresponding to realistic open quantum systems.

One-Dimensional Fluorescent Nanosized-Diamond Nanowires with Fluorescent Detection of Vitamin B12

NANO ◽  
2019 ◽  
Vol 14 (07) ◽  
pp. 1950084 ◽  
Author(s):  
Jilong Wang ◽  
Siheng Su ◽  
Jingjing Qiu ◽  
Shiren Wang
Keyword(s):  
Electron Microscopy ◽  
Photoelectron Spectroscopy ◽  
High Sensitivity ◽  
Anodic Aluminum Oxide Template ◽  
Fluorescent Detection ◽  
Dimensional Structure ◽  
Fluorescent Properties ◽  
One Dimensional ◽  
Sensitivity And Selectivity ◽  
The One

In this paper, a novel and facile method to achieve fluorescent nanosized-diamond based nanowire (NW) is reported. One-dimensional (1D) organic NW has received tremendous attention due to its superior chemical functionality and size-, shape-, and material-dependent properties. In addition, nanosized-diamond is comprehensively studied and investigated due to superior tunable fluorescent properties, cost-effectiveness, facile manufacturing and high biocompatibility. Through thermal treatment, sulfur-modified nanosized-diamond was fabricated by mixing oxidized nanosized-diamond and dibenzyl disulfide at 900∘C. Fourier transform infrared spectroscopy (FTIR), X-ray photoelectron spectroscopy (XPS) and zeta potential were employed to characterize sulfur-modified nanosized-diamond. After that, porous anodic aluminum oxide template-assisted cathodic electrophoretic deposition method was used to achieve sulfur-modified nanosized-diamond NW. Scanning electron microscopy and transmission electron microscopy were applied to present the one-dimensional structure of the NWs. The optical properties of sulfur nanosized-diamond NW were characterized via ultraviolet-visible spectroscopy and photoluminescence spectroscopy. Finally, the as-synthesized sulfur-modified nanosized-diamond NW-based optical sensor was fabricated to detect vitamin B[Formula: see text] with high sensitivity and selectivity.

scholarly journals Quasi-Lie Brackets and the Breaking of Time-Translation Symmetry for Quantum Systems Embedded in Classical Baths

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 518 ◽  
Author(s):  
Alessandro Sergi ◽  
Gabriel Hanna ◽  
Roberto Grimaudo ◽  
Antonino Messina
Keyword(s):  
Constant Temperature ◽  
Degrees Of Freedom ◽  
Open Quantum Systems ◽  
Hamiltonian Dynamics ◽  
Quantum Systems ◽  
Classical Dynamics ◽  
Open Quantum ◽  
Time Translation ◽  
Translation Symmetry ◽  
Lie Brackets

Many open quantum systems encountered in both natural and synthetic situations are embedded in classical-like baths. Often, the bath degrees of freedom may be represented in terms of canonically conjugate coordinates, but in some cases they may require a non-canonical or non-Hamiltonian representation. Herein, we review an approach to the dynamics and statistical mechanics of quantum subsystems embedded in either non-canonical or non-Hamiltonian classical-like baths which is based on operator-valued quasi-probability functions. These functions typically evolve through the action of quasi-Lie brackets and their associated Quantum-Classical Liouville Equations, or through quasi-Lie brackets augmented by dissipative terms. Quasi-Lie brackets possess the unique feature that, while conserving the energy (which the Noether theorem links to time-translation symmetry), they violate the time-translation symmetry of their algebra. This fact can be heuristically understood in terms of the dynamics of the open quantum subsystem. We then describe an example in which a quantum subsystem is embedded in a bath of classical spins, which are described by non-canonical coordinates. In this case, it has been shown that an off-diagonal open-bath geometric phase enters into the propagation of the quantum-classical dynamics. Next, we discuss how non-Hamiltonian dynamics may be employed to generate the constant-temperature evolution of phase space degrees of freedom coupled to the quantum subsystem. Constant-temperature dynamics may be generated by either a classical Langevin stochastic process or a Nosé–Hoover deterministic thermostat. These two approaches are not equivalent but have different advantages and drawbacks. In all cases, the calculation of the operator-valued quasi-probability function allows one to compute time-dependent statistical averages of observables. This may be accomplished in practice using a hybrid Molecular Dynamics/Monte Carlo algorithms, which we outline herein.

scholarly journals Optimising Matrix Product State Simulations of Shor's Algorithm

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 116 ◽  
Author(s):  
Aidan Dang ◽  
Charles D. Hill ◽  
Lloyd C. L. Hollenberg
Keyword(s):  
Dimensional Structure ◽  
Matrix Product ◽  
Product State ◽  
One Dimensional ◽  
Matrix Product State ◽  
Shor's Algorithm ◽  
The One ◽  
High Level ◽  
Space Requirements ◽  
Factoring Algorithm

We detail techniques to optimise high-level classical simulations of Shor's quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure of a matrix product state. Compared to previous approaches whose space requirements depend on r, the solution to the underlying order-finding problem of Shor's algorithm, our approach depends on its factors. We performed a matrix product state simulation of a 60-qubit instance of Shor's algorithm that would otherwise be infeasible to complete without an optimised entanglement mapping.

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