skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Quantum transport in d-dimensional lattices

Abstract

We show that both fermionic and bosonic uniform d-dimensional lattices can be reduced to a set of independent one-dimensional chains. This reduction leads to the expression for ballistic energy fluxes in uniform fermionic and bosonic lattices. By the use of the Jordan–Wigner transformation we can extend our analysis to spin lattices, proving the coexistence of both ballistic and non-ballistic subspaces in any dimension and for any system size. Lastly, we then relate the nature of transport to the number of excitations in the homogeneous spin lattice, indicating that a single excitation always propagates ballistically and that the non-ballistic behaviour of uniform spin lattices is a consequence of the interaction between different excitations.

Authors:
 [1];  [2];  [2]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Singapore Univ. of Technology and Design (Singapore)
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1257761
Grant/Contract Number:  
SC0001088
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
New Journal of Physics
Additional Journal Information:
Journal Volume: 18; Journal Issue: 4; Journal ID: ISSN 1367-2630
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; quantum transport; fermion; boson; spin; lattice; current; Lindblad

Citation Formats

Manzano, Daniel, Chuang, Chern, and Cao, Jianshu. Quantum transport in d-dimensional lattices. United States: N. p., 2016. Web. doi:10.1088/1367-2630/18/4/043044.
Manzano, Daniel, Chuang, Chern, & Cao, Jianshu. Quantum transport in d-dimensional lattices. United States. https://doi.org/10.1088/1367-2630/18/4/043044
Manzano, Daniel, Chuang, Chern, and Cao, Jianshu. 2016. "Quantum transport in d-dimensional lattices". United States. https://doi.org/10.1088/1367-2630/18/4/043044. https://www.osti.gov/servlets/purl/1257761.
@article{osti_1257761,
title = {Quantum transport in d-dimensional lattices},
author = {Manzano, Daniel and Chuang, Chern and Cao, Jianshu},
abstractNote = {We show that both fermionic and bosonic uniform d-dimensional lattices can be reduced to a set of independent one-dimensional chains. This reduction leads to the expression for ballistic energy fluxes in uniform fermionic and bosonic lattices. By the use of the Jordan–Wigner transformation we can extend our analysis to spin lattices, proving the coexistence of both ballistic and non-ballistic subspaces in any dimension and for any system size. Lastly, we then relate the nature of transport to the number of excitations in the homogeneous spin lattice, indicating that a single excitation always propagates ballistically and that the non-ballistic behaviour of uniform spin lattices is a consequence of the interaction between different excitations.},
doi = {10.1088/1367-2630/18/4/043044},
url = {https://www.osti.gov/biblio/1257761}, journal = {New Journal of Physics},
issn = {1367-2630},
number = 4,
volume = 18,
place = {United States},
year = {Thu Apr 28 00:00:00 EDT 2016},
month = {Thu Apr 28 00:00:00 EDT 2016}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 20 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Heat conduction in low-dimensional quantum magnets
journal, December 2007


Far-from-Equilibrium Spin Transport in Heisenberg Quantum Magnets
journal, October 2014


Quantum many-body phenomena in coupled cavity arrays
journal, December 2008


Controlling and Measuring Quantum Transport of Heat in Trapped-Ion Crystals
journal, July 2013


Nonequilibrium density-matrix description of steady-state quantum transport
journal, January 2012


Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms
journal, January 2012


Expansion Dynamics of Interacting Bosons in Homogeneous Lattices in One and Two Dimensions
journal, May 2013


Heat transport in low-dimensional systems
journal, September 2008


Exact solution for a diffusive nonequilibrium steady state of an open quantum chain
journal, May 2010


Quantum transport efficiency and Fourier's law
journal, December 2012


Heat transport through lattices of quantum harmonic oscillators in arbitrary dimensions
journal, January 2013


Coherent quantum transport in disordered systems: A unified polaron treatment of hopping and band-like transport
journal, April 2015


Coexistence of Diffusive and Ballistic Transport in a Simple Spin Ladder
journal, February 2013


Magnetization transport in spin ladders and next-nearest-neighbor chains
journal, November 2013


Quantum walks: a comprehensive review
journal, July 2012


Discrete Quantum Walks Hit Exponentially Faster
journal, February 2005


Hitting time for quantum walks on the hypercube
journal, March 2006


Quantum walks on embedded hypercubes
journal, August 2014


Search on a hypercubic lattice using a quantum random walk. I. d > 2
journal, September 2010


Spatial search by continuous-time quantum walks on crystal lattices
journal, May 2014


Markovian master equations: a critical study
journal, November 2010


Stationary quantum coherence and transport in disordered networks
journal, September 2013


Efficient energy transfer in light-harvesting systems: Quantum-classical comparison, flux network, and robustness analysis
journal, November 2012


Heat Transport in Ordered Harmonic Lattices
journal, February 2008


�ber das Paulische �quivalenzverbot
journal, September 1928


Strong evidence of normal heat conduction in a one-dimensional quantum system
journal, January 2003


Heat transport in an open transverse-field Ising chain
journal, October 2010


Diffusive-Ballistic Crossover in 1D Quantum Walks
journal, June 2003


Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid
journal, March 2011


A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
journal, July 2012


Symmetry and the thermodynamics of currents in open quantum systems
journal, September 2014


Efficient and coherent excitation transfer across disordered molecular networks
journal, February 2011


Works referencing / citing this record:

A short introduction to the Lindblad master equation
journal, February 2020


Harnessing symmetry to control quantum transport
journal, January 2018


Enhanced exciton transport in an optical cavity field with spatially varying profile
journal, July 2019