Entanglement in an open Heisenberg spin chain

Paul, Subhendu (2018) Entanglement in an open Heisenberg spin chain. Masters thesis, Memorial University of Newfoundland.

[img] [English] PDF - Accepted Version
Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission.

Download (3MB)


We analyze the time evolution of a spin chain of three qubits with nearest-neighbour Heisenberg XX interaction, coupled to two thermal reservoirs. We use the ‘reduced density matrix approach’ to calculate the populations and correlations (concurrence) among the spins. The spin-reservoir interaction is of the energy conserving type. This allows us to analyze the evolution analytically without approximations – yielding explicit, yet complicated formulas for the spin dynamics. To analyze the latter and discuss it as a function of the various physical parameters and time (intial conditions, termperatures, coupling strenghts), we resort to numerical methods. Our main finding is that the external noise (coupling to reservoirs) causes the appearence of an asymptotic, stationary (time-periodic) regime for the dynamics of concurrence. We discuss the dependence of the relaxation time and the characteristics of the regime itself, on the various parameters.

Item Type: Thesis (Masters)
URI: http://research.library.mun.ca/id/eprint/13676
Item ID: 13676
Additional Information: Includes bibliographical references (pages 55-57).
Keywords: open quantum system, spin chain, Heisenberg, density matrix, entanglement
Department(s): Science, Faculty of > Mathematics and Statistics
Date: September 2018
Date Type: Submission
Library of Congress Subject Heading: Quantum systems; Quantum entanglement; Density matrices

Actions (login required)

View Item View Item


Downloads per month over the past year

View more statistics