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arXiv:0901.3637 · Condensed Matter Physics

Non-equilibrium reversible dynamics of work production in four-spin system in a magnetic field

Ivanchenko

Published Jan 1, 2011• 1 citation
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Abstract

A closed system of the equations for the local Bloch vectors and spin correlation functions is obtained by decomplexification of the Liouville-von Neumann equation for 4 magnetic particles with the exchange interaction that takes place in an arbitrary time-dependent external magnetic field.The analytical and numerical analysis of the quantum thermodynamic variables is carried out depending on separable mixed initial state and the magnetic field modulation.Under unitary evolution, non-equilibrium reversible dynamics of power production in the finite environment is investigated.

DOI
10.5488/cmp.14.23005

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A closed system of the equations for the local Bloch vectors and spin correlation functions is obtained by decomplexification of the Liouville-von Neumann equation for 4 magnetic particles with the exchange interaction that takes place in an arbitrary time-dependent external magnetic field.The analytical and numerical analysis of the quantum thermodynamic variables is carried out depending on separable mixed initial state and the magnetic field modulation.Under unitary evolution, non-equilibrium reversible dynamics of power production in the finite environment is investigated.
A closed system of the equations for the local Bloch vectors and spin correlation functions is obtained by decomplexification of the Liouville-von Neumann equation for three magnetic qubits with the exchange interaction, that takes place in an arbitrary time-dependent external magnetic field. The numerical comparative analysis of entanglement is carried out depending on initial conditions and the magnetic field modulation. The present study may be useful for analysis of interference experiments and in the field of quantum computing.
A closed system of equations for the local Bloch vectors and spin correlation functions of three magnetic qubits with exchange interaction, which are in an arbitrary, time-dependent, external magnetic field, is obtained using decomplexification of the Liouville–Neuman equations. A numerical comparative analysis of entanglement measures is performed as a function of the initial conditions and modulation of the magnetic field. The investigation could find applications for the analysis of interference experiments and manipulation of quantum qubits.
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The time evolution of a spin-12\frac{1}{2}21​ particle under the influence of a locally applied external magnetic field, and interacting with anisotropic spin environment in thermal equilibrium at temperature TTT is studied. The exact analytical form of the reduced density matrix of the central spin is calculated explicitly for a finite number of bath spins. The case of an infinite number of environmental spins is investigated using the convergence of the rescaled bath operators to normal Gaussian random variables. In this limit, we derive the analytical form of the components of the Bloch vector for antiferromagnetic interactions within the bath, and we investigate the short-time and long-time behavior of reduced dynamics. The effect of the external magnetic field, the anisotropy, and the temperature of the bath on the decoherence of the central spin are discussed.