Eigen model as a quantum spin chain: Exact dynamics

Eigen model as a quantum spin chain: exact dynamics.

We map the Eigen model of biological evolution [Naturwissenschaften 58, 465 (1971)] into a quantum spin model with non-Hermitian Hamiltonian. Based on such a connection, we derive exact relaxation periods for the Eigen model to approach static energy landscape from various initial conditions. We also study a simple case of dynamic fitness function.

Generating quantum states through spin chain dynamics

The spin chain is a theoretical work-horse of the physicist, providing a convenient, tractablemodel that yields insight into a host of physical phenomena including conduction, frustration, superconductivity, topological phases, localisation, phase transitions, quantum chaos and even string theory.Our ultimate aim, however, is not just to understand the properties of a physical system, but to ha...

Spin dynamics in a double quantum dot: Exact diagonalization study

Exact dynamics in the central-spin model

Using the Bethe ansatz, we present a general formula for the dynamics of the central spin in the central-spin model with inhomogeneous Heisenberg couplings and with a central magnetic field. We evaluate this formula both analytically and numerically for a fully polarized bath. For this configuration, we find, after an initial decay, an oscillatory behaviour of the central spin at all times. PAC...

Exact Solution of a Yang-Baxter Spin-1/2 Chain Model and Quantum Entanglement

Entanglement is believed to be crucial in macroscopic physical systems for understanding the collective quantum phenomena such as quantum phase transitions. We start from and solve exactly a novel Yang-Baxter spin-1/2 chain model with inhomogeneous and anisotropic short-range interactions. For the ground state, we show the behavior of neighboring entanglement in the parameter space and find tha...