Some remarks on the quantum mechanics of a lattice gas

Léon Van Hove

Toshiyuki Nishiyama, Masahisa Fukushima, Shokichi Kanno

С. М. Сергеев

The method of q -oscillator lattices, proposed recently in Bazhanov and Sergeev 2005 ( Preprint hep-th/0509181), provides the tool for a construction of various integrable models of quantum mechanics in (2 + 1)-dimensional spacetime. In contrast to any one-dimensional quantum chain, its two-dimensional generalizations—quantum lattices—admit different geometrical structures. In this paper, we consider the q -oscillator model on a special lattice. The model may be interpreted as a two-dimensional lattice Bose gas. The most remarkable feature of the model is that it allows the coordinate Bethe ansatz: the p -particles' wavefunction is the sum of plane waves. Consistency conditions is the set of 2 p equations for p one-particle wave vectors. These 'Bethe ansatz' equations are the main result of this paper.

Boyuan Wang, Zhaoyuan Meng, Yaomin Zhao +1 more

Quantum computing holds transformative potential for simulating nonlinear physical systems, such as fluid turbulence. However, mapping nonlinear dynamics to the linear operations required by quantum hardware remains a fundamental challenge. Here, we bridge this gap by introducing a novel node-level ensemble description of a lattice gas, which enables the simulation of nonlinear fluid dynamics on quantum computers. This approach combines the advantages of the lattice Boltzmann method with low-dimensional representation (computational cost) and lattice gas cellular automata with linear collision treatment (quantum compatibility). Building on this framework, we propose a quantum lattice Boltzmann method that relies on linear operations with medium dimensionality, offering the potential for quantum speedup. We validated the algorithm through simulations of vortex-pair merging and decaying turbulence on up to 16.8 million computational grid points. The results demonstrate remarkable agreement with direct numerical simulation, effectively capturing the essential nonlinear mechanisms of fluid dynamics. This work potentially advances the development of quantum algorithms for other nonlinear problems across various transport phenomena in engineering.

Manuel Gadella