Group Analysis of Nonlinear Internal Waves in Oceans. II: The symmetries and rotationally invariant solution

Group Analysis of Nonlinear Internal Waves in Oceans. III: Additional conservation laws

Using the maximal Lie algebra of point symmetries of a system of nonlinear equations used in geophysical fluid dynamics, two conservation laws are found in addition to the conservation of energy.

Group Analysis of Nonlinear Internal Waves in Oceans. I: Self-adjointness, conservation laws, invariant solutions

The paper is devoted to the group analysis of equations of motion of two-dimensional uniformly stratified rotating fluids used as a basic model in geophysical fluid dynamics. It is shown that the nonlinear equations in question have a remarkable property to be self-adjoint. This property is crucial for constructing conservation laws provided in the present paper. Invariant solutions are constructed using certain symmetries. The invariant solutions are used for defining internal wave beams.

Conformal generation of an exotic rotationally invariant harmonic oscillator

An exotic rotationally invariant harmonic oscillator (ERIHO) is constructed by applying a non-unitary isotropic conformal bridge transformation (CBT) to a free planar particle. It is described by the isotropic harmonic oscillator Hamiltonian supplemented by a Zeeman type term with a real coupling constant $g$. The model reveals the Euclidean ($|g|<1$) and Minkowskian ($|g|>1$) phases separated by the phases $g=+1$ and $g=-1$ of the Landau problem in the symmetric gauge with opposite orientation of the magnetic field. A hidden symmetry emerges in the system at rational values of $g$. Its genera…

旋转不变电路：借助交换相互作用与两个辅助量子比特实现通用性

Rotationally-Invariant Circuits: Universality with the exchange interaction and two ancilla qubits

针对连续对称下局域幺正变换通用性失效的问题，研究刻画了k局域旋转不变量子比特电路的约束，证明借助两个辅助量子比特可通过2局域Heisenberg交换相互作用实现任意旋转不变幺正变换，单个辅助量子比特则无法实现，并探讨了相关应用场景。

Bianchi models with a free massless scalar field: invariant sets and higher symmetries

We scrutinize the overall structure of the space of cosmological models of Bianchi type I-VII$_h$ that contain a free massless scalar field, with a spatially homogeneous gradient $\nabla_μφ$ that generally breaks isotropy, in addition to a standard perfect fluid. Specifically, state space is written as a union of disjoint invariant sets, each corresponding to a particular cosmological model that is classified with respect to the Bianchi type and the matter content. Subsets corresponding to higher-symmetry models, including all locally rotationally symmetric models and FLRW models, and models w…

Invariant parameterization of geostrophic eddies in the ocean

The framework of invariant parameterization is extended to higher-order closure schemes. We also define, for the first time, generalized invariant parameterization schemes, where symmetries of the corresponding original model are preserved as equivalence transformations of related classes of closed system of differential equations. As a particular problem, we consider invariant parameterization schemes for geostrophic eddies in a barotropic ocean. Here the initial model is the barotropic vorticity equation, which is equivalent to the system of incompressible inviscid two-dimensional Euler equa…