Related papers: Conserved quantities in parity-time symmetric syst…
Topological invariants have played a fundamental role in the advancement of theoretical high energy physics. Physicists have used several kinematic techniques to distinguish new physics predictions from the Standard Model (SM) of particle…
We investigate $n$-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classification of such systems is reduced to the projective classification of linear congruences…
How do symmetries induce natural and useful quantum structures? This question is investigated in the context of models of three interacting particles in one-dimension. Such models display a wide spectrum of possibilities for dynamical…
We outline a procedure for counting and identifying a complete set of local and quasilocal conserved operators in integrable lattice systems. The method yields a systematic generation of all independent, conserved quasilocal operators…
To what extent does Noether's principle apply to quantum channels? Here, we quantify the degree to which imposing a symmetry constraint on quantum channels implies a conservation law, and show that this relates to physically impossible…
We investigate branched PT-symmetric optical lattices. We consider both the linear and nonlinear Schr\"odinger equations with a PT-symmetric periodic potential on the graph and solve them by imposing weighted vertex boundary conditions. A…
We develop an action principle for those models arising from isotropic loop quantum cosmology, and show that there is a natural conserved quantity $Q$ for the discrete difference equation arising from the Hamiltonian constraint. This…
The aim of this note is to discuss the relation between one-parameter continuous symmetries of the dynamics, defined on physical grounds, and conservation laws. In the Hamiltonian formulation, such symmetries of the dynamics in general…
During the evolution of coupled nonlinear oscillators on a lattice, with dynamics dictated by the discrete nonlinear Schr\"odinger equation (DNLSE systems), two quantities are conserved: system energy (Hamiltonian) and system density…
One-dimensional scattering mediated by non-Hermitian Hamiltonians is studied. A schematic set of models is used which simulate two point interactions at a variable strength and distance. The feasibility of the exact construction of the…
Structure-preserving geometric algorithm for the Vlasov-Maxwell (VM) equations is currently an active research topic. We show that spatially-discretized Hamiltonian systems for the VM equations admit a local energy conservation law in…
We carry out an extensive investigation of conservation laws and potential symmetries for the class of linear (1+1)-dimensional second-order parabolic equations. The group classification of this class is revised by employing admissible…
We investigate the effects of competition between two complex, $\mathcal{PT}$-symmetric potentials on the $\mathcal{PT}$-symmetric phase of a "particle in a box". These potentials, given by $V_Z(x)=iZ\mathrm{sign}(x)$ and…
Large families of Hamiltonians that are non-Hermitian in the conventional sense have been found to have all eigenvalues real, a fact attributed to an unbroken PT symmetry. The corresponding quantum theories possess an unconventional scalar…
In the study of $\mathcal{P}\mathcal{T}$-symmetric quantum systems with non-Hermitian perturbations, one of the most important questions is whether eigenvalues stay real or whether $\mathcal{P}\mathcal{T}$-symmetry is spontaneously broken…
The inspiration for this theoretical paper comes from recent experiments on a PT-symmetric system of two coupled optical whispering galleries (optical resonators). The optical system can be modeled as a pair of coupled linear oscillators,…
Partial differential equations (PDEs) describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated quantities (like entropy). Preserving these conservation and…
As Noether's theorem states any differentiable symmetry of the action of a physical system has a corresponding conservation law. Lipkin introduced the conservation laws of zilches. But the corresponding symmetries are yet to be determined.…
We investigate the effect that spatially modulated continuous conserved quantities can have on quantum ground states. We do so by introducing a family of one-dimensional local quantum rotor and bosonic models which conserve finite Fourier…
In this paper, we extend the well-known Noether theorem for Lagrangian systems to contact Lagrangian systems. We introduce a classification of infinitesimal symmetries and obtain the corresponding dissipated quantities. We notice that in…