Related papers: Conserved quantities in parity-time symmetric syst…
Topology in quench dynamics gives rise to intriguing dynamic topological phenomena, which are intimately connected to the topology of static Hamiltonians yet challenging to probe experimentally. Here we experimentally detect momentum-time…
The asymptotic behavior of the integrated density of states for a randomly perturbed lattice at the infimum of the spectrum is investigated. The leading term is determined when the decay of the single site potential is slow. The leading…
An optical-lattice quantum simulator is an ideal experimental platform to investigate non-equilibrium dynamics of a quantum many-body system, which is in general hard to simulate with classical computers. Here, we use our quantum simulator…
Canonical quantum mechanics postulates Hermitian Hamiltonians to ensure real eigenvalues. Counterintuitively, a non-Hermitian Hamiltonian, satisfying combined parity-time (PT) symmetry, could display entirely real spectra above some…
We exhibit two symmetries of one-dimensional Newtonian mechanics whereby a solution is built from the history of another solution via a generally nonlinear and complex potential-dependent transformation of the time. One symmetry intertwines…
This work presents a general geometric framework for simulating and learning the dynamics of Hamiltonian systems that are invariant under a Lie group of transformations. This means that a group of symmetries is known to act on the system…
In this paper we study the infinitesimal symmetries, Newtonoid vector fields, infinitesimal Noether symmetries and conservation laws of Hamiltonian systems. Using the dynamical covariant derivative and Jacobi endomorphism on the cotangent…
We study conservation laws for gravity theories invariant under general coordinate transformations. The class of models under consideration includes Einstein's general relativity theory as a special case as well as its generalizations to…
The diagrammatic analysis of interacting particle assemblies harbors a fundamental mismatch between two of its main implementations: Phi-derivable (conserving) approximations and parquet (crossing symmetric) models. No termwise expansion,…
The elementary quadratic plus inverse sextic interaction containing a strongly singular repulsive core in the origin is made regular by a complex shift of coordinate $x = s-{\rm i}\varepsilon$. The shift $\varepsilon>0$ is fixed while the…
Polymer quantum mechanics has been studied as a simplified picture that reflects some of the key properties of Loop Quantum Gravity; however, while the fate of relativistic symmetries in Loop Quantum Gravity is still not established, it is…
A closed form PT symmetric quadrimer optical waveguide structure, reminiscent of the four-state quantum system found in quantum optics, is studied. The beam dynamics of the structure is studied numerically. The effect of inclusion of…
For the non-conservative Caldirola-Kanai system, describing a quantum damped harmonic oscillator, a couple of constant-of-motion operators generating the Heisenberg-Weyl algebra can be found. The inclusion of the standard time evolution…
Many systems in biology, physics, and engineering are modeled by nonlinear dynamical systems where the states are usually unknown and only a subset of the state variables can be physically measured. Can we understand the full system from…
Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…
We study stochastic particle systems that conserve the particle density and exhibit a condensation transition due to particle interactions. We restrict our analysis to spatially homogeneous systems on finite lattices with stationary product…
Lattice models with non-hermitian, parity and time-reversal ($\mathcal{PT}$) symmetric Hamiltonians, realized most readily in coupled optical systems, have been intensely studied in the past few years. A $\mathcal{PT}$-symmetric dimer…
The nonlinear dynamics of a balanced parity-time symmetric optical microring arrangement are analytically investigated. By considering gain and loss saturation effects, the pertinent conservation laws are explicitly obtained in the Stokes…
Multi-dimensional complex optical potentials with partial parity-time (PT) symmetry are proposed. The usual PT symmetry requires that the potential is invariant under complex conjugation and simultaneous reflection in all spatial…
In a previous paper we began our analysis on the role of non self-adjoint Hamiltonians in connection with the Heisenberg dynamics for quantum systems. Here, motivated by the growing interest on this topic and on some recent results on…