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In this work, we propose an experimentally feasible nonlinear optical realization of a type of non-integrable phase found in interacting quantum systems at quantum phase transitions. We show that an exotic term in the dynamical equation…
Several simple models of strongly correlated bosons on three-dimensional lattices have been shown to possess exotic fractionalized Mott insulating phases with a gapless `photon' excitation. In this paper we show how to view the physics of…
We investigate the influence of boundaries and spatial nonreciprocity on nonequilibrium driven-dissipative phase transitions. We focus on a one-dimensional lattice of nonlinear bosons described by a Lindblad master equation, where the…
Quantum degenerate cold-atom gases provide a remarkable opportunity to study strongly interacting systems. Recent experimental progress in producing ultracold polar molecules with a net electric dipole moment opens up new possibilities to…
We study a family of Laguerre--Sobolev orthogonal polynomials associated with a Sobolev inner product arising from second--order boundary value problems on the semi--infinite interval $(0,+\infty)$. These polynomials generate an orthogonal…
In two recent articles a detailed study has been presented of the out of equilibrium dynamics of an infinite system of self-gravitating points initially located on a randomly perturbed lattice. In this article we extend the treatment of the…
For reproducing the anomalous -- i.e., sub- or super-diffusive -- behavior in some stochastic dynamical systems, the Generalized Langevin Equation (GLE) has gained considerable popularity in recent years. Motivated by the question whether…
This paper explores the feasibility of quantum simulation for partial differential equations (PDEs) with physical boundary or interface conditions. Semi-discretisation of such problems does not necessarily yield Hamiltonian dynamics and…
The paper interprets the cubic nonlinear Schr\"odinger equation as a Hamiltonian system with infinite dimensional phase space. There is a Gibbs measure which is invariant under the flow associated with the canonical equations of motion. The…
Quantum phase transitions in the two-dimensional Kugel-Khomski model on a square lattice are studied using the plaquette mean field theory and the entanglement renormalization ansatz. When $3z^2-r^2$ orbitals are favored by the crystal…
Exceptional orthogonal Hermite and Laguerre polynomials have been linked to the k-step extension of harmonic and singular oscillators. The exceptional polynomials allow the existence of different supercharges from the Darboux-Crum and…
We study the dynamics and the phase-space structures of Coulombic and self-gravitating versions of the classical one-dimensional 3-body system with periodic boundary conditions. We demonstrate that such a 3-body system may be reduced…
Orbital physics plays a significant role for a vast number of important phenomena in complex condensed matter systems such as high-T$_c$ superconductivity and unconventional magnetism. In contrast, phenomena in superfluids -- especially in…
The system of a cold atomic gas in an optical lattice is governed by two factors: nonlinearity originating from the interparticle interaction, and the periodicity of the system set by the lattice. The high level of controllability…
Phase transitions and the associated symmetry breaking are at the heart of many physical phenomena. Coupled systems with multiple interacting degrees of freedom provide a fertile ground for emergent dynamics that is otherwise inaccessible…
Recent studies have found an unusual way of dissociation in formaldehyde. It can be characterized by a hydrogen atom that separates from the molecule, but instead of dissociating immediately it roams around the molecule for a considerable…
We show that the extended attractive Hubbard model on a square lattice hosts a variety of superconducting phases, including exotic mixed-symmetry phases with $d_{x^2-y^2} + {\rm i} [s + d_{x^2+y^2}]$ and $ d_{x^2-y^2} + p_{x}$ symmetries,…
Recent advances in the study of synthetic dimensions revealed a possibility to employ the frequency space as an additional degree of freedom which allows for investigating and exploiting higher-dimensional phenomena in a priori…
We study phase transitions and the nature of order in a class of classical generalized $O(N)$ nonlinear $\sigma$-models (NLS) constructed by minimally coupling pure NLS with additional degrees of freedom in the form of (i) Ising…
We investigate elastic, inelastic, and coalescent collisions between two-dimensional flat-top solitons supported by the cubic-quintic nonlinear Schr\"odinger equation. Numerical simulations reveal distinct collision regimes ranging from…