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For nonlinear dispersive systems, the nonlinear Schr\"odinger (NLS) equation can usually be derived as a formal approximation equation describing slow spatial and temporal modulations of the envelope of a spatially and temporally…
We derive an effective nonpolynomial Schrodinger equation (NPSE) for self-repulsive or attractive BEC in the nearly-1D cigar-shaped trap, with the transverse confining frequency periodically modulated along the axial direction. Besides the…
An important goal is to understand better the relation between full loop quantum gravity (LQG) and the simplified, reduced theory known as loop quantum cosmology (LQC), {\em directly at the quantum level}. Such a firmer understanding would…
We introduce a new structure preserving, second order in time relaxation-type scheme for approximating solutions of the Schr\"odinger-Poisson system. More specifically, we use the Crank-Nicolson scheme as a time stepping mechanism, whilst…
A quantum time topological space is developed and applied to solve some problems about quantum theory. It is disconnected and satifies specific separation axioms. The degree of disconnectedness of the time-space is a decreasing function of…
The question of whether features and behaviors that are characteristic to completely integrable systems persist in the transition to non-integrable settings is a central one in the field of nonlinear dispersive equations. In this work, we…
When using Einstein's equations, there exist a number of techniques for embedding non-linear structures in cosmological backgrounds. These include Swiss cheese models, in which spherically symmetric vacua are patched onto Friedmann…
The quantum evolution equation of Loop Quantum Cosmology (LQC) -- the quantum Hamiltonian constraint -- is a difference equation. We relate the LQC constraint equation in vacuum Bianchi I separable (locally rotationally symmetric) models…
We develop resonance-based low-regularity numerical integrators for stochastic Schr"odinger equations with additive $Q$-Wiener noise, covering both the linear equation with rough potential and the cubic nonlinear case. For the linear…
We consider the Cauchy problem for the integrable nonlocal nonlinear Schr\"odinger (NNLS) equation $ \I\partial_t q(x,t)+\partial_{x}^2q(x,t)+2\sigma q^{2}(x,t)\overline{q(-x,t)}=0 $ with initial data $q(x,0)\in H^{1,1}(\mathbb{R})$. It is…
We study the non-equilibrium dynamics obtained by an abrupt change (a {\em quench}) in the parameters of an integrable classical field theory, the nonlinear Schr\"odinger equation. We first consider explicit one-soliton examples, which we…
We consider PT-symmetric, nonlocal nonlinear Schrodinger equation on metric graphs. Vertex boundary conditions are derived from the conservation laws. Soliton solutions are obtained for simplest graph topologies, such as star and tree…
In this paper, we study integrable multilayer spin systems, namely, the multilayer M-LIII equation. We investigate their relation with the geometric flows of interacting curves and surfaces in some space $R^{n}$. Then we present their the…
We investigate the coupling between the nonlinear Schr\"odinger equation and the inviscid Burgers equation, a system which models interactions between short and long waves, for instance in fluids. Well-posedness for the associated Cauchy…
Based upon the intrinsic symmetries approach to inhomogeneous cosmologies, we propose an exact solution to Einstein's field equations where the spatial sections are flat and the source is a non-perfect fluid such that the dissipative terms…
The Schwinger model (quantum electrodynamics in 1+1 dimensions) is a testbed for the study of quantum gauge field theories. We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and…
We prove new local and global well-posedness results for the cubic one-dimensional nonlinear Schr\"odinger equation in modulation spaces. Local results are obtained via multilinear interpolation. Global results are proven using conserved…
We study the problem of the boundary conditions in the numerical simulation of closed and open quantum systems, described by a Schr\"odinger equation. On one hand, we show that a closed quantum system is defined by local boundary…
If there exists a formulation of quantum mechanics which does not refer to a background classical spacetime manifold, it then follows as a consequence, (upon making one plausible assumption), that a quantum description of gravity should be…
A new integrable nonlocal nonlinear Schroedinger (NLS) equation with clear physical motivations is proposed. This equation is obtained from a special reduction of the Manakov system, and it describes Manakov solutions whose two components…