相关论文: Energy Ambiguity in Nonlinear Quantum Mechanics

We give a general description of the system evolution under the interaction between qubit and quantum field theory up to the second order perturbation, which is also referred to as the simplified model of light-matter interaction. The…

We investigate existence and asymptotic completeness of the wave operators for nonlinear Klein-Gordon and Schr\"odinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on…

A principle is proposed according to which the dynamics of a quantum particle in a one-dimensional configuration space (OCS) is determined by a variational problem for two functionals: one is based on the mean value of the Hamilton…

Quasi-constant external fields in nonlinear electromagnetism generate a contribution to the energy-momentum tensor with the form of dark energy. To provide a thorough understanding of the origin and strength of the effects, we undertake a…

Many-body states described by a Schr\"{o}dinger equation include states of overlapping waves of non-vanishing interaction energies. These peculiar states formed in many-body transitions remain in asymptotic regions, and lead a new component…

We start from a variational model for nematic elastomers that involves two energies: mechanical and nematic. The first one consists of a nonlinear elastic energy which is influenced by the orientation of the molecules of the nematic…

First, we briefly outline some aspects of the starting project to design non-empirical energy functionals based on low-momentum vacuum interactions and many-body perturbation theory. Second, we present results obtained within an…

In this paper, classical small perturbations against a stationary solution of the nonlinear Schrodinger equation with the general form of nonlinearity are examined. It is shown that in order to obtain correct (in particular, conserved over…

In the framework of the theoretical model of the phase transition of binary solutions into spatially inhomogeneous states proposed earlier by the autors [1], which takes into account nonlinear effects, the role of the cubic in concentration…

We shall use the variational decomposition technique in order to calculate equations of motion and Noether energy-momentum complex for some classes of non-linear gravitational Lagrangians within the first-order (Palatini) formalism. In…

In this paper, we investigate the dynamics of radial solutions at threshold energy for a 3-component Schr\"{o}dinger system with cubic nonlinearity in four dimensions. The main difference from the cases previously addressed in the…

Quantum non-linear SCHROEDINGER equation is equivalent to Lieb-Liniger model. It has non-trivial conservation laws. Recently these conservation laws were used for evaluation of the three-body recombination rate for interacting gas of…

We define a deformed kinetic energy operator for a discrete position space with a finite number of points. The structure may be either periodic or nonperiodic with well-defined end points. It is shown that for the nonperiodic case the…

We review some recent results on nonlinear Schrodinger equations with potential, with emphasis on the case where the potential is a second order polynomial, for which the interaction between the linear dynamics caused by the potential, and…

We consider the nonlinear derivative Schrodinger equation with a quintic nonlinearity, on the one dimensional torus. We exhibit that the nonlinear dynamic properties consist of four frequency modes initially excited, whose frequencies…

We consider the periodic non-linear Schr\"odinger equation with non-linearity given by $|u|^{p-1}u$ for odd $p > 1$ in dimension $1$. We first establish that the difference between the non-linear evolution and a phase rotation of the the…

Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…

The spacelike reduction of the Chern-Simons Lagrangian yields a modified Nonlinear Schr\"odinger Equation (jNLS) where in the non-linearity the particle density is replaced by current. When the phase is linear in the position, this latter…

We investigate certain invariance properties of quantum fluids subject to a nonlinear gauge potential. In particular, we derive the covariant transformation laws for the nonlinear potentials under a space-time Galilean boost and consider…

Nonlinear dynamics on graphs has rapidly become a topical issue with many physical applications, ranging from nonlinear optics to Bose-Einstein condensation. Whenever in a physical experiment a ramified structure is involved, it can prove…