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Authors
M. Cemal Yalabik
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Utilization of a quantum system whose time-development is described by the nonlinear Schrodinger equation in the transformation of qubits would make it possible to construct quantum algorithms which would be useful in a large class of problems. An example of such a system for implementing the logical NOR operation is demonstrated.
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We show that a nonlinear Schrodinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory governed by a nonlinear classical wave equation to quantum theory. The classical wave equation includes a nonlinear classicality enforcing potential which when eliminated transforms the wave equation into the linear Schrodinger equation. We show that it is not necessary to completely cancel this nonlinearity to recover the linear behavior of quantum mechanics. Scaling the classicality enforcing potential is sufficient to have quantum-like features appear and is equivalent to scaling Plancks constant.
Irrotational ow of a spherical thin liquid layer surrounding a rigid core is described using the defocusing nonlinear Schrodinger equation. Accordingly, azimuthal moving nonlinear waves are modeled by periodic dark solitons expressed by elliptic functions. In the quantum regime the algebraic Bethe ansatz is used in order to capture the energy levels of such motions, which we expect to be relevant for the dynamics of the nuclear clusters in deformed heavy nuclei surface modeled by quantum liquid drops. In order to validate the model we match our theoretical energy spectra with experimental results on energy, angular momentum and parity for alpha particle clustering nuclei.
I begin by reviewing the arguments leading to a nonlinear generalisation of Schrodingers equation within the context of the maximum uncertainty principle. Some exact and perturbative properties of that equation are then summarised: those results depend on a free regulating/interpolation parameter $eta$. I discuss here how one may fix that parameter using energetics. Other issues discussed are, a linear theory with an external potential that reproduces some unusual exact solutions of the nonlinear equation, and possible symmetry enhancements in the nonlinear theory.
We consider a system of $N$ bosons interacting through a singular two-body potential scaling with $N$ and having the form $N^{3beta-1} V (N^beta x)$, for an arbitrary parameter $beta in (0,1)$. We provide a norm-approximation for the many-body evolution of initial data exhibiting Bose-Einstein condensation in terms of a cubic nonlinear Schrodinger equation for the condensate wave function and of a unitary Fock space evolution with a generator quadratic in creation and annihilation operators for the fluctuations.
Large deviation principle by the weak convergence approach is established for the stochastic nonlinear Schrodinger equation in one-dimension and as an application the exit problem is investigated.
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