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Some Connections Between Stochastic Mechanics, Optimal Control, and Nonlinear Schrödinger Equations
We first recall how the quantum mechanics of N particles is related, in the limit of large N, to certain nonlinear Schrödinger equations, used also...
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Multilinear Smoothing and Local Well-Posedness of a Stochastic Quadratic Nonlinear Schrödinger Equation
In this article, we study a d -dimensional stochastic quadratic nonlinear Schrödinger equation (SNLS), driven by a fractional derivative (of order
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Spectral theory of the multi-frequency quasi-periodic operator with a Gevrey type perturbation
In this paper we study the multi-frequency quasi-periodic operator with a Gevrey type perturbation. We first establish the large deviation theorem...
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Random numerical stability of attractors for nonlinear Schrodinger equations on infinite lattices
We study both numerical and random approximations of the global attractor for the nonlinear Schrodinger lattice equation. First, for a discrete-time...
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Multi solitary waves to stochastic nonlinear Schrödinger equations
In this paper, we present a pathwise construction of multi-soliton solutions for focusing stochastic nonlinear Schrödinger equations with linear...
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Gap Labelling for Discrete One-Dimensional Ergodic Schrödinger Operators
In this survey, we give an introduction to and proof of the gap labelling theorem for discrete one-dimensional ergodic Schrödinger operators via the...
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Mixed Random-Quasiperiodic Cocycles
We introduce the concept of mixed random-quasiperiodic linear cocycles. We characterize the ergodicity of the base dynamics and establish a large...
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On Spectral Problems of Discrete Schrödinger Operators
A special type of Jacobi matrices, discrete Schrödinger operators, is found to play an important role in quantum physics. In this paper, we show that...
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Fast Huygens Swee** Methods for a Class of Nonlocal Schrödinger Equations
We present efficient numerical methods for solving a class of nonlinear Schrödinger equations involving a nonlocal potential. Such a nonlocal...
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Entanglement of Pseudo-Hermitian Random States
By using an abstract model of pseudo-Hermitian random matrices and Dyson’s scheme to deal with density matrix of non-Hermitian matrix, the...
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Fractal Dimension of Random Attractor for a Stochastic Lattice System with White Noise
In this paper, it was studied the finite fractal dimension of random attractor for the stochastic Klein-Gordon-Schrödinger (KGS) lattice equation...
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A Second-Order Fast Huygens Swee** Method for Time-Dependent Schrödinger Equations with Perfectly Matched Layers
The time-dependent Schrödinger equation is generally challenging to solve numerically since the problem is often defined in the infinite domain and...
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Schrödinger operators with potentials generated by hyperbolic transformations: I—positivity of the Lyapunov exponent
We consider discrete one-dimensional Schrödinger operators whose potentials are generated by sampling along the orbits of a general hyperbolic...
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Blow-Up of States in the Dynamics Given by the Schrödinger Equation with a Power-Law Nonlinearity in the Potential
AbstractWe study specific features of the dynamics of quantum states generated by the focusing nonlinear Schrödinger equation. Relationships between...
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Numerical Integrators for Continuous Disordered Nonlinear Schrödinger Equation
In this paper, we consider the numerical solution of the continuous disordered nonlinear Schrödinger equation, which contains a spatial random...
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Large Deviations Principles for Symplectic Discretizations of Stochastic Linear Schrödinger Equation
In this paper, we consider the large deviations principles (LDPs) for the stochastic linear Schrödinger equation and its symplectic discretizations....
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Random tensors, propagation of randomness, and nonlinear dispersive equations
We introduce the theory of random tensors , which naturally extends the method of random averaging operators in our earlier work (Deng et al. in:...
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A stochastic thermalization of the Discrete Nonlinear Schrödinger Equation
We introduce a mass conserving stochastic perturbation of the discrete nonlinear Schrödinger equation that models the action of a heat bath at a...