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We consider a class of deterministic local collisional dynamics, showing how to approximate them by means of stochastic models and then studying the fluctuations of the current of energy. We show first that the variance of the time-integrated current is finite and related to the conductivity by...
We evaluate Shannon entropy for the position and momentum eigenstates of some conditionally exactly solvable potentials which are isospectral to harmonic oscillator and whose solutions are given in terms of exceptional orthogonal polynomials. The Bialynicki–Birula–Mycielski inequality has...
In this paper we provide a sufficient condition for regularity of solutions to the 3D nematic liquid crystal flow in the entire space in terms of one directional derivative of the velocity field. More precisely, we prove that if ∂ 3 u belongs to L β (0,T;L α ( R 3 )) with 3 α + 2 β ≤1 and...
Starting from approximate Skyrmion solutions obtained using the rational map ansatz, improved approximate Skyrmions are constructed using scaling arguments. Although the energy improvement is small, the change of shape clarifies whether the true Skyrmions are more oblate or prolate.
By introducing a new set of independent variables, we first transform a modified two-component Camassa–Holm shallow water system into a semilinear system. To obtain a dissipative solution, we modify the corresponding system into a discontinuous system. Then we map the solution of system to the...
The d’Alembert–Lagrange principle (DLP) is designed primarily for dynamical systems under ideal geometric constraints. Although it can also cover linear-velocity constraints, its application to nonlinear kinematic constraints has so far remained elusive, mainly because there is no clear...
In this paper we attempt to give a new understanding of quantum double-slit interference of fermions in the framework of general nonlocality (GN) J. Math. Phys. 49 , 033513 (2008) by studying the self-(inter)action of matter wave. From the metric of the GN, we derive a special formalism to...
The purpose of this paper is to investigate the Cauchy problem for the Gross–Pitaevskii infinite linear hierarchy of equations on R n , n ⩾ 1. We prove local existence and uniqueness of solutions in certain Sobolev-type spaces H ξ α of sequences of marginal density operators with α > n /2....
A Lyapunov operator is a self-adjoint quantum observable whose expectation value varies monotonically as time increases and may serve as a marker for the flow of time in a quantum system. In this paper it is shown that the existence of a certain type of Lyapunov operator leads to representations...
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