517,612 research outputs found
P.A.M. Dirac and the Discovery of Quantum Mechanics
Dirac's contributions to the discovery of non-relativistic quantum mechanics
and quantum electrodynamics, prior to his discovery of the relativistic wave
equation, are described
Higher-order integrable evolution equation and its soliton solutions
We consider an extended nonlinear Schrödinger equation with higher-order odd and even terms with
independent variable coefficients. We demonstrate its integrability, provide its Lax pair, and, applying
the Darboux transformation, present its first and second order soliton solutions. The equation and its
solutions have two free parameters. Setting one of these parameters to zero admits two limiting cases:
the Hirota equation on the one hand and the Lakshmanan–Porsezian–Daniel (LPD) equation on the other
hand. When both parameters are zero, the limit is the nonlinear Schrödinger equation.A.A. and N.A. acknowledge the support of the Australian Research
Council (Discovery Project DP110102068) and also thank
the Volkswagen Foundation for financial support
Approach to first-order exact solutions of the Ablowitz-Ladik equation
We derive exact solutions of the Ablowitz-Ladik (A-L) equation using a special ansatz that linearly relates the real and imaginary parts of the complex function. This ansatz allows us to derive a family of first-order solutions of the A-L equation with two independent parameters. This novel technique shows that every exact solution of the A-L equation has a direct analog among first-order solutions of the nonlinear Schrödinger equation (NLSE).Two of the authors (A.A. and N.A.) acknowledge the
support of the Australian Research Council (Discovery Project
No. DP0985394). N.A. is a grateful recipient of support from
the Alexander von Humboldt Foundation (Germany)
Data-driven PDE discovery with evolutionary approach
The data-driven models allow one to define the model structure in cases when
a priori information is not sufficient to build other types of models. The
possible way to obtain physical interpretation is the data-driven differential
equation discovery techniques. The existing methods of PDE (partial derivative
equations) discovery are bound with the sparse regression. However, sparse
regression is restricting the resulting model form, since the terms for PDE are
defined before regression. The evolutionary approach described in the article
has a symbolic regression as the background instead and thus has fewer
restrictions on the PDE form. The evolutionary method of PDE discovery (EPDE)
is described and tested on several canonical PDEs. The question of robustness
is examined on a noised data example
An introduction to operational quantum dynamics
In the summer of 2016, physicists gathered in Torun, Poland for the 48th
annual Symposium on Mathematical Physics. This Symposium was special; it
celebrated the 40th anniversary of the discovery of the
Gorini-Kossakowski-Sudarshan-Lindblad master equation, which is widely used in
quantum physics and quantum chemistry. This article forms part of a Special
Volume of the journal Open Systems & Information Dynamics arising from that
conference; and it aims to celebrate a related discovery -- also by Sudarshan
-- that of Quantum Maps (which had their 55th anniversary in the same year).
Nowadays, much like the master equation, quantum maps are ubiquitous in physics
and chemistry. Their importance in quantum information and related fields
cannot be overstated. In this manuscript, we motivate quantum maps from a
tomographic perspective, and derive their well-known representations. We then
dive into the murky world beyond these maps, where recent research has yielded
their generalisation to non-Markovian quantum processes.Comment: Submitted to Special OSID volume "40 years of GKLS
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