Related papers: On the non-linearity of the master equation descri…
Recently, spin-selective radical pair reactions have been studied using concepts from quantum measurement theory. In this Article, we show that the approach taken by Kominis (Physical Review E, 83, 2011, 056118) leads to erroneous results…
Radical-ion-pair reactions were recently shown to represent a rich biophysical laboratory for the application of quantum measurement theory methods and concepts. We here show that radical-ion-pair reactions essentially form a non-linear…
Spin-selective reactions of radical pairs have traditionally been modelled theoretically by adding phenomenological rate equations to the quantum mechanical equation of motion of the radical pair spin density matrix. More recently an…
We derive a new representation for spin-spin correlation functions of the finite XXZ spin-1/2 Heisenberg chain in terms of a single multiple integral, that we call the master equation. Evaluation of this master equation gives rise on the…
In his Comment on a recent paper by two of us Kominis claims that the recently proposed quantum measurement model for spin-selective reactions of radical pairs leads to ambiguous predictions in a simple case. Here we show that this claim is…
The quantum master equation obtained by generalizing the geometric formulation of nonequilibrium thermodynamics to dissipative quantum systems is seriously nonlinear. We argue that nonlinearity occurs naturally in the step from reversible…
A master equation ( $n$ dimensional non--Abelian current conservation law with mutually commuting current components ) is introduced for multi-dimensional non-linear field theories. It is shown that the master equation provides a systematic…
Radical pair recombination reactions are normally described using a quantum mechanical master equation for the electronic and nuclear spin density operator. The electron spin state selective (singlet and triplet) recombination processes are…
In theories of spin-dependent radical pair reactions, the time evolution of the radical pair, including the effect of the chemical kinetics, is described by a master equation in the Liouville formalism. For the description of the chemical…
In an effort to provide an alternative method to represent a quantum spin, a precise nonlinear dynamics semi-classical model is used to show that standard quantum spin analysis can be obtained. The model includes a multi-body,…
Nonlinear complexity is an important measure for assessing the randomness of sequences. In this paper we investigate how circular shifts affect the nonlinear complexities of finite-length binary sequences and then reveal a more explicit…
This article is dedicated to the proof of the existence of classical solutions for a class of non-linear integral variational problems. Those problems are involved in nonlocal image and signal processing.
Magnetic field effects on radical pair reactions arise due to the interplay of coherent electron spin dynamics and spin relaxation effects, a rigorous treatment of which requires the solution of the Liouville-von Neumann equation. However,…
The fully nonlinear governing equations for spin 1/2 quantum plasmas are presented. Starting from the Pauli equation, the relevant plasma equations are derived, and it is shown that nontrivial quantum spin couplings arise, enabling studies…
We present a general method based on nonlinear response theory to obtain effective interactions between ions in an electron gas which can also be applied to other systems where an adiabatic separation of time-scales is possible. Nonlinear…
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…
We obtain novel nonlinear Schr\"{o}dinger-Pauli equations through a formal non-relativistic limit of appropriately constructed nonlinear Dirac equations. This procedure automatically provides a physical regularisation of potential…
The quantum master equation obtained from two different thermodynamic arguments is seriously nonlinear. We argue that, for quantum systems, nonlinearity occurs naturally in the step from reversible to irreversible equations and we analyze…
It is is explained why physical consistency requires substituting linear observables by nonlinear ones for quantum systems with nonlinear time evolution of pure states. The exact meaning and the concrete physical interpretation are…
The so-called "phenomenological" kinetic equation for one-pair density operator for spin-selective reactions is defended. We derive this equation from the kinetic equation for density operator of all pairs which are treated as singlet and…