Related papers: The Hautus test for non-autonomous linear evolutio…
The time evolution of correlation functions in statistical systems is described by an exact functional differential equation for the corresponding generating functionals. This allows for a systematic discussion of non-equilibrium physics…
We study conditions for the well-posedness of nonautonomous perturbation of evolution equations of the form \[ u'(t)=(A+B(t))u(t), \quad t \in [a,b], \] where $A$ generates a $\mathrm{C}_0$-semigroup $\left (T(t)\right )_{t\ge 0}$ with $\|…
The exact controllability to the origin for linear evolution control equation is considered.The problem is investigated by its transformation to infinite linear moment problem. Conditions for the existence of solution for infinite linear…
Two models of candidates for hereditary symmetry operators are proposed and thus many nonlinear systems of evolution equations possessing infinitely many commutative symmetries may be generated. Some concrete structures of hereditary…
In this paper we study the evolution operator of a time-dependent Hamiltonian in the three level system. The evolution operator is based on $SU(3)$ and its dimension is $8$, so we obtain three complex Riccati differential equations…
We provide general product formulas for the solutions of non-autonomous abstract Cauchy problems. The main technical tool is the application of evolution semigroup methods, allowing the direct application of existing results on autonomous…
We discuss time dependent quantum systems on bounded domains. Our work may be viewed as a framework for several models, including linear iterations involved in time dependent density functional theory (TDDFT), the Hartree-Fock model, or…
We derive a Riemann--Hilbert representation for the solution of an integrable nonlinear evolution equation with a $3 \times 3$ Lax pair. We use the derived representation to obtain formulas for the long-time asymptotics.
Recently hybrid evolutionary computation (EC) techniques are successfully implemented for solving large sets of linear equations. All the recently developed hybrid evolutionary algorithms, for solving linear equations, contain both the…
All non-equivalent integrable evolution equations of the fifth order of the form $u_t=D_x\frac{\delta H}{\delta u}$ are found.
In this work we construct an approximate time evolution operator for a system composed by two coupled Jaynes-Cummings Hamiltonians. We express the full time evolution operator as a product of exponentials and we analyze the validity of our…
We discuss linear autonomous evolution equations on function spaces which have the property that a positive initial value leads to a solution which initially changes sign, but then becomes - and stays - positive again for sufficiently large…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…
We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators $H(t)$ that generate a real phase in their time-evolution. This involves the use of invariant operators $I_{PH}(t)$ that are pseudo-Hermitian with…
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially…
Linear evolution PDE $\partial_t u(x,t) = -\mathcal{L} u$, where $\mathcal{L}$ is a strongly elliptic operator independent of time, is studied as an example to show if one can superpose snapshots of a single (or a finite number of)…
The design space of networked embedded systems is very large, posing challenges to the optimisation of such platforms when it comes to support applications with real-time guarantees. Recent research has shown that a number of inter-related…
In a number of model contexts, evolution across space-time singularities (reminiscent of the cosmological singularities) involves time-dependent quantum Hamiltonians developing a singularity as a function of time. In this contribution to…
The initial-boundary value problems for linear non-autonomous first order evolution equations are examined. Our assumptions provide a unified treatment which is applicable to many situations, where the domains of the operators may change…
We consider a class of space-time coupled evolution equations (CEEs), obtained by a subordination of the heat operator. Our CEEs reformulate and extend known governing equations of non-Markovian processes arising as scaling limits of…