Related papers: Projection operator based expansion of the evoluti…
The Schwinger--DeWitt expansion for the evolution operator kernel is used to investigate analytical properties of the Schr\"odinger equation solution in time variable. It is shown, that this expansion, which is in general asymptotic,…
We present a rigorous framework to obtain evolution equations for the momentum distribution and higher order correlation functions in weakly interacting systems based on the Projection Operator Technique. These equations can be numerically…
The state of quantum systems, their energetics, and their time evolution is modeled by abstract operators. How can one visualize such operators for coupled spin systems? A general approach is presented which consists of several shapes…
The problem of defining time (or phase) operator for three-dimensional harmonic oscillator has been analyzed. A new formula for this operator has been derived. The results have been used to demonstrate a possibility of representing…
We develop a theory of the Klein-Gordon equation on curved spacetimes. Our main tool is the method of (non-autonomous) evolution equations on Hilbert spaces. This approach allows us to treat low regularity of the metric, of the…
We consider Koopman operator theory in the context of nonlinear infinite-dimensional systems, where the operator is defined over a space of bounded continuous functionals. The properties of the Koopman semigroup are described and a…
Nonlinear quantum optical systems are of paramount relevance for modern quantum technologies, as well as for the study of dissipative phase transitions. Their nonlinear nature makes their theoretical study very challenging and hence they…
With the aim of improving the reconstruction of stochastic evolution equations from empirical time-series data, we derive a full representation of the generator of the Kramers-Moyal operator via a power-series expansion of the exponential…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
This work proposes and analyzes an efficient numerical method for solving the nonlinear Schr\"odinger equation with quasiperiodic potential, where the projection method is applied in space to account for the quasiperiodic structure and the…
A mechanism deriving new well-posed evolutionary equations from given ones is inspected. It turns out that there is one particular spatial operator from which many of the standard evolutionary problems of mathematical physics can be…
Projection operators are important in Analysis, Optimization and Algorithm. It is well known that these operators are firmly nonexpansive. In this paper, we provide an exact result that sharpens this well-known result. We develop the theory…
An alternative triplet-wave expansion formalism for dimerized spin systems is presented, a modification of the 'bond operator' formalism of Sachdev and Bhatt. Projection operators are used to confine the system to the physical subspace,…
We show that the discrete operator stemming from the time and space discretization of evolutionary partial differential equations can be represented in terms of a single Sylvester matrix equation. A novel solution strategy that combines…
When deriving exact generalized master equations for the evolution of a reduced set of degrees of freedom, one is free to choose what quantities are relevant by specifying projection operators. However, obtaining a reduced description does…
We give a general procedure to obtain non perturbative evolution operators in closed form for quantized linearly polarized two Killing vector reductions of general relativity with a cosmological interpretation. We study the representation…
Utilization of a quantum system whose time-development is described by the nonlinear Schrodinger equation in the transformation of qubits would make it possible to construct quantum algorithms which would be useful in a large class of…
A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique…
For a densely defined self-adjoint operator $\mathcal{H}$ in Hilbert space $\mathcal{F}$ the operator $\exp(-it\mathcal{H})$ is the evolution operator for the Schr\"odinger equation $i\psi'_t=\mathcal{H}\psi$, i.e. if $\psi(0,x)=\psi_0(x)$…
We first rewrite the perturbation expansion of the time evolution operator [An Min Wang, quant-ph/0611216] in a form as concise as possible. Then we derive out the perturbation expansion of the time-dependent complete Green operator and…