Related papers: Formulae for partial widths derived from the Lindb…
The Lindblad master equation is a foundational tool for modeling the dynamics of open quantum systems. As its use has extended far beyond its original domain, the boundaries of its validity have grown opaque. In particular, the rise of new…
We consider dynamical systems that are described by fractional power of coordinates and momenta. The fractional powers can be considered as a convenient way to describe systems in the fractional dimension space. For the usual space the…
Although the path-integral formalism is known to be equivalent to conventional quantum mechanics, it is not generally obvious how to implement path-based calculations for multi-qubit entangled states. Whether one takes the formal view of…
The linearized Boltzmann equation is considered to describe small spatial perturbations of the homogeneous cooling state. The corresponding macroscopic balance equations for the density, temperature, and flow velocity are derived from it as…
A fractional Hamiltonian formalism is introduced for the recent combined fractional calculus of variations. The Hamilton-Jacobi partial differential equation is generalized to be applicable for systems containing combined Caputo fractional…
An investigation of classical fields with fractional derivatives is presented using the fractional Hamiltonian formulation. The fractional Hamilton's equations are obtained for two classical field examples. The formulation presented and the…
Balance equations are derived from Enskog's kinetic equation for a two-dimensional system of hard disks using Grad's moment expansion method. This set of equations constitute an extended hydrodynamics for moderately dense bi-dimensional…
In the sciences and engineering, the concept of bandwidth is often subject to interpretation depending upon context and the requirements of a specific community. The focus of this work is to formulate this concept for a general class of…
In the framework of Lindblad theory for open quantum systems, we calculate the entropy of a damped quantum harmonic oscillator which is initially in a quasi-free state. The maximally predictable states are identified as those states…
We present analytic formulae that simplify the evaluation of the normalization of continuous spectrum stationary states in the one-dimensional Schr\"odinger equation.
Using continuation methods, we study the global solution structure of periodic solutions for a class of periodically forced equations, generalizing the case of relativistic pendulum. We obtain results on the existence and multiplicity of…
The bound state energy eigenvalues and the corresponding eigenfunctions of the generalized Woods-Saxon potential reported in [Phys. Rev. C 72, 027001 (2005)] is extended to the fractional forms using the generalized fractional derivative…
The celebrated Lindblad equation governs the non-unitary time evolution of density operators used in the description of open quantum systems. It is usually derived from the von Neumann equation for a large system, at given physical…
In the paper the generalisation of classical rate independent plasticity using fractional calculus is presented. This new formulation is non-local due to properties of applied fractional differential operator during definition of…
In this paper, we consider the indefinite fractional elliptic problem. A corresponding Liouville-type theorem for the indefinite fractional elliptic equations is established. Furthermore, we obtain a priori bound for solutions in a bounded…
Third quantization is used in open quantum systems to construct a superoperator basis in which quadratic Lindbladians can be turned into a normal form. From it follows the spectral properties of the Lindbladian, including eigenvalues and…
The Lindblad approach to open quantum systems is introduced for studying the dynamics of a single trapped ion prepared in nonclassical motional states and subjected to continuous measurement of its internal population. This results in an…
An extended Designed regression analysis of experimental data on density and refractive indices of several classes of ionic liquids yielded statistically averaged atomic volumes and polarizabilities of the constituting atoms. These values…
In this note, we propose an unbalanced version of the quantum mechanical version of optimal mass transport that was based on the Lindblad equation. We formulate a natural interpolation framework between density matrices and matrix-valued…
In this paper we obtain some new inhomogeneous Strichartz estimates for the fractional Schr\"odinger equation in the radial case. Then we apply them to the well-posedness theory for the equation $i\partial_{t}u+|\nabla|^{\alpha}u=V(x,t)u$,…