Related papers: Quantum-based solution of time-dependent complex R…
We consider a system associated to Klein-Gordon equations with homogeneous time-dependent electric fields. The upper and lower boundaries of a time-evolution propagator for this system were proven by Veseli\'c in 1991 for electric fields…
Systems of Hamilton-Jacobi equations arise naturally when we study the optimal control problems with pathwise deterministic trajectories with random switching. In this work, we are interested in the large time behavior of weakly coupled…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…
A variety of dynamics in nature and society can be approximately treated as a driven and damped parametric oscillator. An intensive investigation of this time-dependent model from an algebraic point of view provides a consistent method to…
The discrete-time algebraic Riccati equation (DARE) have extensive applications in optimal control problems. We provide new theoretical supports to the stability properties of solutions to the DARE and reduce the convergence conditions…
We discuss the calculation of collective excitations in atomic clusters using the time-dependent local density approximation. In principle there are many formulations of the TDLDA, but we have found that a particularly efficient method for…
We study solutions to the Cauchy problem for the linear and nonlinear Schroedinger equation with a quadratic Hamiltonian depending on time. For the linear case the evolution operator can be expressed as an integral operator with the…
This paper proposes a novel lifting method which converts the standard discrete-time linear periodic system to an augmented linear time-invariant system. The linear quadratic optimal control is then based on the solution of the…
Functional relation for commuting quantum transfer matrices of quantum integrable models is identified with classical Hirota's bilinear difference equation. This equation is equivalent to the completely discretized classical 2D Toda lattice…
The generalized quantum master equation provides a powerful tool to describe the dynamics in quantum impurity models driven away from equilibrium. Two complementary approaches, one based on Nakajima--Zwanzig--Mori time-convolution (TC) and…
In this paper, inspired by Tsallis' probability distribution based on a $q$-deformed Boltzmann factor, we stipulate a new $q$-deformed quantum dynamics by applying the inverse Wick rotation $ \beta \rightarrow i t$ to the Tsallis-deformed…
The central theme of my thesis is to explore various simple prototype models that are exactly solvable in the framework of time dependent noncommutative spaces. By adopting the methodology provided by the Lewis Riesenfeld theory, we…
We obtain the complexity geometry associated with the Hamiltonian of a quantum mechanical system, specifically in cases where the Hamiltonian is explicitly time-dependent. Using Nielsen's geometric formulation of circuit complexity, we…
Non-stationary version of unitary quantum mechanics formulated in non-Hermitian (or, more precisely, in hiddenly Hermitian) interaction-picture representation is illustrated via an elementary $N$ by $N$ matrix Hamiltonian $H(t)$ mimicking a…
The generalized time-dependent harmonic oscillator is studied. Though several approaches to the solution of this model have been available, yet a new approach is presented here, which is very suitable for the study of cyclic solutions and…
TRecX is a C++ code for solving generalized inhomogeneous time-dependent Schr\"odinger-type equations $id\Psi/dt = H[t,\Psi] + \Phi$ in arbitrary dimensions and in a variety of coordinate systems. The operator $H[t,\Psi]$ may have simple…
For the description of quantum evolution, the use of a manifestly time-dependent quantum Hamiltonian $\mathfrak{h}(t) =\mathfrak{h}^\dagger(t)$ is shown equivalent to the work with its simplified, time-independent alternative $G\neq…
We illustrate through explicit numerical calculations how the Born-rule probability densities of non-relativistic quantum mechanics emerge naturally from the particle dynamics of de Broglie-Bohm pilot-wave theory. The time evolution of a…
Quantum systems driven by time-dependent Hamiltonians are considered here within the framework of steepest-entropy-ascent quantum thermodynamics (SEAQT) and used to study the thermodynamic characteristics of such systems. In doing so, a…
Emerging tensor network techniques for solutions of Partial Differential Equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultrafast numerical solutions of high-dimensional…