Related papers: Effective Hamiltonian, Mori Product and Quantum Dy…
We discuss the properties of superintegrable Hamiltonian systems, in particular those that admit separation of variables in cartesian coordinates. We show that the superintegrability of such potentials is equivalent to the isochronicity of…
The quantization of a constant of motion for the harmonic oscillator with a time-explicitly depending external force is carried out. This quantization approach is compared with the normal Hamiltonian quantization approach. Numerical results…
The method of the effective action for the composite operators $\Phi^2(x)$ and $\Phi^4(x)$ is applied to the termodynamics of the scalar quantum field with $\lambda\Phi^4$ interaction. An expansion of the finite temperature effective…
We discuss a general and efficient approach for "bootstrapping" short-time correlation data in chaotic or complex quantum systems to obtain information about long-time dynamics and stationary properties, such as the local density of states.…
General analytical solutions of the Quantum Hamilton Jacobi Equation for conservative one-dimensional or reducible motion are presented and discussed. The quantum Hamilton's characteristic function and its derivative, i.e. the quantum…
How useful is a quantum dynamical operation for quantum information processing? Motivated by this question we investigate several strength measures quantifying the resources intrinsic to a quantum operation. We develop a general theory of…
This thesis offers novel strategies for the measurement of quantum correlations present in controllable quantum systems, as well as for a full-fledged implementation of the models of light-matter interaction through which these correlations…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
The statistical mechanical properties of interacting quantum fields in terms of the dynamics of the correlation functions are investigated. We show how the Dyson - Schwinger equations may be derived from a formal action functional, the…
We consider 1D lattices described by Hubbard or Bose-Hubbard models, in the presence of periodic high-frequency perturbations, such as uniform ac force or modulation of hopping coefficients. Effective Hamiltonians for interacting particles…
The Hamiltonian operator plays a central role in quantum theory being a generator of unitary quantum dynamics. Its expectation value describes the energy of a quantum system. Typically being a non-unitary operator, the action of the…
For quantum systems with competing potentials, the conventional perturbation theory often yields an asymptotic series and the subsequent numerical outcome becomes uncertain. To tackle such kind of problems, we develop a general solution…
The dissociation of molecules, even the most simple hydrogen molecule, cannot be described accurately within density functional theory because none of the currently available functionals accounts for strong on-site correlation. This problem…
A new method for controlling harmonic generation, in the framework of quantum optimal control theory (QOCT), is developed. The problem is formulated in the frequency domain using a new maximization functional. The relaxation method is used…
An analytical description of polymer melts and their mixtures as liquids of interacting soft colloidal particles is obtained from liquid-state theory. The derived center-of-mass pair correlation functions with no adjustable parameters…
Microscopically conserving reduced models of many-body systems have a long, highly successful history. Established theories of this type are the random-phase approximation for Coulomb fluids and the particle-particle ladder model for…
We derive a local approximation for the correlation energy in two-dimensional electronic systems. In the derivation we follow the scheme originally developed by Colle and Salvetti for three dimensions, and consider a Gaussian approximation…
This contribution presents a derivation of the steady-state distribution of velocities and distances of driven particles on a onedimensional periodic ring. We will compare two different situations: (i) symmetrical interaction forces…
The dynamics of classical and quantum systems which are driven by a high frequency ($\omega$) field is investigated. For classical systems the motion is separated into a slow part and a fast part. The motion for the slow part is computed…
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…