Related papers: Exact Solutions of the Caldeira-Leggett Master Equ…
In this paper we motivate, formulate and analyze the Multi-Configuration Time-Dependent Hartree-Fock (MCTDHF) equations for molecular systems under Coulomb interaction. They consist in approximating the N-particle Schrodinger wavefunction…
A method to derive the charge current density and its quantum mechanical correlation from the scattering matrix is discussed for quantum scattering systems described by a time-dependent Hamiltonian operator. The current density and charge…
We write exact equations for the thermodynamic properties of a linear polymer molecule confined to walk on a lattice of finite size. The dimension of the space in which the lattice resides can be arbitrary. We also calculate polymer…
Recently it was obtained in [Tarzia, Thermal Sci. 21A (2017) 1-11] for the classical two-phase Lam\'e-Clapeyron-Stefan problem an equivalence between the temperature and convective boundary conditions at the fixed face under a certain…
We consider the vorticity formulation of the 2-D viscous Camassa-Holm equations in the whole space. We establish global existence for solutions corresponding to initial data in $L^1$ and describe the large time behavior of solutions with…
Reduced density matrices are central to describing observables in many-body quantum systems. In electronic structure theory, the two-particle reduced density matrix (2-RDM) suffices to determine the energy and other key properties. Recent…
The density matrix in the Lindblad form is used to describe the behavior of the Free-Electron Laser (FEL) operating in a quantum regime. The detrimental effects of the spontaneous emission on coherent FEL operation are taken into account.…
We determine the exact time-dependent non-idempotent one-particle reduced density matrix and its spectral decomposition for a harmonically confined two-particle correlated one-dimensional system when the interaction terms in the…
Quantum Brownian motion of a harmonic oscillator in the Markovian approximation is described by the respective Caldeira-Leggett master equation. This master equation can be brought into Lindblad form by adding a position diffusion term to…
The exact solution for a system with two-particle annihilation and decoagulation has been studied. The spectrum of the Hamiltonian of the system is found. It is shown that the steady state is two-fold degenerate. The average number density…
The Schroedinger equation with an energy-dependent complex absorbing potential, associated with a scattering system, can be reduced for a special choice of the energy-dependence to a harmonic inversion problem of a discrete pseudo-time…
In the framework of the Lindblad theory for open quantum systems the damping of the harmonic oscillator is studied. A generalization of the fundamental constraints on quantum mechanical diffusion coefficients which appear in the master…
An exact theoretical framework based on Time Dependent Density Functional Theory (TDDFT) is proposed in order to deal with the time-dependent quantum transport in fully interacting systems. We use a \textit{partition-free} approach by Cini…
We evaluate the density matrix of an arbitrary quantum mechanical system in terms of the quantities pertinent to the solution of the time-dependent density functional theory (TDDFT) problem. Our theory utilizes the adiabatic connection…
We present the first exact solution for the time dependent equations of the macroscopic fluctuation theory (MFT) for the symmetric simple exclusion process by combining a generalization of the canonical Cole-Hopf transformation with the…
In this paper we present a formulation of the unit commitment problem with AC power flow constraints. It is solved by a Benders decomposition in which the unit commitment master problem is formulated as a mixed-integer problem with…
Two coupled particles of identical masses but opposite charges, with a constant transverse external magnetic field and an external potential, interacting with a bath of harmonic oscillators are studied. We show that the problem cannot be…
We show how several important classical problems, with positive definite potential energy, can be solved by starting from the factorization of the total mechanical energy using complex numbers. In particular, we derive in a new way exact…
We prove the existence of the exact density-functional theory formalism for open electronic systems, and develop subsequently an exact time-dependent density-functional theory (TDDFT) formulation for the dynamic response. The TDDFT…
The thorough treatment of electron-lattice interactions from first principles is one of the main goals in condensed matter physics. While the commonly applied adiabatic Born-Oppenheimer approximation is sufficient for describing many…