Related papers: On Reduced Time Evolution for Initially Correlated…
Two bounds on the minimal time of dynamic rotating an initial state by arbitrary angle have been obtained. These bounds have been applied to study the evolutions in the Hadamard-Walsch gate, the Control-NOT quantum gate, and the Grover…
We introduce a new dynamical picture, referred to as correlation picture,' which connects a correlated state to its uncorrelated counterpart. Using this picture allows us to derive an exact dynamical equation for a general open-system…
We consider a coupled system of Schr\"odinger equations, arising in quantum mechanics via the so-called time-dependent self-consistent field method. Using Wigner transformation techniques we study the corresponding classical limit dynamics…
We present a theory of modified reduced dynamics in the presence of counting fields. Reduced dynamics techniques are useful for describing open quantum systems at long emergent timescales when the memory timescales are short. However, they…
We study the evolution of a general open quantum system when the system and its environment are initially correlated. We show that the trace distance between two states of the open system can increase above its initial value, and derive…
We discuss a new approach to solve the low lying states of the Schroedinger equation. For a fairly large class of problems, this new approach leads to convergent iterative solutions, in contrast to perturbative series expansions. These…
The correlated projection superoperator techniques provide a better understanding about how correlations lead to strong non-Markovian effects in open quantum systems. Their superoperators are independent of initial state, which may not be…
Time evolution of initially prepared entangled state in the system of coupled quantum dots has been analyzed by means of two different theoretical approaches: equations of motion for the all orders localized electron correlation functions,…
The trace distance between two states of an open quantum system quantifies their distinguishability, and for a fixed environmental state can increase above its initial value only in the presence of initial system-environment correlations.…
We prove unique continuation properties for solutions of the evolution Schr\"odinger equation with time dependent potentials. As an application of our method we also obtain results concerning the possible concentration profiles of blow up…
In this work, we investigate the dynamics of an inhomogeneous coupled nonlinear Schrodinger system with quadratic-type interactions. Such systems arise naturally in nonlinear dynamics and mathematical physics, particularly in nonlinear…
We develop a novel approach to the coupled motion of electrons and ions that focuses on the dynamics of the electronic subsystem. Usually the description of electron dynamics involves an electronic Schr\"odinger equation where the nuclear…
The amount of correlation attainable between the components of a quantum system is constrained if the system is closed. We provide some examples, largely from the field of quantum thermodynamics, where knowing the maximal possible variation…
The time dependent complex Schr\"odinger equation with cubic nonlinearity is solved by constructing differential quadrature algorithm based on sinc functions. Reduction to a coupled system of real equations enables to approach the space…
We apply technique developed in [2] to study the long-time behavior of Schrodinger evolution.
We propose a new approach for the solution of initial value problems for integrable evolution equations in the periodic setting based on the unified transform. Using the nonlinear Schr\"odinger equation as a model example, we show that the…
It is shown that the Schrodinger equation can be cast in the form of two coupled real conservation equations, in Euclidean spacetime in the free case and in a five-dimensional Eisenhart geometry in the presence of an external potential.…
The basic concepts of classical mechanics are given in the operator form. Then, the hybrid systems approach, with the operator formulation of both quantum and classical sector, is applied to the case of an ideal nonselective measurement. It…
A non-Markovian stochastic Schroedinger equation for a quantum system coupled to an environment of harmonic oscillators is presented. Its solutions, when averaged over the noise, reproduce the standard reduced density operator without any…
We review a new iterative procedure to solve the low-lying states of the Schroedinger equation, done in collaboration with Richard Friedberg. For the groundstate energy, the $n^{th}$ order iterative energy is bounded by a finite limit,…