Related papers: On Reduced Time Evolution for Initially Correlated…
The mixed states are important in quantum optics since they frequently appear in the decoherence problems. When one of the components of the system is prepared in the mixed state and the evolution operator of this system is not available,…
We investigate the mechanism in the tunneling dynamics of open ultracold few-boson systems by numerically solving the time-dependent few-boson Schr\"{o}dinger equation exactly. By starting from a weakly repulsive, initially coherent…
A derivation of the time-dependent Schr\"odinger equation from the time-independent one is considered. Instead of time, the coordinate of an additional degree of freedom, the clock, is introduced into the original time-independent…
Following a recent proposal of L. Wang and D. Babikov, J. Chem. Phys. 137, 064301 (2012), we theoretically illustrate the possibility of using the motional states of a $Cd^+$ ion trapped in a slightly anharmonic potential to simulate the…
We establish a generic method to analyze the time evolution of open quantum many-body systems. Our approach is based on a variational integration of the quantum master equation describing the dynamics and naturally connects to a variational…
This paper explores the feasibility of quantum simulation for partial differential equations (PDEs) with physical boundary or interface conditions. Semi-discretisation of such problems does not necessarily yield Hamiltonian dynamics and…
We characterize to what extent it is possible to modify the stationary states of a quantum dynamical semigroup, that describes the irreversible evolution of a two-level system, by means of an auxiliary two-level system. We consider systems…
Non-positive Markov approximations are sometimes used to describe the dynamics of qubits in weak interaction with suitable environments; the appearance of negative probabilities is avoided by assuming that the transient regime eliminates…
This work is concerned with the time optimal control problem for evolution equations in Hilbert spaces. The attention is focused on the maximum principle for the time optimal controllers having the dimension smaller that of the state…
A variety of physically relevant bilinear Schr\"odinger equations are known to be approximately controllable in large times. There are however examples which are approximately controllable in large times, but not in small times. This…
The dynamical behavior of interacting systems plays a fundamental role for determining quantum correlations, such as entanglement. In this Letter, we describe temporal quantum effects of the inseparable evolution of composite quantum states…
We propose a reconstruction of the initial system of ordinary differential equations from a single observed variable. The suggested approach is applied to a certain class of systems which includes, in particular, the Rossler system and…
We present solutions of the time dependent Schrodinger equation for a SQUID ring coupled to an electromagnetic field, both treated quantum mechanically. We that show the SQUID ring can be used to create a maximally entangled state with the…
We study symmetry properties of the Schr\"odinger equation with the potential as a new dependent variable, i.e., the transformations which do not change the form of the class of equations. We also consider systems of the Schr\"odinger…
We consider systems of weakly coupled Schr\"odinger equations with nonconstant potentials and we investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and…
It is shown that a large subset of initial data with finite energy ($L^2$ norm)evolves nearly linearly in nonlinear Schr\" odinger equation with periodic boundary conditions. These new solutions are not perturbations of the known ones such…
We consider the motion of a non relativistic quantum particle in R^3 subject to n point interactions which are moving on given smooth trajectories. Due to the singular character of the time-dependent interaction, the corresponding…
The dynamics of a single quantum state embedded in one or several (quasi-)continua is one of the most studied phenomena in quantum mechanics. In this work we investigate its discrete analogue and consider short and long time dynamics based…
Using a variational approach based on a Lagrangian formulation and Gaussian trial functions, we derive a simple dynamical system that captures the main features of the time-dependent Schr\"odinger-Newton equations. With little analytical or…
We consider the inverse coefficient problem of simultaneously determining the space dependent electromagnetic potential, the zero-th order coupling term and the first order coupling vector of a two-state Schr\"odinger equation in a bounded…