Related papers: Power-Law Bounds on Transfer Matrices and Quantum …
We extend the work in New J. Phys. 19, 103015 (2017) by deriving a lower bound for the minimum time necessary to implement a unitary transformation on a generic, closed quantum system with an arbitrary number of classical control fields.…
A 1-dimensional model for coherent quantum energy transfer through a complex of compressible boxes is investigated by numerical integration of the time-dependent Schr\"odinger equation. Energy is communicated from one box to the next by the…
In quantum control, quantum speed limits provide fundamental lower bounds on the time that is needed to implement certain unitary transformations. Using Lie algebraic methods, we link these speed limits to symmetries of the control…
The transport of excitation probabilities amongst weakly coupled subunits is investigated for a class of finite quantum systems. It is demonstrated that the dynamical behavior of the transported quantity depends on the considered length…
A major challenge to the control of infinite dimensional quantum systems is the irreversibility which is often present in the system dynamics. Here we consider systems with discrete-spectrum Hamiltonians operating over a Schwartz space…
In this paper we obtain upper quantum dynamical bounds as a corollary of positive Lyapunov exponent for Schr\"odinger operators $H_{f,\theta} u(n)=u(n+1)+u(n-1)+ \phi(f^n\theta)u(n)$, where $\phi : \mathcal{M}\to {\Bbb R}$ is a piecewise…
We show that the critical magnetic fields at which a few-electron quantum dot undergoes transitions between successive values of its angular momentum (M), for large M values follow a very simple power-law dependence on the effective…
In this paper we study some particular types of matrix Schr\"odinger semigroups of the form $\exp(-it\mathbb{H})$ where $\mathbb{H}\in M_N(\mathbf{C})$ is the Hamiltonian of a given quantum dynamical system modeled in the finite dimensional…
We examine the one-dimensional quantum dynamics of a Schroedinger particle in a potential represented by a generalized function of the form $U(x) = -\alpha \delta (x) + \beta d(\delta (x))/dx$ superposed on a well behaved potential $V(x)$.…
We consider the nonlinear derivative Schrodinger equation with a quintic nonlinearity, on the one dimensional torus. We exhibit that the nonlinear dynamic properties consist of four frequency modes initially excited, whose frequencies…
This note points out some bounds for the number of negative eigenvalues of Schroedinger operators with Hardy-type potentials, which follow from a simple coordinate transformation, and could prove useful in a spectral analysis of certain…
In this note we provide an explicit lower bound on the spectral gap of one-dimensional Schr\"odinger operators with non-negative bounded potentials and subject to Neumann boundary conditions.
As examples of models having interesting constraint structures, we derive a quantum mechanical model from the spatial freezing of a well known relativistic field theory - the chiral Schwinger model. We apply the Hamiltonian constraint…
We discuss the problem of consistency of quantum mechanics as applied to low energy nucleon dynamics with the symmetries of QCD. It is shown that the dynamics consistent with these symmetries is not governed by the Schrodinger equation. We…
In this paper, we analyze, by using a matrix approach, the dynamics of a non-relativistic particle in presence of a quaternionic potential barrier. The matrix method used to solve the quaternionic Schrodinger equation allows to obtain a…
We develop a computationally and numerically efficient method to calculate binding energies and corresponding wave functions of quantum mechanical three-body problems in low dimensions. Our approach exploits the tensor structure of the…
We introduce a general method for transforming the equations of motion following from a Das-Jevicki-Sakita Hamiltonian, with boundary conditions, into a boundary value problem in one-dimensional quantum mechanics. For the particular case of…
In this paper we address the problem of a particle moving in singular one dimensional potentials in the framework of quantum mechanics with minimal length. Using the momentum space representation we solve exactly the Schrodinger equation…
A contradiction arises when applying standard boundary conditions to a simple quantum rotator with a single coordinate. New boundary conditions for the Schroedinger equation are proposed that involve only gauge invariant quantities, and…
In this paper, we show that one-dimensional discrete multi-frequency quasiperiodic Schr\"odinger operators with smooth potentials demonstrate ballistic motion on the set of energies on which the corresponding Schr\"odinger cocycles are…