Related papers: Uniform dynamical bounds for the Fibonacci Hamilto…
We consider transport exponents associated with the dynamics of a wavepacket in a discrete one-dimensional quantum system and develop a general method for proving upper bounds for these exponents in terms of the norms of transfer matrices…
We develop further the approach to upper and lower bounds in quantum dynamics via complex analysis methods which was introduced by us in a sequence of earlier papers. Here we derive upper bounds for non-time averaged outside probabilities…
Following the Killip-Kiselev-Last method, we prove quantum dynamical upper bounds for discrete one-dimensional Schr\"odinger operators with Sturmian potentials. These bounds hold for sufficiently large coupling, almost every rotation…
The Fibonacci Hamiltonian, that is a Schr\"{o}dinger operator associated to a quasiperiodical sturmian potential with respect to the golden mean has been investigated intensively in recent years. Damanik and Tcheremchantsev developed a…
We derive rigorous upper bounds on the distance between quantum states in an open system setting, in terms of the operator norm between the Hamiltonians describing their evolution. We illustrate our results with an example taken from…
I obtain the dynamics of the continuous time quantum walk on a $d$-dimensional lattice, with periodic boundary conditions, as an appropriate limit of the dynamics of the discrete time quantum walk on the same lattice. This extends the main…
We study two versions of quasicrystal model, both subcases of Jacobi matrices. For Off-diagonal model, we show an upper bound of dynamical exponent and the norm of the transfer matrix. We apply this result to the Off-diagonal Fibonacci…
Quantum dynamical lower bounds for continuous and discrete one-dimensional Dirac operators are established in terms of transfer matrices. Then such results are applied to various models, including the Bernoulli-Dirac one and, in contrast to…
In this article we address the issue of uniqueness for differential and algebraic operator Riccati equations, under a distinctive set of assumptions on their unbounded coefficients. The class of boundary control systems characterized by…
One method to determine whether or not a system of partial differential equations is consistent is to attempt to construct a solution using merely the "algebraic data" associated to the system. In technical terms, this translates to the…
In this paper we investigate the limits of control for mixed-state quantum systems. The constraint of unitary evolution for non-dissipative quantum systems imposes kinematical bounds on the optimization of arbitrary observables. We…
Hamilton's equations of motion are local differential equations and boundary conditions are required to determine the solution uniquely. Depending on the choice of boundary conditions, a Hamiltonian may thereby describe several different…
A method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random (possibly correlated) Jacobi matrix. As an application, one obtains sharp upper bounds…
We consider divergence form operators with complex coefficients on an open subset of Euclidean space. Boundary conditions in the corresponding parabolic problem are dynamical, that is, the time derivative appears on the boundary. As a…
Leveraging quantum information geometry, we derive generalized quantum speed limits on the rate of change of the expectation values of observables. These bounds subsume and, for Hilbert space dimension $\geq 3$, tighten existing bounds --…
We prove that a variety of oscillatory and polynomial Carleson operators are uniformly bounded on the family of parameters under considerations. As a particular application of our techniques, we prove uniform bounds for oscillatory Carleson…
We derive a uniform bound for the difference of two contractive semigroups, if the difference of their generators is form-bounded by the Hermitian parts of the generators themselves. We construct a semigroup dynamics for second order…
We study quantum transport for the discrete one-dimensional random Jacobi operator of divergence-gradient type. For strictly positive and bounded random variables, we analyze the q-moments of the position operator and establish both upper…
Analog quantum simulators with global control fields have emerged as powerful platforms for exploring complex quantum phenomena. Despite these advances, a fundamental theoretical question remains unresolved: to what extent can such systems…
We present general, computable, improvable, and rigorous bounds for the total energy of a finite heterogeneous volume element or a periodically distributed unit cell of an elastic composite of any known distribution of inhomogeneities of…