Related papers: Upper limit on the acceleration of a quantum evolu…
We investigate the roles of the relativistic effect on the speed of evolution of a quantum system coupled with amplitude damping channels. We find that the relativistic effect speed-up the quantum evolution to a uniform evolution speed of…
In quantum physics, disturbance due to a measurement is not negligible. This requires the time parameter $t$ in the Schr\"odinger or Heisenberg equation to be considered differently from a time continuum of experimenter's clock $T$ on which…
We show that the total time of evolution from the initial quantum state to final quantum state and then back to the initial state, i.e., making a round trip along the great circle over S^2, must have a lower bound in quantum mechanics, if…
The influence of the noncommutativity on the average speed of a relativistic electron interacting with a uniform magnetic field within the minimum evolution time is investigated. We find that it is possible for the wave packet of the…
We exactly solve a quantum Fermi accelerator model consisting of a time-independent non-Hermitian Hamiltonian with time-dependent Dirichlet boundary conditions. A Hilbert space for such systems can be defined in two equivalent ways, either…
Inequalities of Mandelstam-Tamm and Margolus-Levitin type provide lower bounds on the time it takes for a quantum system to evolve from one state into another. Knowledge of such bounds, called quantum speed limits, is of utmost importance…
We introduce a framework for computing time-dependent quantum transition rates (QTRs) that describe the pace of evolution of a quantum state from a given subspace to a target subspace. QTRs are expressed in terms of flux-flux correlators…
A genuine feature of projective quantum measurements is that they inevitably alter the mean energy of the observed system if the measured quantity does not commute with the Hamiltonian. Compared to the classical case, Jacobs proved that…
We investigate the question of unitarity of evolution between hypersurfaces in quantum field theory in curved spacetime from the perspective of the general boundary formulation. Unitarity thus means unitarity of the quantum operator that…
We use geometric concepts originally proposed by Anandan and Aharonov to show that the Farhi-Gutmann time optimal analog quantum search evolution between two orthogonal quantum states is characterized by unit efficiency dynamical…
Motivated by the research on upper bounds on the rate of quantum transport for one-dimensional operators, particularly, the recent works of Jitomirskaya--Liu and Jitomirskaya--Powell and the earlier ones of Damanik--Tcheremchantsev, we…
To find and realize the optimal evolution between two states is significant both in theory and application. In quantum mechanics, the minimal evolution is bounded by the gap between the largest and smallest eigenvalue of the Hamiltonian. In…
The evaluation of the minimal evolution time between two distinguishable states of a system is important for assessing the maximal speed of quantum computers and communication channels. Lower bounds for this minimal time have been proposed…
We address the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. Complexity is understood here as the shortest geodesic distance between the…
Finding the solutions of the equations that describe the dynamics of a given physical system is crucial in order to obtain important information about its evolution. However, by using estimation theory, it is possible to obtain, under…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
We investigate the evolution of a single qubit subject to a continuous unitary dynamics and an additional interrupting influence which occurs periodically. One may imagine a dynamically evolving closed quantum system which becomes open at…
The aim of this dissertation is to clarify the debate over the explanation of quantum speedup and to submit a tentative resolution to it. In particular, I argue that the physical explanation for quantum speedup is precisely the fact that…
Stochastic dynamics of a quantum system driven by $N$ statistically independent random sudden quenches in a fixed time interval is studied. We reveal that with growing $N$ the system approaches a deterministic limit indicating…
The linear growth of operators in local quantum systems leads to an effective lightcone even if the system is non-relativistic. We show that consistency of diffusive transport with this lightcone places an upper bound on the diffusivity: $D…