Related papers: Particle Trajectories for Quantum Maps
Weak quantum measurements enable real-time tracking and control of dynamical quantum systems, producing quantum trajectories -- evolutions of the quantum state of the system conditioned on measurement outcomes. For classical systems, the…
The statistics of quantum transport through chaotic cavities with two leads is encoded in transport moments $M_m={\rm Tr}[(t^\dag t)^m]$, where $t$ is the transmission matrix, which have a known universal expression for systems without…
We present a method for obtaining evolution operators for linear quantum trajectories. We apply this to a number of physical examples of varying mathematical complexity, in which the quantum trajectories describe the continuous projection…
We study classical and quantum maps on the torus phase space, in the presence of noise. We focus on the spectral properties of the noisy evolution operator, and prove that for any amount of noise, the quantum spectrum converges to the…
Quantum state estimation, based on the numerical integration of stochastic master equations (SMEs), provides estimates for the evolution of quantum systems subject to continuous weak measurements. The approach is similar to classical state…
Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…
The effect of repetitive measurement for quantum dynamics of driven by an intensive external force of the simple few-level systems as well as of the multilevel systems that exhibit the quantum localisation of classical chaos is…
We present a semiclassical analysis of the quantum propagator of a particle confined on one side by a steeply, monotonically rising potential. The models studied in detail have potentials proportional to $x^{\alpha}$ for $x>0$; the limit…
Theoretical tools used in processing continuous measurement records from real experiments to obtain quantum trajectories can easily lead to numerical errors due to a non-infinitesimal time resolution. In this work, we propose a systematic…
We present a new model for the continuous measurement of a coupled quantum dot charge qubit. We model the effects of a realistic measurement, namely adding noise to, and filtering, the current through the detector. This is achieved by…
We consider highly inaccurate measurements made on classical stochastic and quantum systems. In the quantum case such a \e{weak} measurement preserves coherence between the system's alternatives. We demonstrate that in both cases the…
A century after its conception, quantum mechanics still hold surprises that contradict many "common sense" notions. The contradiction is especially sharp in case one consider trajectories of truly quantum objects such as single photons.…
We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from…
A common knowledge suggests that trajectories of particles in quantum mechanics always have quantum uncertainties. These quantum uncertainties set by the Heisenberg uncertainty principle limit precision of measurements of fields and forces,…
We define a class of dynamical systems on the sphere analogous to the baker map on the torus. The classical maps are characterized by dynamical entropy equal to ln 2. We construct and investigate a family of the corresponding quantum maps.…
We investigate if the degradation of a quantum directional reference frame through repeated use can be modeled as a classical direction undergoing a random walk on a sphere. We demonstrate that the behaviour of the fidelity for a degrading…
Electronic transport through chaotic quantum dots exhibits universal behaviour which can be understood through the semiclassical approximation. Within the approximation, transport moments reduce to codifying classical correlations between…
We investigate the behavior of quantum trajectories conditioned on measurement outcomes. Under a condition related to the absence of so-called dark subspaces, K\"{u}mmerer and Maassen had shown that such trajectories almost surely purify in…
We study the quantum tunnel effect through a potential barrier employing a semiclassical formulation of quantum mechanics based on expectation values of configuration variables and quantum dispersions as dynamical variables. The evolution…
We describe a quantum perturbative approach to evaluating the phase shift of an atom interferometer in a weakly anharmonic trap. This provides a simple way to evaluate quantum corrections to the standard semi-classical approximation. The…