Quantum Fidelity Decay of Quasi-Integrable Systems

We show, via numerical simulations, that the fidelity decay behavior of quasi-integrable systems is strongly dependent on the location of the initial coherent state with respect to the underlying classical phase space. In parallel to classical fidelity, the quantum fidelity generally exhibits Gaussian decay when the perturbation affects the frequency of periodic phase space orbits and power-law decay when the perturbation changes the shape of the orbits. For both behaviors the decay rate also depends on initial state location. The spectrum of the initial states in the eigenbasis of the system reflects the different fidelity decay behaviors. In addition, states with initial Gaussian decay exhibit a stage of exponential decay for strong perturbations. This elicits a surprising phenomenon: a strong perturbation can induce a higher fidelity than a weak perturbation of the same type.Comment: 11 pages, 11 figures, to be published Phys. Rev.

Rapid induction of false memory for pictures

In this thesis, a new procedure is proposed which achieves the rapid induction of false recognition memory for rich pictorial stimuli. Chapter 2 presents the basic three-step procedure in which participants study some pictures, imagine others in response to words, and perform a picture recognition test. Imagining pictures leads to a false alarm rate of 27% above baseline (Experiments 1a and 1b). In Chapter 3, a source monitoring test is used to demonstrate that this effect is not solely due to diffuse familiarity (Experiment 2) and does not appear to be driven by perceptual processing (Experiment 3). Chapter 4 investigates whether imagination impairs discrimination between studied and new items presented side by side. On a two-alternative forced choice test, participants are less accurate in indicating the studied picture when it is paired with an imagined picture than when paired with a new picture (Experiment 4). The role of indirect tests in verbal false memory research and the value of applying them to pictorial stimuli is discussed in Chapter 5. An indirect perceptual identification test previously used for words is adapted to pictures and shown to be highly perceptually driven (Experiment 5). Chapter 6 presents consistent evidence for the lack of perceptual priming of imagined items in the current procedure despite high levels of false recognition (Experiments 6-7), again indicating that the effect is conceptually driven. Chapter 7 discusses how the new procedure presented in the thesis can further our understanding of the similarities and differences between true and false memories

Equilibrium Configuration of Black Holes and the Inverse Scattering Method

The inverse scattering method is applied to the investigation of the equilibrium configuration of black holes. A study of the boundary problem corresponding to this configuration shows that any axially symmetric, stationary solution of the Einstein equations with disconnected event horizon must belong to the class of Belinskii-Zakharov solutions. Relationships between the angular momenta and angular velocities of black holes are derived.Comment: LaTeX, 14 pages, no figure

Local well-posedness and blow up in the energy space for a class of L2 critical dispersion generalized Benjamin-Ono equations

We consider a family of dispersion generalized Benjamin-Ono equations (dgBO) which are critical with respect to the L2 norm and interpolate between the critical modified (BO) equation and the critical generalized Korteweg-de Vries equation (gKdV). First, we prove local well-posedness in the energy space for these equations, extending results by Kenig, Ponce and Vega concerning the (gKdV) equations. Second, we address the blow up problem in the spirit of works of Martel and Merle on the critical (gKdV) equation, by studying rigidity properties of the (dgBO) flow in a neighborhood of solitons. We prove that when the model is close to critical (gKdV), solutions of negative energy close to solitons blow up in finite or infinite time in the energy space. The blow up proof requires in particular extensions to (dgBO) of monotonicity results for localized versions of L2 norms by pseudo-differential operator tools.Comment: Submitte

Semi-optimal Practicable Algorithmic Cooling

Algorithmic Cooling (AC) of spins applies entropy manipulation algorithms in open spin-systems in order to cool spins far beyond Shannon's entropy bound. AC of nuclear spins was demonstrated experimentally, and may contribute to nuclear magnetic resonance (NMR) spectroscopy. Several cooling algorithms were suggested in recent years, including practicable algorithmic cooling (PAC) and exhaustive AC. Practicable algorithms have simple implementations, yet their level of cooling is far from optimal; Exhaustive algorithms, on the other hand, cool much better, and some even reach (asymptotically) an optimal level of cooling, but they are not practicable. We introduce here semi-optimal practicable AC (SOPAC), wherein few cycles (typically 2-6) are performed at each recursive level. Two classes of SOPAC algorithms are proposed and analyzed. Both attain cooling levels significantly better than PAC, and are much more efficient than the exhaustive algorithms. The new algorithms are shown to bridge the gap between PAC and exhaustive AC. In addition, we calculated the number of spins required by SOPAC in order to purify qubits for quantum computation. As few as 12 and 7 spins are required (in an ideal scenario) to yield a mildly pure spin (60% polarized) from initial polarizations of 1% and 10%, respectively. In the latter case, about five more spins are sufficient to produce a highly pure spin (99.99% polarized), which could be relevant for fault-tolerant quantum computing.Comment: 13 pages, 5 figure

Quantum Sensor Miniaturization

The classical bound on image resolution defined by the Rayleigh limit can be beaten by exploiting the properties of quantum mechanical entanglement. If entangled photons are used as signal states, the best possible resolution is instead given by the Heisenberg limit, an improvement proportional to the number of entangled photons in the signal. In this paper we present a novel application of entanglement by showing that the resolution obtained by an imaging system utilizing separable photons can be achieved by an imaging system making use of entangled photons, but with the advantage of a smaller aperture, thus resulting in a smaller and lighter system. This can be especially valuable in satellite imaging where weight and size play a vital role.Comment: 3 pages, 1 figure. Accepted for publication in Photonics Technology Letter

Stable self-similar blow-up dynamics for slightly L2L^2-supercritical generalized KdV equations

In this paper we consider the slightly $L^2$-supercritical gKdV equations $\partial_t u+(u_{xx}+u|u|^{p-1})_x=0$, with the nonlinearity $5<p<5+\varepsilon$ and $0<\varepsilon\ll 1$ . We will prove the existence and stability of a blow-up dynamic with self-similar blow-up rate in the energy space $H^1$ and give a specific description of the formation of the singularity near the blow-up time.Comment: 38 page

Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons

We present a unified approach for qualitative and quantitative analysis of stability and instability dynamics of positive bright solitons in multi-dimensional focusing nonlinear media with a potential (lattice), which can be periodic, periodic with defects, quasiperiodic, single waveguide, etc. We show that when the soliton is unstable, the type of instability dynamic that develops depends on which of two stability conditions is violated. Specifically, violation of the slope condition leads to an amplitude instability, whereas violation of the spectral condition leads to a drift instability. We also present a quantitative approach that allows to predict the stability and instability strength

Implementation of the Quantum Fourier Transform

The quantum Fourier transform (QFT) has been implemented on a three bit nuclear magnetic resonance (NMR) quantum computer, providing a first step towards the realization of Shor's factoring and other quantum algorithms. Implementation of the QFT is presented with fidelity measures, and state tomography. Experimentally realizing the QFT is a clear demonstration of NMR's ability to control quantum systems.Comment: 6 pages, 2 figure