Browsing by Subject "Hamiltonians"
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Item Open Access Computational modeling of quantum-confined impact ionization in Si nanocrystals embedded in SiO2(2007) Sevik, C.; Bulutay, C.Injected carriers from the contacts to delocalized bulk states of the oxide matrix via Fowler-Nordheim tunneling can give rise to quantum-confined impact ionization (QCII) of the nanocrystal (NC) valence electrons. This process is responsible for the creation of confined excitons in NCs, which is a key luminescence mechanism. For a realistic modeling of QCII in Si NCs, a number of tools are combined: ensemble Monte Carlo (EMC) charge transport, ab initio modeling for oxide matrix, pseudopotential NC electronic states together with the closed-form analytical expression for the Coulomb matrix element of the QCII. To characterize the transport properties of the embedding amorphous SiO2, ab initio band structure and density of states of the α-quartz phase of SiO2 are employed. The confined states of the Si NC are obtained by solving the atomistic pseudopotential Hamiltonian. With these ingredients, realistic modeling of the QCII process involving a SiO2 bulk state hot carrier and the NC valence electrons is provided.Item Open Access A Hamiltonian-based solution to the mixed sensitivity optimization problem for stable pseudorational plants(Elsevier, 2005-11) Kashima, K.; Özbay, Hitay; Yamamoto, Y.This paper considers the mixed sensitivity optimization problem for a class of infinite-dimensional stable plants. This problem is reducible to a two- or one-block H∞ control problem with structured weighting functions. We first show that these weighting functions violate the genericity assumptions of existing Hamiltonian-based solutions such as the well-known Zhou-Khargonekar formula. Then, we derive a new closed form formula for the computation of the optimal performance level, when the underlying plant structure is specified by a pseudorational transfer function.Item Open Access A model-based scheme for anticontrol of some chaotic systems(World Scientific Publishing, 2003) Morgül, Ö.We consider a model-based approach for the anticontrol of some continuous time systems. We assume the existence of a chaotic model in an appropriate form. By using a suitable input, we match the dynamics of the controlled system and the chaotic model. We show that controllable systems can be chaotifled with the proposed method. We give a procedure to generate such chaotic models. We also apply an observer-based synchronization scheme to compute the required input.Item Open Access A model-based scheme for anticontrol of some discrete-time chaotic systems(World Scientific, 2004) Morgül, Ö.We consider a model-based approach for the anticontrol of some discrete-time systems. We first assume the existence of a chaotic model in an appropriate form. Then by using an appropriate control input we try to match the controlled system with the chaotic system model. We also give a procedure to generate the model chaotic systems in arbitrary dimensions. We show that with this approach, controllable systems can always be chaotified. Moreover, if the system to be controlled is stable, control input can be chosen arbitrarily small.Item Open Access Non-local, non-commutative picture in quantum mechanics and distinguished continuous canonical maps(IOP Science, 2002) Hakioglu, T.It is shown that continuous classical nonlinear canonical (Poisson) maps have a distinguished role in quantum mechanics. They act unitarily on the quantum phase space and generate h-independent quantum nonlinear canonical maps. It is also shown that such maps act in the non-commutative phase space under the classical covariance. A crucial result of the work is that under the action of Poisson maps a local quantum mechanical picture is converted onto a non-local picture which is then represented in a non-local Hilbert space. On the other hand, it is known that a non-local picture is equivalent by the Weyl map to a non-commutative picture which, in the context of this work, corresponds to a phase space formulation of the theory. As a result of this equivalence, a phase space Schrödinger picture can be formulated. In particular, we obtain the *-genvalue equation of Fairlie [Proc. Camb. Phil. Soc., 60, 581 (1964)] and Curtright, Fairlie and Zachos [Phys. Rev., D 58, 025002 (1998)]. In a non-local picture entanglement becomes a crucial concept. The connection between the entanglement and non-locality is explored in the context of Poisson maps and specific examples of the generation of entanglement from a local wavefunction are provided by using the concept of generalized Bell states. The results obtained are also relevant for the non-commutative soliton picture in the non-commutative field theories. We elaborate on this in the context of the scalar non-commutative field theory.Item Open Access Nonthermal Quantum Channels as a Thermodynamical Resource(American Physical Society, 2015) Navascués, M.; García-Pintos L.P.Quantum thermodynamics can be understood as a resource theory, whereby thermal states are free and the only allowed operations are unitary transformations commuting with the total Hamiltonian of the system. Previous literature on the subject has just focused on transformations between different state resources, overlooking the fact that quantum operations which do not commute with the total energy also constitute a potentially valuable resource. In this Letter, given a number of nonthermal quantum channels, we study the problem of how to integrate them in a thermal engine so as to distill a maximum amount of work. We find that, in the limit of asymptotically many uses of each channel, the distillable work is an additive function of the considered channels, computable for both finite dimensional quantum operations and bosonic channels. We apply our results to bound the amount of distillable work due to the natural nonthermal processes postulated in the Ghirardi-Rimini-Weber (GRW) collapse model. We find that, although GRW theory predicts the possibility of extracting work from the vacuum at no cost, the power which a collapse engine could, in principle, generate is extremely low. © 2015 American Physical Society. © 2015 American Physical Society.Item Open Access Parity effect in mesoscopic and nanoscopic superconducting particles(Elsevier B.V., 2001) Kulik, I. O.; Boyaci, H.; Gedik, Z.Superconductivity in small metallic specimens is studied with regard to the size dependence of the parity gap (ΔP), a parameter distinguishing between the energy of even and odd number of electrons in the granule. ΔP is shown to be an increasing function of level spacing δ. The energy gap of superconductor Δ, on the other hand, decreases with increasing δ and vanishes at δ = δc which is of the order of Δ. However, non-zero value of ΔP persists above δc in a gapless superconducting-insulating state. Level degeneracy in small specimens having perfect geometry changes the size dependence of the parity gap, the Josephson effect, and flux quantization. Parity gap is evaluated using an interpolation procedure between the continuum limit (δ ≪ Δ), the moderate mesoscopic regime (δ ∼ Δ), and the nanoscopic scale (δ ≫ Δ), for which an exact solution to the pairing problem is provided with the numeric diagonalization of system Hamiltonian in a small metallic clusterItem Open Access Persistent perfect entanglement in atomic systems(IOP, 2004) Çakır, Özgür; Can, M. Ali; Klyachko, Alexander A.; Shumovsky, Alexander S.It is shown that the system of an even number of three-level atoms in the Λ configuration in a cavity can evolve into a persistent maximum entangled state. The time of formation of such an entangled state is estimated.Item Open Access Spontaneous and persistent currents in superconductive and mesoscopic structures(American Institute of Physics, 2004) Kulik, I. O.We briefly review aspects of superconductive persistent currents in Josephson junctions of the S/I/S, S/O/S and S/N/S types, focusing on the origin of jumps in the current versus phase dependences, and discuss in more detail the persistent as well as «spontaneous» currents in the Aharonov-Bohm mesoscopic and nanoscopic (macromolecular) structures. A fixed-number-of- electrons mesoscopic or macromolecular conducting ring is shown to be unstable against structural transformation removing spatial symmetry (in particular, azimuthal periodicity) of its electron-lattice Hamiltonian. In case when the transformation is blocked by strong coupling to an external azimuthally symmetric environment, the system becomes bistable in its electronic configuration at certain number of electrons. At such a condition, the persistent current has a nonzero value even at the (almost) zero applied Aharonov-Bohm flux, and results in very high magnetic susceptibility dM/dH at small nonzero fields, followed by an oscillatory dependence at larger fields. We tentatively assume that previously observed oscillatory magnetization in cyclic metallo-organic molecules by Gatteschi et al. can be attributed to persistent currents. If this proves correct, it may open an opportunity (and, more generally, macromolecular cyclic structures may suggest the possibility) of engineering quantum computational tools based on the Aharonov-Bohm effect in ballistic nanostructures and macromolecular cyclic aggregates.Item Open Access Vortex lattice of a Bose-Einstein condensate in a rotating anisotropic trap(American Physical Society, 2004) Oktel, M. Ö.The behavior of Bose-Einstein condensates (BEC) with a vortex lattice in a rotating anisotropic trap was studied. The single-particle wave functions for a rotating anisotropy trap were found by exactly diagonalizing the Hamiltonian. The wave functions in the lowest Landau level (LLL) were shown to be written as simple analytic functions in the small anisotropy limit. The results show that the regularity of the vortex configurations observed in an axisymmetric trap is disturbed by the anisotropy of the confinement.