Search results for "Hamiltonian"
showing 10 items of 662 documents
Random Walk in a N-cube Without Hamiltonian Cycle to Chaotic Pseudorandom Number Generation: Theoretical and Practical Considerations
2017
Designing a pseudorandom number generator (PRNG) is a difficult and complex task. Many recent works have considered chaotic functions as the basis of built PRNGs: the quality of the output would indeed be an obvious consequence of some chaos properties. However, there is no direct reasoning that goes from chaotic functions to uniform distribution of the output. Moreover, embedding such kind of functions into a PRNG does not necessarily allow to get a chaotic output, which could be required for simulating some chaotic behaviors. In a previous work, some of the authors have proposed the idea of walking into a $\mathsf{N}$-cube where a balanced Hamiltonian cycle has been removed as the basis o…
Laplacian versus Adjacency Matrix in Quantum Walk Search
2015
A quantum particle evolving by Schr\"odinger's equation contains, from the kinetic energy of the particle, a term in its Hamiltonian proportional to Laplace's operator. In discrete space, this is replaced by the discrete or graph Laplacian, which gives rise to a continuous-time quantum walk. Besides this natural definition, some quantum walk algorithms instead use the adjacency matrix to effect the walk. While this is equivalent to the Laplacian for regular graphs, it is different for non-regular graphs, and is thus an inequivalent quantum walk. We algorithmically explore this distinction by analyzing search on the complete bipartite graph with multiple marked vertices, using both the Lapla…
The spin-1/2 Kagome XXZ model in a field: competition between lattice nematic and solid orders
2016
We study numerically the spin-1/2 XXZ model in a field on an infinite Kagome lattice. We use different algorithms based on infinite Projected Entangled Pair States (iPEPS) for this, namely: (i) with simplex tensors and 9-site unit cell, and (ii) coarse-graining three spins in the Kagome lattice and mapping it to a square-lattice model with nearest-neighbor interactions, with usual PEPS tensors, 6- and 12-site unit cells. Similarly to our previous calculation at the SU(2)-symmetric point (Heisenberg Hamiltonian), for any anisotropy from the Ising limit to the XY limit, we also observe the emergence of magnetization plateaus as a function of the magnetic field, at $m_z = \frac{1}{3}$ using 6-…
Transfer of arbitrary two-qubit states via a spin chain
2015
We investigate the fidelity of the quantum state transfer (QST) of two qubits by means of an arbitrary spin-1/2 network, on a lattice of any dimensionality. Under the assumptions that the network Hamiltonian preserves the magnetization and that a fully polarized initial state is taken for the lattice, we obtain a general formula for the average fidelity of the two qubits QST, linking it to the one- and two-particle transfer amplitudes of the spin-excitations among the sites of the lattice. We then apply this formalism to a 1D spin chain with XX-Heisenberg type nearest-neighbour interactions adopting a protocol that is a generalization of the single qubit one proposed in Ref. [Phys. Rev. A 8…
Hyperspectral optical near-field imaging: Looking graded photonic crystals and photonic metamaterials in color
2012
International audience; Using a scanning near-field optical microscope operating with a hyperspectral detection scheme, we report the direct observation of the mirage effect within an on-chip integrated artificial material made of a two dimensional graded photonic crystal. The light rainbow due to the material dispersion is quantified experimentally and quantitatively compared to three dimensional plane wave assisted Hamiltonian optics predictions of light propagation.
Scattering theory for a class of fermionic Pauli–Fierz models
2004
Abstract The scattering theory for a class of fermionic Pauli–Fierz models is considered. We give a proof of the asymptotic completeness of the dynamics in the case of massive fermions. The result applied to the Hamiltonian of a quantized spin- 1 2 Dirac particle interacting with an external field through a cutoff Yukawa interaction and to the Hamiltonian of a system of finitely many confined particles coupled to a fermionic field with a quadratic interaction.
Minimal change list for Lucas strings and some graph theoretic consequences
2005
AbstractWe give a minimal change list for the set of order p length-n Lucas strings, i.e., the set of length-n binary strings with no p consecutive 1's nor a 1ℓ prefix and a 1m suffix with ℓ+m⩾p. The construction of this list proves also that the order p n-dimensional Lucas cube has a Hamiltonian path if and only if n is not a multiple of p+1, and its second power always has a Hamiltonian path.
Quantum Nekhoroshev Theorem for Quasi-Periodic Floquet Hamiltonians
1998
A quantum version of Nekhoroshev estimates for Floquet Hamiltonians associated to quasi-periodic time dependent perturbations is developped. If the unperturbed energy operator has a discrete spectrum and under finite Diophantine conditions, an effective Floquet Hamiltonian with pure point spectrum is constructed. For analytic perturbations, the effective time evolution remains close to the original Floquet evolution up to exponentially long times. We also treat the case of differentiable perturbations.
Diffusive energy growth in classical and quantum driven oscillators
1991
We study the long-time stability of oscillators driven by time-dependent forces originating from dynamical systems with varying degrees of randomness. The asymptotic energy growth is related to ergodic properties of the dynamical system: when the autocorrelation of the force decays sufficiently fast one typically obtains linear diffusive growth of the energy. For a system with good mixing properties we obtain a stronger result in the form of a central limit theorem. If the autocorrelation decays slowly or does not decay, the behavior can depend on subtle properties of the particular model. We study this dependence in detail for a family of quasiperiodic forces. The solution involves the ana…
Dynamical stability of a many-body Kapitza pendulum
2015
We consider a many-body generalization of the Kapitza pendulum: the periodically-driven sine-Gordon model. We show that this interacting system is dynamically stable to periodic drives with finite frequency and amplitude. This finding is in contrast to the common belief that periodically-driven unbounded interacting systems should always tend to an absorbing infinite-temperature state. The transition to an unstable absorbing state is described by a change in the sign of the kinetic term in the effective Floquet Hamiltonian and controlled by the short-wavelength degrees of freedom. We investigate the stability phase diagram through an analytic high-frequency expansion, a self-consistent vari…