3,494 research outputs found

    Robustness of adiabatic passage trough a quantum phase transition

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    We analyze the crossing of a quantum critical point based on exact results for the transverse XY model. In dependence of the change rate of the driving field, the evolution of the ground state is studied while the transverse magnetic field is tuned through the critical point with a linear ramping. The excitation probability is obtained exactly and is compared to previous studies and to the Landau-Zener formula, a long time solution for non-adiabatic transitions in two-level systems. The exact time dependence of the excitations density in the system allows to identify the adiabatic and diabatic regions during the sweep and to study the mesoscopic fluctuations of the excitations. The effect of white noise is investigated, where the critical point transmutes into a non-hermitian ``degenerate region''. Besides an overall increase of the excitations during and at the end of the sweep, the most destructive effect of the noise is the decay of the state purity that is enhanced by the passage through the degenerate region.Comment: 16 pages, 15 figure

    Stochastic perturbation of sweeping process and a convergence result for an associated numerical scheme

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    Here we present well-posedness results for first order stochastic differential inclusions, more precisely for sweeping process with a stochastic perturbation. These results are provided in combining both deterministic sweeping process theory and methods concerning the reflection of a Brownian motion. In addition, we prove convergence results for a Euler scheme, discretizing theses stochastic differential inclusions.Comment: 30 page

    Correlation density matrices for 1- dimensional quantum chains based on the density matrix renormalization group

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    A useful concept for finding numerically the dominant correlations of a given ground state in an interacting quantum lattice system in an unbiased way is the correlation density matrix. For two disjoint, separated clusters, it is defined to be the density matrix of their union minus the direct product of their individual density matrices and contains all correlations between the two clusters. We show how to extract from the correlation density matrix a general overview of the correlations as well as detailed information on the operators carrying long-range correlations and the spatial dependence of their correlation functions. To determine the correlation density matrix, we calculate the ground state for a class of spinless extended Hubbard models using the density matrix renormalization group. This numerical method is based on matrix product states for which the correlation density matrix can be obtained straightforwardly. In an appendix, we give a detailed tutorial introduction to our variational matrix product state approach for ground state calculations for 1- dimensional quantum chain models. We show in detail how matrix product states overcome the problem of large Hilbert space dimensions in these models and describe all techniques which are needed for handling them in practice.Comment: 50 pages, 34 figures, to be published in New Journal of Physic

    Density Matrix Renormalization Group study on incommensurate quantum Frenkel-Kontorova model

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    By using the density matrix renormalization group (DMRG) technique, the incommensurate quantum Frenkel-Kontorova model is investigated numerically. It is found that when the quantum fluctuation is strong enough, the \emph{g}-function featured by a saw-tooth map in the depinned state will show a different kind of behavior, similar to a standard map, but with reduced magnitude. The related position correlations are studied in details, which leads to a potentially interesting application to the recently well-explored phase transitions in cold atoms loaded in optical lattices.Comment: 11 figures, submitted to Phys. Rev.

    Quantum computing with a single molecular ensemble and a Cooper pair box

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    We propose to encode quantum information in rotational excitations in a molecular ensemble. Using a stripline cavity field for quantum state transfer between the molecular ensemble and a Cooper pair box two-level system, our proposal offers a linear scaling of the number of qubits in our register with the number of rotationally excited states available in the molecules.Comment: 4 pages, 3 figures Minor corrections from reviewing proces

    A discrete contact model for crowd motion

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    The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: We first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people; The actual velocity is then computed as the projection of the spontaneous velocity onto the set of admissible velocities (i.e. velocities which do not violate the non-overlapping constraint). We describe here the underlying mathematical framework, and we explain how recent results by J.F. Edmond and L. Thibault on the sweeping process by uniformly prox-regular sets can be adapted to handle this situation in terms of well-posedness. We propose a numerical scheme for this contact dynamics model, based on a prediction-correction algorithm. Numerical illustrations are finally presented and discussed.Comment: 22 page

    A variational method based on weighted graph states

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    In a recent article [Phys. Rev. Lett. 97 (2006), 107206], we have presented a class of states which is suitable as a variational set to find ground states in spin systems of arbitrary spatial dimension and with long-range entanglement. Here, we continue the exposition of our technique, extend from spin 1/2 to higher spins and use the boson Hubbard model as a non-trivial example to demonstrate our scheme.Comment: 36 pages, 13 figure

    Transport of interface states in the Heisenberg chain

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    We demonstrate the transport of interface states in the one-dimensional ferromagnetic Heisenberg model by a time dependent magnetic field. Our analysis is based on the standard Adiabatic Theorem. This is supplemented by a numerical analysis via the recently developed time dependent DMRG method, where we calculate the adiabatic constant as a function of the strength of the magnetic field and the anisotropy of the interaction.Comment: minor revision, final version; 13 pages, 4 figure
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