Lattice oscillator model, scattering theory and a many-body problem

We propose a model for the quantum harmonic oscillator on a discrete lattice which can be written in supersymmetric form, in contrast with the more direct discretization of the harmonic oscillator. Its ground state is easily found to be annihilated by the annihilation operator defined here, and its excitation spectrum is obtained numerically. The versatility of the model is then used to calculate, in a simple way, the generalized position-dependent scattering length for a particle colliding with a single static impurity in a periodic potential and the exact ground state of an interacting many-body problem in a one-dimensional ring.Comment: 3 Figures. Version accepted in J. Phys.

Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model

The adiabatic quantum evolution of the Lipkin-Meshkov-Glick (LMG) model across its quantum critical point is studied. The dynamics is realized by linearly switching the transverse field from an initial large value towards zero and considering different transition rates. We concentrate our attention on the residual energy after the quench in order to estimate the level of diabaticity of the evolution. We discuss a Landau-Zener approximation of the finite size LMG model, that is successful in reproducing the behavior of the residual energy as function of the transition rate in the most part of the regimes considered. We also support our description through the analysis of the entanglement entropy of the evolved state. The system proposed is a paradigm of infinite-range interaction or high-dimensional models.Comment: 8 pages, 7 figures. (v2) minor revisions, published versio

Multiple Schr\"odinger pictures and dynamics in shortcuts to adiabaticity

A Schr\"odinger equation may be transformed by unitary operators into dynamical equations in different interaction pictures which share with it a common physical frame, i.e., the same underlying interactions, processes and dynamics. In contrast to this standard scenario, other relations are also possible, such as a common interaction-picture dynamical equation corresponding to several Schr\"odinger equations that represent different physics. This may enable us to design alternative and feasible experimental routes for operations that are a priori difficult or impossible to perform. The power of this concept is exemplified by engineering Hamiltonians that improve the performance or make realizable several shortcuts to adiabaticity

Einstein-Yang-Mills-Chern-Simons solutions in D=2n+1 dimensions

We investigate finite energy solutions of the Einstein--Yang-Mills--Chern-Simons system in odd spacetime dimensions, D=2n+1, with n>1. Our configurations are static and spherically symmetric, approaching at infinity a Minkowski spacetime background. In contrast with the Abelian case, the contribution of the Chern-Simons term is nontrivial already in the static, spherically symmetric limit. Both globally regular, particle-like solutions and black holes are constructed numerically for several values of D. These solutions carry a nonzero electric charge and have finite mass. For globally regular solutions, the value of the electric charge is fixed by the Chern-Simons coupling constant. The black holes can be thought as non-linear superpositions of Reissner-Nordstrom and non-Abelian configurations. A systematic discussion of the solutions is given for D=5, in which case the Reissner-Nordstrom black hole becomes unstable and develops non-Abelian hair. We show that some of these non-Abelian configurations are stable under linear, spherically symmetric perturbations. A detailed discussion of an exact D=5 solution describing extremal black holes and solitons is also provided.Comment: 34 pages, 14 figures; v2: misprints corrected and references adde

Exact solutions of the isoholonomic problem and the optimal control problem in holonomic quantum computation

The isoholonomic problem in a homogeneous bundle is formulated and solved exactly. The problem takes a form of a boundary value problem of a variational equation. The solution is applied to the optimal control problem in holonomic quantum computer. We provide a prescription to construct an optimal controller for an arbitrary unitary gate and apply it to a $k$-dimensional unitary gate which operates on an $N$-dimensional Hilbert space with $N \geq 2k$. Our construction is applied to several important unitary gates such as the Hadamard gate, the CNOT gate, and the two-qubit discrete Fourier transformation gate. Controllers for these gates are explicitly constructed.Comment: 19 pages, no figures, LaTeX2

Rotational Doppler Effect in Magnetic Resonance

We compute the shift in the frequency of the spin resonance in a solid that rotates in the field of a circularly polarized electromagnetic wave. Electron spin resonance, nuclear magnetic resonance, and ferromagnetic resonance are considered. We show that contrary to the case of the rotating LC circuit, the shift in the frequency of the spin resonance has strong dependence on the symmetry of the receiver. The shift due to rotation occurs only when rotational symmetry is broken by the anisotropy of the gyromagnetic tensor, by the shape of the body, or by magnetocrystalline anisotropy. General expressions for the resonance frequency and power absorption are derived and implications for experiment are discussed.Comment: 8 pages, 4 figure

Speeding up critical system dynamics through optimized evolution

The number of defects which are generated on crossing a quantum phase transition can be minimized by choosing properly designed time-dependent pulses. In this work we determine what are the ultimate limits of this optimization. We discuss under which conditions the production of defects across the phase transition is vanishing small. Furthermore we show that the minimum time required to enter this regime is $T\sim \pi/\Delta$, where $\Delta$ is the minimum spectral gap, unveiling an intimate connection between an optimized unitary dynamics and the intrinsic measure of the Hilbert space for pure states. Surprisingly, the dynamics is non-adiabatic, this result can be understood by assuming a simple two-level dynamics for the many-body system. Finally we classify the possible dynamical regimes in terms of the action $s=T\Delta$.Comment: 6 pages, 6 figure

Nonequilibrium thermodynamics of interacting tunneling transport: variational grand potential, density-functional formulation, and nature of steady-state forces

The standard formulation of tunneling transport rests on an open-boundary modeling. There, conserving approximations to nonequilibrium Green function or quantum-statistical mechanics provide consistent but computational costly approaches; alternatively, use of density-dependent ballistic-transport calculations [e.g., Phys. Rev. B 52, 5335 (1995)], here denoted `DBT', provide computationally efficient (approximate) atomistic characterizations of the electron behavior but has until now lacked a formal justification. This paper presents an exact, variational nonequilibrium thermodynamic theory for fully interacting tunneling and provides a rigorous foundation for frozen-nuclei DBT calculations as a lowest order approximation to an exact nonequilibrium thermodynamics density functional evaluation. The theory starts from the complete electron nonequilibrium quantum statistical mechanics and I identify the operator for the nonequilibrium Gibbs free energy. I demonstrate a minimal property of a functional for the nonequilibrium thermodynamic grand potential which thus uniquely identifies the solution as the exact nonequilibrium density matrix. I also show that a uniqueness-of-density proof from a closely related study [Phys. Rev. B 78, 165109 (2008)] makes it possible to provide a single-particle formulation based on universal electron-density functionals. I illustrate a formal evaluation of the thermodynamics grand potential value which is closely related to the variation in scattering phase shifts and hence to Friedel density oscillations. This paper also discusses the difference between the here-presented exact thermodynamics forces and the often-used electrostatic forces. Finally the paper documents an inherent adiabatic nature of the thermodynamics forces and observes that these are suited for a nonequilibrium implementation of the Born-Oppenheimer approximation.Comment: 37 pages, 3 Figure

Faster annealing schedules for quantum annealing

New annealing schedules for quantum annealing are proposed based on the adiabatic theorem. These schedules exhibit faster decrease of the excitation probability than a linear schedule. To derive this conclusion, the asymptotic form of the excitation probability for quantum annealing is explicitly obtained in the limit of long annealing time. Its first-order term, which is inversely proportional to the square of the annealing time, is shown to be determined only by the information at the initial and final times. Our annealing schedules make it possible to drop this term, thus leading to a higher order (smaller) excitation probability. We verify these results by solving numerically the time-dependent Schrodinger equation for small size systemsComment: 10 pages, 5 figures, minor correction

External field control of donor electron exchange at the Si/SiO2 interface

We analyze several important issues for the single- and two-qubit operations in Si quantum computer architectures involving P donors close to a SiO2 interface. For a single donor, we investigate the donor-bound electron manipulation (i.e. 1-qubit operation) between the donor and the interface by electric and magnetic fields. We establish conditions to keep a donor-bound state at the interface in the absence of local surface gates, and estimate the maximum planar density of donors allowed to avoid the formation of a 2-dimensional electron gas at the interface. We also calculate the times involved in single electron shuttling between the donor and the interface. For a donor pair, we find that under certain conditions the exchange coupling (i.e. 2-qubit operation) between the respective electron pair at the interface may be of the same order of magnitude as the coupling in GaAs-based two-electron double quantum dots where coherent spin manipulation and control has been recently demonstrated (for example for donors ~10 nm below the interface and \~40 nm apart, J~10^{-4} meV), opening the perspective for similar experiments to be performed in Si.Comment: 11 pages, 15 figures. Changes in Eq. 24 plus minor typo