Quantum Spin Dynamics and Quantum Computation

We describe a simulation method for a quantum spin model of a generic, general purpose quantum computer. The use of this quantum computer simulator is illustrated through several implementations of Grover's database search algorithm. Some preliminary results on the stability of quantum algorithms are presented.Comment: 6 pages, 4 figures ; Minor errors corrected and figures update

Quantum Nonlinear Switching Model

We present a method, the dynamical cumulant expansion, that allows to calculate quantum corrections for time-dependent quantities of interacting spin systems or single spins with anisotropy. This method is applied to the quantum-spin model \hat{H} = -H_z(t)S_z + V(\bf{S}) with H_z(\pm\infty) = \pm\infty and \Psi (-\infty)=|-S> we study the quantity P(t)=(1-_t/S)/2. The case V(\bf{S})=-H_x S_x corresponds to the standard Landau-Zener-Stueckelberg model of tunneling at avoided-level crossing for N=2S independent particles mapped onto a single-spin-S problem, P(t) being the staying probability. Here the solution does not depend on S and follows, e.g., from the classical Landau-Lifshitz equation. A term -DS_z^2 accounts for particles' interaction and it makes the model nonlinear and essentially quantum mechanical. The 1/S corrections obtained with our method are in a good accord with a full quantum-mechanical solution if the classical motion is regular, as for D>0.Comment: 4 Phys. Rev. pages 2 Fig

Effects of nonlinear sweep in the Landau-Zener-Stueckelberg effect

We study the Landau-Zener-Stueckelberg (LZS) effect for a two-level system with a time-dependent nonlinear bias field (the sweep function) W(t). Our main concern is to investigate the influence of the nonlinearity of W(t) on the probability P to remain in the initial state. The dimensionless quantity epsilon = pi Delta ^2/(2 hbar v) depends on the coupling Delta of both levels and on the sweep rate v. For fast sweep rates, i.e., epsilon << l and monotonic, analytic sweep functions linearizable in the vicinity of the resonance we find the transition probability 1-P ~= epsilon (1+a), where a>0 is the correction to the LSZ result due to the nonlinearity of the sweep. Further increase of the sweep rate with nonlinearity fixed brings the system into the nonlinear-sweep regime characterized by 1-P ~= epsilon ^gamma with gamma neq 1 depending on the type of sweep function. In case of slow sweep rates, i.e., epsilon >>1 an interesting interference phenomenon occurs. For analytic W(t) the probability P=P_0 e^-eta is determined by the singularities of sqrt{Delta ^2+W^2(t)} in the upper complex plane of t. If W(t) is close to linear, there is only one singularity, that leads to the LZS result P=e^-epsilon with important corrections to the exponent due to nonlinearity. However, for, e.g., W(t) ~ t^3 there is a pair of singularities in the upper complex plane. Interference of their contributions leads to oscillations of the prefactor P_0 that depends on the sweep rate through epsilon and turns to zero at some epsilon. Measurements of the oscillation period and of the exponential factor would allow to determine Delta, independently.Comment: 11 PR pages, 12 figures. To be published in PR

Temperature dependence of ESR intensity for the nanoscale molecular magnet V15

The electron spin resonance (ESR) of nanoscale molecular magnet ${\rm V}_{15}$ is studied. Since the Hamiltonian of ${\rm V}_{15}$ has a large Hilbert space and numerical calculations of the ESR signal evaluating the Kubo formula with exact diagonalization method is difficult, we implement the formula with the help of the random vector technique and the Chebyshev polynominal expansion, which we name the double Chebyshev expansion method. We calculate the temperature dependence of the ESR intensity of ${\rm V}_{15}$ and compare it with the data obtained in experiment. As another complementary approach, we also implement the Kubo formula with the subspace iteration method taking only important low-lying states into account. We study the ESR absorption curve below $100{\rm K}$ by means of both methods. We find that side peaks appear due to the Dzyaloshinsky-Moriya interaction and these peaks grows as temperature decreases.Comment: 9 pages, 4 figures. To appear in J. Phys. Soc. Jpn. Supp

Origin of the Canonical Ensemble: Thermalization with Decoherence

We solve the time-dependent Schrodinger equation for the combination of a spin system interacting with a spin bath environment. In particular, we focus on the time development of the reduced density matrix of the spin system. Under normal circumstances we show that the environment drives the reduced density matrix to a fully decoherent state, and furthermore the diagonal elements of the reduced density matrix approach those expected for the system in the canonical ensemble. We show one exception to the normal case is if the spin system cannot exchange energy with the spin bath. Our demonstration does not rely on time-averaging of observables nor does it assume that the coupling between system and bath is weak. Our findings show that the canonical ensemble is a state that may result from pure quantum dynamics, suggesting that quantum mechanics may be regarded as the foundation of quantum statistical mechanics.Comment: 12 pages, 4 figures, accepted for publication by J. Phys. Soc. Jp

Galactic Cosmic Ray Origins and OB Associations: Evidence from SuperTIGER Observations of Elements 26_{26}Fe through 40_{40}Zr

We report abundances of elements from $_{26}$Fe to $_{40}$Zr in the cosmic radiation measured by the SuperTIGER (Trans-Iron Galactic Element Recorder) instrument during 55 days of exposure on a long-duration balloon flight over Antarctica. These observations resolve elemental abundances in this charge range with single-element resolution and good statistics. These results support a model of cosmic-ray origin in which the source material consists of a mixture of 19$^{+11}_{-6}$\% material from massive stars and $\sim$81\% normal interstellar medium (ISM) material with solar system abundances. The results also show a preferential acceleration of refractory elements (found in interstellar dust grains) by a factor of $\sim$4 over volatile elements (found in interstellar gas) ordered by atomic mass (A). Both the refractory and volatile elements show a mass-dependent enhancement with similar slopes.Comment: 9 pages, 12 figures, 2 tables, accepted by Ap

Fast Algorithm for Finding the Eigenvalue Distribution of Very Large Matrices

A theoretical analysis is given of the equation of motion method, due to Alben et al., to compute the eigenvalue distribution (density of states) of very large matrices. The salient feature of this method is that for matrices of the kind encountered in quantum physics the memory and CPU requirements of this method scale linearly with the dimension of the matrix. We derive a rigorous estimate of the statistical error, supporting earlier observations that the computational efficiency of this approach increases with matrix size. We use this method and an imaginary-time version of it to compute the energy and the specific heat of three different, exactly solvable, spin-1/2 models and compare with the exact results to study the dependence of the statistical errors on sample and matrix size.Comment: 24 pages, 24 figure

Measurement of the cosmic-ray antiproton spectrum at solar minimum with a long-duration balloon flight over Antarctica

The energy spectrum of cosmic-ray antiprotons from 0.17 to 3.5 GeV has been measured using 7886 antiprotons detected by BESS-Polar II during a long-duration flight over Antarctica near solar minimum in December 2007 and January 2008. This shows good consistency with secondary antiproton calculations. Cosmologically primary antiprotons have been investigated by comparing measured and calculated antiproton spectra. BESS-Polar II data show no evidence of primary antiprotons from evaporation of primordial black holes.Comment: 4 pages, 4 figures, submitted to Physical Review Letter

Cosmic-Ray Nuclei, Antiprotons and Gamma-rays in the Galaxy: a New Diffusion Model

We model the transport of cosmic ray nuclei in the Galaxy by means of a new numerical code. Differently from previous numerical models we account for a generic spatial distribution of the diffusion coefficient. We found that in the case of radially uniform diffusion, the main secondary/primary ratios (B/C, N/O and sub-Fe/Fe) and the modulated antiproton spectrum match consistently the available observations. Convection and re-acceleration do not seem to be required in the energy range we consider: $1 < E < 10^3$ GeV/nucleon. We generalize these results accounting for radial dependence of the diffusion coefficient, which is assumed to trace that of the cosmic ray sources. While this does not affect the prediction of secondary/primary ratios, the simulated longitude profile of the diffuse $\gamma$-ray emission is significantly different from the uniform case and may agree with EGRET measurements without invoking ad hoc assumptions on the galactic gas density distribution.Comment: 17 pages, 6 figures. v3: Added detailed references to nuclear cross-section networ