Adiabatic times for Markov chains and applications

We state and prove a generalized adiabatic theorem for Markov chains and provide examples and applications related to Glauber dynamics of Ising model over Z^d/nZ^d. The theorems derived in this paper describe a type of adiabatic dynamics for l^1(R_+^n) norm preserving, time inhomogeneous Markov transformations, while quantum adiabatic theorems deal with l^2(C^n) norm preserving ones, i.e. gradually changing unitary dynamics in C^n

Phase diagram of glassy systems in an external field

We study the mean-field phase diagram of glassy systems in a field pointing in the direction of a metastable state. We find competition among a ``magnetized'' and a ``disordered'' phase, that are separated by a coexistence line as in ordinary first order phase transitions. The coexistence line terminates in a critical point, which in principle can be observed in numerical simulations of glassy models.Comment: 4 pages, 5 figure

Tricritical Points in Random Combinatorics: the (2+p)-SAT case

The (2+p)-Satisfiability (SAT) problem interpolates between different classes of complexity theory and is believed to be of basic interest in understanding the onset of typical case complexity in random combinatorics. In this paper, a tricritical point in the phase diagram of the random $2+p$-SAT problem is analytically computed using the replica approach and found to lie in the range $2/5 \le p_0 \le 0.416$. These bounds on $p_0$ are in agreement with previous numerical simulations and rigorous results.Comment: 7 pages, 1 figure, RevTeX, to appear in J.Phys.

Anomalous Pinning Fields in Helical Magnets: Screening of the Quasiparticle Interaction

The spin-orbit interaction strength g_so in helical magnets determines both the pitch wave number q and the critical field H_c1 where the helix aligns with an external magnetic field. Within a standard Landau-Ginzburg-Wilson (LGW) theory, a determination of g_so in MnSi and FeGe from these two observables yields values that differ by a factor of 20. This discrepancy is remedied by considering the fermionic theory underlying the LGW theory, and in particular the effects of screening on the effective electron-electron interaction that results from an exchange of helical fluctuations.Comment: 4pp, 2 fig

Metal-superconductor transition at zero temperature: A case of unusual scaling

An effective field theory is derived for the normal metal-to-superconductor quantum phase transition at T=0. The critical behavior is determined exactly for all dimensions d>2. Although the critical exponents \beta and \nu do not exist, the usual scaling relations, properly reinterpreted, still hold. A complete scaling description of the transition is given, and the physics underlying the unusual critical behavior is discussed. Quenched disorder leads to anomalously strong T_c-fluctuations which are shown to explain the experimentally observed broadening of the transition in low-T_c thin films.Comment: 4 pp., no figs, final version as publishe

Heteroepitaxy of deposited amorphous layer by pulsed electron-beam irradiation

We demonstrate that a single short pulse of electron irradiation of appropriate energy is capable of recrystallizing epitaxially an amorphous Ge layer deposited on either or Si single-crystal substrate. The primary defects observed in the case were dislocations, whereas stacking faults were observed in samples

Quantum critical behavior in disordered itinerant ferromagnets: Logarithmic corrections to scaling

The quantum critical behavior of disordered itinerant ferromagnets is determined exactly by solving a recently developed effective field theory. It is shown that there are logarithmic corrections to a previous calculation of the critical behavior, and that the exact critical behavior coincides with that found earlier for a phase transition of undetermined nature in disordered interacting electron systems. This confirms a previous suggestion that the unspecified transition should be identified with the ferromagnetic transition. The behavior of the conductivity, the tunneling density of states, and the phase and quasiparticle relaxation rates across the ferromagnetic transition is also calculated.Comment: 15pp., REVTeX, 8 eps figs, final version as publishe

Accelerated Sampling of Boltzmann distributions

The sampling of Boltzmann distributions by stochastic Markov processes, can be strongly limited by the crossing time of high (free) energy barriers. As a result, the system may stay trapped in metastable states, and the relaxation time to the equilibrium Boltzmann distribution may be very large compared to the available computational time. In this paper, we show how, by a simple modification of the Hamiltonian, one can dramatically decrease the relaxation time of the system, while retaining the same equilibrium distribution. The method is illustrated on the case of the one-dimensional double-well potential

A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem

A quantum system will stay near its instantaneous ground state if the Hamiltonian that governs its evolution varies slowly enough. This quantum adiabatic behavior is the basis of a new class of algorithms for quantum computing. We test one such algorithm by applying it to randomly generated, hard, instances of an NP-complete problem. For the small examples that we can simulate, the quantum adiabatic algorithm works well, and provides evidence that quantum computers (if large ones can be built) may be able to outperform ordinary computers on hard sets of instances of NP-complete problems.Comment: 15 pages, 6 figures, email correspondence to [email protected] ; a shorter version of this article appeared in the April 20, 2001 issue of Science; see http://www.sciencemag.org/cgi/content/full/292/5516/47

Quantum critical behavior of disordered itinerant ferromagnets

The quantum ferromagnetic transition at zero temperature in disordered itinerant electron systems is considered. Nonmagnetic quenched disorder leads to diffusive electron dynamics that induces an effective long-range interaction between the spin or order parameter fluctuations of the form r^{2-2d}, with d the spatial dimension. This leads to unusual scaling behavior at the quantum critical point, which is determined exactly. In three-dimensional systems the quantum critical exponents are substantially different from their finite temperature counterparts, a difference that should be easily observable. Experiments to check these predictions are proposed.Comment: 14pp., REVTeX, 3 eps figs, final version as publishe