Ergodic Properties of Microcanonical Observables

The problem of the existence of a Strong Stochasticity Threshold in the FPU-beta model is reconsidered, using suitable microcanonical observables of thermodynamic nature, like the temperature and the specific heat. Explicit expressions for these observables are obtained by exploiting rigorous methods of differential geometry. Measurements of the corresponding temporal autocorrelation functions locate the threshold at a finite value of the energy density, that results to be indipendent of the number of degrees of freedom.Comment: 19 pages, 6 figure

Spin-Glass Stochastic Stability: a Rigorous Proof

We prove the property of stochastic stability previously introduced as a consequence of the (unproved) continuity hypothesis in the temperature of the spin-glass quenched state. We show that stochastic stability holds in beta-average for both the Sherrington-Kirkpatrick model in terms of the square of the overlap function and for the Edwards-Anderson model in terms of the bond overlap. We show that the volume rate at which the property is reached in the thermodynamic limit is V^{-1}. As a byproduct we show that the stochastic stability identities coincide with those obtained with a different method by Ghirlanda and Guerra when applyed to the thermal fluctuations only.Comment: 12 pages, revised versio

A microprocessor application to a strapdown laser gyro navigator

The replacement of analog circuit control loops for laser gyros (path length control, cross axis temperature compensation loops, dither servo and current regulators) with digital filters residing in microcomputers is addressed. In addition to the control loops, a discussion is given on applying the microprocessor hardware to compensation for coning and skulling motion where simple algorithms are processed at high speeds to compensate component output data (digital pulses) for linear and angular vibration motions. Highlights are given on the methodology and system approaches used in replacing differential equations describing the analog system in terms of the mechanized difference equations of the microprocessor. Standard one for one frequency domain techniques are employed in replacing analog transfer functions by their transform counterparts. Direct digital design techniques are also discussed along with their associated benefits. Time and memory loading analyses are also summarized, as well as signal and microprocessor architecture. Trade offs in algorithm, mechanization, time/memory loading, accuracy, and microprocessor architecture are also given

Thermodynamic Limit for Mean-Field Spin Models

If the Boltzmann-Gibbs state $\omega_N$ of a mean-field $N$-particle system with Hamiltonian $H_N$ verifies the condition $$\omega_N(H_N) \ge \omega_N(H_{N_1}+H_{N_2})$$ for every decomposition $N_1+N_2=N$, then its free energy density increases with $N$. We prove such a condition for a wide class of spin models which includes the Curie-Weiss model, its p-spin generalizations (for both even and odd p), its random field version and also the finite pattern Hopfield model. For all these cases the existence of the thermodynamic limit by subadditivity and boundedness follows.Comment: 15 pages, few improvements. To appear in MPE

Matching with shift for one-dimensional Gibbs measures

We consider matching with shifts for Gibbsian sequences. We prove that the maximal overlap behaves as $c\log n$, where $c$ is explicitly identified in terms of the thermodynamic quantities (pressure) of the underlying potential. Our approach is based on the analysis of the first and second moment of the number of overlaps of a given size. We treat both the case of equal sequences (and nonzero shifts) and independent sequences.Comment: Published in at http://dx.doi.org/10.1214/08-AAP588 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

The inclusion process: duality and correlation inequalities

We prove a comparison inequality between a system of independent random walkers and a system of random walkers which either interact by attracting each other -- a process which we call here the symmetric inclusion process (SIP) -- or repel each other -- a generalized version of the well-known symmetric exclusion process. As an application, new correlation inequalities are obtained for the SIP, as well as for some interacting diffusions which are used as models of heat conduction, -- the so-called Brownian momentum process, and the Brownian energy process. These inequalities are counterparts of the inequalities (in the opposite direction) for the symmetric exclusion process, showing that the SIP is a natural bosonic analogue of the symmetric exclusion process, which is fermionic. Finally, we consider a boundary driven version of the SIP for which we prove duality and then obtain correlation inequalities.Comment: This is a new version: correlation inequalities for the Brownian energy process are added, and the part of the asymmetric inclusion process is removed

Energy Landscape Statistics of the Random Orthogonal Model

The Random Orthogonal Model (ROM) of Marinari-Parisi-Ritort [MPR1,MPR2] is a model of statistical mechanics where the couplings among the spins are defined by a matrix chosen randomly within the orthogonal ensemble. It reproduces the most relevant properties of the Parisi solution of the Sherrington-Kirckpatrick model. Here we compute the energy distribution, and work out an extimate for the two-point correlation function. Moreover, we show exponential increase of the number of metastable states also for non zero magnetic field.Comment: 23 pages, 6 figures, submitted to J. Phys.

Optimization Strategies in Complex Systems

We consider a class of combinatorial optimization problems that emerge in a variety of domains among which: condensed matter physics, theory of financial risks, error correcting codes in information transmissions, molecular and protein conformation, image restoration. We show the performances of two algorithms, the``greedy'' (quick decrease along the gradient) and the``reluctant'' (slow decrease close to the level curves) as well as those of a``stochastic convex interpolation''of the two. Concepts like the average relaxation time and the wideness of the attraction basin are analyzed and their system size dependence illustrated.Comment: 8 pages, 3 figure