1,720,968 research outputs found
Resonant harmonic oscillators and eigenvalue multiplicity
No full textExplicit formulas are worked out for the eigenvalue multiplicity of a systemof independent quantum harmonic oscillators in the general case of 1\leq s\leqn-1 resonance relations among the frequencies\om_1,\ldots,\om_n. As a particular case we prove that, even though the quantumnumbers are always less than the degrees of freedom, the \ev s are in generalintrinsically degenerate only in the completely resonant case
Rigorous results on the bipartite mean-field model
No full textWe consider a bipartite mean-field model in which interaction coefficients and magnetic fields depend only on the groups the particles belong to. We rigorously compute the value of the limiting pressure per particle using tail estimation techniques. We study the phase space of the model in the symmetric regime without an external field and when the interaction coefficients within the two groups are identical. Magnetic field perturbations are considered
Ground states for a class of deterministic spin models with glassy behaviour
No full textWe consider the deterministic model with glassy behaviour, recently introduced by Marinari, Parisi and Ritort, with \ha\ , where is the discrete sine Fourier transform. The ground state found by these authors for odd and prime is shown to become asymptotically dege\-ne\-ra\-te when is a product of odd primes, and to disappear for even. This last result is based on the explicit construction of a set of eigenvectors for , obtained through its formal identity with the imaginary part of the propagator of the quantized unit symplectic matrix over the -torus.
Local Order at Arbitrary Distances in Finite-Dimensional Spin-Glass Models
No full textFor a finite dimensional spin-glass model we prove local order at low temperatures for both localobservables and for products of observables at arbitrary mutual distance. When the Hamiltonianincludes the Edwards-Anderson interaction we prove bond local order, when it includes the random-field interaction we prove site local order
Absence of glassy behaviour in the deterministic spherical and XY models.
No full textWe consider the infinite-range spin models with Hamiltonian H = ni,j=1 Ji,j i j , where J is the quantization of a map of the torus. Although deterministic, these models are known to exhibit glassy behaviour. We show, through explicit computation of the Gibbs free energy, that unlike the random case this behaviour disappears in the corresponding spherical and continuous XY models. The only minimum of the Gibbs free energy is indeed the trivial one, even though the ground state is highly degenerate
Correlation Inequalities for Spin Glass in one Dimension
No full textWe prove two inequalities for the direct and truncated correlation for the nearest-neighboor one-dimensional Edwards-Anderson model with symmetric quenched dis-order. The second inequality has the opposite sign of the GKS inequality of typeII. In the non symmetric case with positive average we show that while the directcorrelation keeps its sign the truncated one changes sign when crossing a suitableline in the parameter space. That line separates the regions satisfying the GKSsecond inequality and the one proved here
Applicazione di un metodo attribuzionistico quantitativo alla monodia liturgica
No full textL’articolo mostra come tecniche di analisi stilo-metriche comunemente usate in ambito letterario (basate sulla distanza tra vettori delle frequenze di n-grammi di lettere) possano essere adattate con successo allo studio di repertori musicali “unidimensionali” (ovvero melodie prive di rit-mo e di accompagnamento). I buoni risultati ot-tenuti su un corpus di monodie liturgie (Canto Gregoriano e Canto Romano Antico) sono un primo passo verso l’adozione e la creazione di tecniche automatiche a supporto di studi stilome-trici a carattere e interesse strettamente musico-logico.We adapt a technique commonly used in the stylometric attribution of literary texts (based on a pseudo-distance between frequency-vectors of n-grams of letters) to the analysis of “unidimen-sional” musical repertoires (rhythm-free melody without accompaniment). We successfully apply the method to a corpus of liturgical monodies of medieval origin (the so-called Gregorian Chant, in comparison with the Old Roman Chant). Our results give a first indication that automatic stylometric techniques can be fruitfully adopted to support the study of refined problems in musi-cology
Deterministic spin models with a glassy phase transition
No full textWe consider the infinite-range deterministic spin models with Hamiltonian H = ni,j=1 Ji,j i j , where J is the quantization of a chaotic map of the torus. The mean-field Thouless - Anderson - Palmer (TAP) equations are derived by summing the high-temperature expansion. They predict a glassy phase transition at the critical temperature T near 0.8
Lack of monotonicity in spin glass correlation functions
No full textWe study the response of a spin glass system with respect to the rescaling of its interaction random variables and investigate numerically the behaviour of the correlation functions with respect to the volume. While for a ferromagnet the local energy correlation functions increase monotonically with the scale and, by consequence, with respect to the volume of the system we find that in a general spin glass model those monotonicities are violated
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