Remarks on Shannon's Statistical Inference and the Second Law in Quantum Statistical Mechanics

We comment on a formulation of quantum statistical mechanics, which incorporates the statistical inference of Shannon. Our basic idea is to distinguish the dynamical entropy of von Neumann, $H = -k Tr \hat{\rho}\ln\hat{\rho}$, in terms of the density matrix $\hat{\rho}(t)$, and the statistical amount of uncertainty of Shannon, $S= -k \sum_{n}p_{n}\ln p_{n}$, with $p_{n}=$ in the representation where the total energy and particle numbers are diagonal. These quantities satisfy the inequality $S\geq H$. We propose to interprete Shannon's statistical inference as specifying the {\em initial conditions} of the system in terms of $p_{n}$. A definition of macroscopic observables which are characterized by intrinsic time scales is given, and a quantum mechanical condition on the system, which ensures equilibrium, is discussed on the basis of time averaging. An interesting analogy of the change of entroy with the running coupling in renormalization group is noted. A salient feature of our approach is that the distinction between statistical aspects and dynamical aspects of quantum statistical mechanics is very transparent.Comment: 16 pages. Minor refinement in the statements in the previous version. This version has been published in Journal of Phys. Soc. Jpn. 71 (2002) 6

The foundations of statistical mechanics from entanglement: Individual states vs. averages

We consider an alternative approach to the foundations of statistical mechanics, in which subjective randomness, ensemble-averaging or time-averaging are not required. Instead, the universe (i.e. the system together with a sufficiently large environment) is in a quantum pure state subject to a global constraint, and thermalisation results from entanglement between system and environment. We formulate and prove a "General Canonical Principle", which states that the system will be thermalised for almost all pure states of the universe, and provide rigorous quantitative bounds using Levy's Lemma.Comment: 12 pages, v3 title changed, v2 minor change

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

Fractional recurrence in discrete-time quantum walk

Quantum recurrence theorem holds for quantum systems with discrete energy eigenvalues and fails to hold in general for systems with continuous energy. We show that during quantum walk process dominated by interference of amplitude corresponding to different paths fail to satisfy the complete quantum recurrence theorem. Due to the revival of the fractional wave packet, a fractional recurrence characterized using quantum P\'olya number can be seen.Comment: 10 pages, 11 figure : Accepted to appear in Central European Journal of Physic

Long-Time Tails and Anomalous Slowing Down in the Relaxation of Spatially Inhomogeneous Excitations in Quantum Spin Chains

Exact analytic calculations in spin-1/2 XY chains, show the presence of long-time tails in the asymptotic dynamics of spatially inhomogeneous excitations. The decay of inhomogeneities, for $t\to \infty$, is given in the form of a power law $$(t/\tau_{Q}) ^{-\nu_{Q}}$$ where the relaxation time $\tau_{Q}$ and the exponent $\nu_{Q}$ depend on the wave vector $Q$, characterizing the spatial modulation of the initial excitation. We consider several variants of the XY model (dimerized, with staggered magnetic field, with bond alternation, and with isotropic and uniform interactions), that are grouped into two families, whether the energy spectrum has a gap or not. Once the initial condition is given, the non-equilibrium problem for the magnetization is solved in closed form, without any other assumption. The long-time behavior for $t\to \infty$ can be obtained systematically in a form of an asymptotic series through the stationary phase method. We found that gapped models show critical behavior with respect to $Q$, in the sense that there exist critical values $Q_{c}$, where the relaxation time $\tau_{Q}$ diverges and the exponent $\nu_{Q}$ changes discontinuously. At those points, a slowing down of the relaxation process is induced, similarly to phenomena occurring near phase transitions. Long-lived excitations are identified as incommensurate spin density waves that emerge in systems undergoing the Peierls transition. In contrast, gapless models do not present the above anomalies as a function of the wave vector $Q$.Comment: 25 pages, 2 postscript figures. Manuscript submitted to Physical Review

Analytic results for Gaussian wave packets in four model systems: II. Autocorrelation functions

The autocorrelation function, A(t), measures the overlap (in Hilbert space) of a time-dependent quantum mechanical wave function, psi(x,t), with its initial value, psi(x,0). It finds extensive use in the theoretical analysis and experimental measurement of such phenomena as quantum wave packet revivals. We evaluate explicit expressions for the autocorrelation function for time-dependent Gaussian solutions of the Schrodinger equation corresponding to the cases of a free particle, a particle undergoing uniform acceleration, a particle in a harmonic oscillator potential, and a system corresponding to an unstable equilibrium (the so-called `inverted' oscillator.) We emphasize the importance of momentum-space methods where such calculations are often more straightforwardly realized, as well as stressing their role in providing complementary information to results obtained using position-space wavefunctions.Comment: 18 pages, RevTeX, to appear in Found. Phys. Lett, Vol. 17, Dec. 200

From Nasion to Sellion: repositioning landmarks for radioprotection-tailored 3D cephalometric analysis

Purpose: The present study aimed to three-dimensionally evaluate the correlation between cephalometric measurements utilizing Sellion in place of Nasion. Material and methods: A pilot study using 25 CBCTs was carried out to determine the required sample size, reaching a minimum of 136 patients was required to validate the correlation between Nasion(N)- and Sellion(Se)-related measurements. Eight landmarks were manually annotated on full cranium CBCTs, resulting in six skeletal and six cutaneous/skeletal measurements. Therefore, data were statistically analysed after outliers’ detection and intraclass correlation coefficient (ICC) calculation. Pearson correlation coefficient (r) was used to assess the correlation between Nasion and Sellion measurements. At the end, simple linear regression was performed. Values of p < 0.01 and r > 0.80 were considered statistically and clinically relevant, respectively. Results: ICC revealed a substantial degree of consistency. A total of 214 CBCTs were included in the present study. Pearson test revealed highly significant correlations for all the tested variables; the highest coefficient was found between N^Me^Go vs Se^Me^Go (r = 0.989, p < 0.001) while the lowest among SNA vs SSeA (ρ = 0.814, p < 0.001). Finally, linear regression provided the new norm range values for the Sellion-based measurements. Conclusion: Pearson’s coefficients between Sellion- and Nasion-related measurements exhibited significantly high levels of correlation, suggesting the potential use of Sellion-based measurements for innovative cephalometric analyses. This method might comply with radiation protection principles in CBCT-based orthodontic cephalometry

Physiotherapists and Osteopaths’ Attitudes: Training in Management of Temporomandibular Disorders

Temporomandibular disorders (TMDs) are a condition which has multifactorial etiology. The most acknowledged method to classify TMDs is the diagnostic criteria (DC) introduced firstly by Dworkin. This protocol considers different aspects that are not only biological, but even psychosocial. Diagnosis is often based on anamnesis, physical examination and instrumental diagnosis. TMDs are classified as intra-articular and/or extra-articular disorders. Common signs and symptoms include jaw pain and dysfunction, earache, headache, facial pain, limitation to opening the mouth, ear pain and temporomandibular joint (TMJ) noises. This study regards two kind of clinicians that started in the last years to be more involved in the treatment of TMDs: osteopaths (OOs) and physiotherapists (PTs). The purpose is to analyze their attitude and clinical approach on patients affected by TMDs. Four hundred therapists answered an anonymous questionnaire regarding TMJ and TMDs. OOs showed greater knowledges on TMDs and TMJ and, the therapists with both qualifications seemed to be most confident in treating patients with TMDs. In conclusion this study highlights OOs and all the clinicians with this qualification, have a higher confidence in treating patients with TMD than the others. Dentists and orthodontists, according to this study, should co-work with OOs and PTs, because they are the specialists more requested by them than other kinds of specialists