202 research outputs found
Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
The renewed interest in the foundations of quantum statistical mechanics in
recent years has led us to study John von Neumann's 1929 article on the quantum
ergodic theorem. We have found this almost forgotten article, which until now
has been available only in German, to be a treasure chest, and to be much
misunderstood. In it, von Neumann studied the long-time behavior of macroscopic
quantum systems. While one of the two theorems announced in his title, the one
he calls the "quantum H-theorem", is actually a much weaker statement than
Boltzmann's classical H-theorem, the other theorem, which he calls the "quantum
ergodic theorem", is a beautiful and very non-trivial result. It expresses a
fact we call "normal typicality" and can be summarized as follows: For a
"typical" finite family of commuting macroscopic observables, every initial
wave function from a micro-canonical energy shell so evolves that for
most times in the long run, the joint probability distribution of these
observables obtained from is close to their micro-canonical
distribution.Comment: 34 pages LaTeX, no figures; v2: minor improvements and additions. The
English translation of von Neumann's article is available as arXiv:1003.213
Predictability of Invisalign® Clear Aligners Using OrthoPulse®: A Retrospective Study
This preliminary retrospective study evaluates how effective the OrthoPulse (Biolux Technology, Austria) is in increasing the predictability of orthodontic treatment in patients treated with Invisalign (R) clear aligners (Align Technology Inc., Tempe, AZ, USA). A group of 376 patients were treated with Invisalign (R) orthodontic clear aligners in association with an OrthoPulse (R) . The OrthoPulse (R) was prescribed for 10 min a day for the entire duration of the orthodontic treatment. The OrthoPulse (R) App remotely tracked the percentage compliance of each patient. The number of aligners planned with the ClinCheck software at the beginning of the treatment and the number of total aligners (including the adjunctive aligners) used to finish the treatment were then considered. After applying inclusion/exclusion criteria, a total of 40 patients remained in the study and were compared with a control group of 40 patients with the same characteristics as the study group. A statistical analysis was carried out to investigate whether using OrthoPulse (R) led to a statistical reduction in the number of adjunctive aligners, thus leading to a more accurate prediction of the treatment. The statistical analysis showed that patients who used OrthoPulse (R) needed fewer finishing aligners and a greater predictability of the treatment was obtained. In fact, in the treated group the average number of additional aligners represented 66.5% of the initial aligners, whereas in the control group 103.4% of the initially planned aligners were needed. In conclusion, in patients treated with clear aligners, OrthoPulse (R) would appear to increase the predictability of orthodontic treatment with clear aligners, thus reducing the number of finishing phase requirements
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
Geometric dynamical observables in rare gas crystals
We present a detailed description of how a differential geometric approach to
Hamiltonian dynamics can be used for determining the existence of a crossover
between different dynamical regimes in a realistic system, a model of a rare
gas solid. Such a geometric approach allows to locate the energy threshold
between weakly and strongly chaotic regimes, and to estimate the largest
Lyapunov exponent. We show how standard mehods of classical statistical
mechanics, i.e. Monte Carlo simulations, can be used for our computational
purposes. Finally we consider a Lennard Jones crystal modeling solid Xenon. The
value of the energy threshold turns out to be in excellent agreement with the
numerical estimate based on the crossover between slow and fast relaxation to
equilibrium obtained in a previous work by molecular dynamics simulations.Comment: RevTeX, 19 pages, 6 PostScript figures, submitted to Phys. Rev.
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
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, , in terms of the density matrix ,
and the statistical amount of uncertainty of Shannon, , with in the representation where the total
energy and particle numbers are diagonal. These quantities satisfy the
inequality . We propose to interprete Shannon's statistical inference
as specifying the {\em initial conditions} of the system in terms of . 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
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
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
Obesity and treatment meanings in bariatric surgery candidates: a qualitative study
Background
This study used a qualitative approach to comprehend how the morbid obese conceptualize and deal with obesity and obesity treatment, with the particular aim of exploring the expectations and beliefs about the exigencies and the impact of bariatric surgery.
Methods
The study population included 30 morbid obese patients (20 women and 10 men) with a mean age of 39.17 years (SD = 8.81) and a mean body mass index of 47.5 (SD = 8.2) interviewed individually before surgery using open-ended questions. The interviews were audiotaped, transcribed, and then coded according to grounded analysis methodology.
Results
Three main thematic areas emerged from the data: obesity, eating behavior, and treatment. Obesity is described as a stable and hereditary trait. Although participants recognize that personal eating behavior exacerbates this condition, patients see their eating behavior as difficult to change and control. Food seems to be an ever-present dimension and a coping strategy, and to follow an adequate diet plan is described as a huge sacrifice. Bariatric surgery emerges as the only treatment for obesity, and participants highlight this moment as the beginning of a new life where health professionals have the main role. Bariatric surgery candidates see their eating behavior as out of their control, and to commit to its demands is seen as a big sacrifice. For these patients, surgery is understood as a miracle moment that will change their lives without requiring an active role or their participation.
Conclusion
According to these results, it is necessary to validate them with qualitative and quantitative studies; it is necessary to promote a new awareness of the weight loss process and to empower patients before and after bariatric surgery.Bolsa de doutoramento SFRH/BD/37069/2007 da Fundação para a Ciência e a Tecnologia (FCT
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 , is given in the
form of a power law where the relaxation time
and the exponent depend on the wave vector ,
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 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 , in the sense that
there exist critical values , where the relaxation time
diverges and the exponent 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 .Comment: 25 pages, 2 postscript figures. Manuscript submitted to Physical
Review
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