Saturday, April 11, 2009

Thermodynanics from Quantum Mechanics

Origin of the Canonical Ensemble: Thermalization with Decoherence
It is shown that a system embedded in a closed quantum mechanical system relaxes to its canonical ensemble equilibrium state if the environment drives this system to a fully decoherent state and the excess energy can release from the system to the environment or backward. Our findings show that the canonical ensemble is a special state that may result from pure quantum dynamics, suggesting that quantum mechanics may be regarded as the foundation of quantum statistical mechanics

Statistical mechanics is one of cornerstones of modern physics but its foundations and basic postulates are still under debate [1, 2, 3, 4]. There is a common believe that a generic “system” that interacts with a generic environment evolves into a state described by the canonical ensemble. Experience shows that this is true but a detailed understanding of this process, which is crucial for a rigorous justification of statistical physics and thermodynamics, is still lacking.

Classical to quantum transition

Classical to quantum transition of a driven nonlinear nanomechanical resonator
Much experimental effort is invested these days in fabricating nanoelectromechanical systems (NEMS) that are sufficiently small, cold, and clean, so as to approach quantum mechanical behavior as their typical quantum energy scale $\hbar\Omega$ becomes comparable to that of the ambient thermal energy $k_{B}T$. Such systems will hopefully enable one to observe the quantum behavior of human-made objects, and test some of the basic principles of quantum mechanics. Here we expand and elaborate on our recent suggestion [PRL 99 (2007) 040404] to exploit the nonlinear nature of a nanoresonator in order to observe its transition into the quantum regime. We study this transition for an isolated resonator, as well as one that is coupled to a heat bath at either zero or finite temperature. We argue that by exploiting nonlinearities, quantum dynamics can be probed using technology that is almost within reach. Numerical solutions of the equations of motion display the first quantum corrections to classical dynamics that appear as the classical-to-quantum transition occurs. This provides practical signatures to look for in future experiments with NEMS resonators.

An empirical Gravity law up to galactic scales

An empirical Gravity law up to galactic scales
Modelling on the MOND proposal, we introduce an empirically motivated gravity law for galactic and sub-galactic scales. This, circumvents the need for the cumbersome and ill-defined transition regime which exists in MOND, when passing from the standard gravitational regime at high accelerations to the MOND regime at low accelerations. We show that the proposed force law does not violate dynamical constraints at sub-galactic and solar system scales, does not degrade the good fit of the MOND proposal at large galactic scales, and in fact, slightly improves the accordance with observations at dSph scales. The proposed gravity law hence yields a good description of gravitational phenomena from terrestrial to large galactic scales, within a unique framework, without the need to invoke the presence of the still undetected and hypothetically dominant dark matter. Isothermal equilibrium density profiles then yield projected surface density profiles for the local dSph galaxies in very good agreement with observational determinations, for values of the relevant parameters as inferred from recent observations of these Galactic satellites. The observed scaling relations for these systems are also naturally accounted for within the proposed scheme.

The Origin of Labor Division

In Bert Hölldobler, E.O. Wilson: "The Superorganism: The Beauty, Elegance, and Strangeness of Insect Societies", p39.
... solitary bees behave like semisocial species when forced forced together experimentally. ... the coerced partners proceed variously to divide labor in foraging, tunneling and guarding. ... The division of labor appears to be the result of a preexisting behavioral groundplan in which solitary individuals tend to move from one job to another after the first is completed. In eusocial special, the algorithm is transferred to the avoidance of a job already being filled by another nestmate. It is evident that progressively providing bees and wasps are already "spring loaded" for a rapid shift to eusociality once ecological factors favor the change.