Statistical Mechanical Ensembles
نویسنده
چکیده
The multidimensional space defined by the microscopic variables of a system. In the example above, it would be a 6x10-dimensional space, with independent variables (r, p) = (r1,r2,r3,.....,rN;p1,p2,p3,....,pN) where bold symbols indicate vectors, r is the position and p the momentum (p = mu). Momenta are used rather than velocities, because the classical and, especially, the quantum equations of change are more elegantly written in terms of momenta. The evolution of such a system in time is described by Newton's laws:
منابع مشابه
Random Feynman Graphs
We investigate a class of random graph ensembles based on the Feynman graphs of multidimensional integrals, representing statistical-mechanical partition functions. We show that the resulting ensembles of random graphs strongly resemble those defined in random graphs with hidden color, generalizing the known relation of the Feynman graphs of simple one-dimensional integrals to random graphs wit...
متن کاملThermodynamics with generalized ensembles: The class of dual orthodes
We address the problem of the foundation of generalized ensembles in statistical physics. The approach is based on Boltzmann’s concept of orthodes. These are the statistical ensembles that satisfy the heat theorem, according to which the heat exchanged divided by the temperature is an exact differential. This approach can be seen as a mechanical approach alternative to the well established info...
متن کاملEquivalence of Statistical Mechanical Ensembles for Non-Critical Quantum Systems
We consider the problem of whether the canonical and microcanonical ensembles are locally equivalent for short-ranged quantum Hamiltonians of N spins arranged on a ddimensional lattices. For any temperature for which the system has a finite correlation length, we prove that the canonical and microcanonical state are approximately equal on regions containing up toO(N) spins. The proof rests on a...
متن کاملSpin Lifetime in Small Electron Spin Ensembles Measured by Magnetic Resonance Force Microscopy
Magnetic Resonance Force Microscopy can enable nanoscale imaging of spin lifetime. We report temperature dependent measurements of the spin correlation time τm of the statistical fluctuations of the spin polarization—the spin noise—of ensembles containing ∼ 100 electron spins by this technique. Magneto-mechanical relaxation due to spin-cantilever coupling was controlled and spurious mechanisms ...
متن کاملPico-canonical Ensembles: a Theoretical Description of Metastable States
We define restricted ensembles, called pico-canonical ensembles, for a statistical-mechanical description of the metastable and glassy phases. In this approach, time-evolution is Markovian, with temperature dependent rates. Below a particular glass-temperature, the system is strongly non-ergodic, and the phase space breaks up into a large number of mutually disconnected sectors. Averages are ca...
متن کاملEntropy and temperature of a static granular assembly: an ab initio approach.
We construct a statistical framework for static assemblies of deformable grains which parallels that of equilibrium statistical mechanics but with a conservation principle based on the mechanical stress tensor. We define a state function that has all the attributes of entropy. In particular, maximizing this function leads to a well-defined granular temperature and the equivalent of the Boltzman...
متن کامل