Modified Bose-Einstein and Fermi-Dirac statistics if excitations are localized on an intermediate length scale: Applications to non-Debye specific heat

Abstract

Disordered systems show deviations from the standard Debye theory of specific heat at low temperatures. These deviations are often attributed to two-level systems of uncertain origin. We find that a source of excess specific heat comes from correlations between quanta of energy if phonon-like excitations are localized on an intermediate length scale. We use simulations of a simplified Creutz model for a system of Ising-like spins coupled to a thermal bath of Einstein-like oscillators. One feature of this model is that energy is quantized in both the system and its bath, ensuring conservation of energy at every step. Another feature is that the exact entropies of both the system and its bath are known at every step, so that their temperatures can be determined independently. We find that there is a mismatch in canonical temperature between the system and its bath. In addition to the usual finite-size effects in the Bose-Einstein Experimental evidence for this model comes from its ability to characterize the excess specific heat of imperfect crystals at low temperatures.

1/f noise from a finite entropy bath: comparison with flux noise in SQUIDs

“…While producing 1/f noise and dynamical freezing similar to a spin glass, this model is fundamentally dierent in that interactions remain homogeneous and the heterogeneity is purely dynamic. Finally, constraints of this type are fungible, having been used to reproduce a number of other physical phenomena [8][9][10][11][12].…”

“…Various mechanisms for similar nonlinear constraints have been considered elsewhere for the Ising model [8][9][10][11][12]. Here, for the Heisenberg model, we attribute the constraint to the additional heat transfer required to change the local configurational entropy within a cluster of spins.…”

“…The addition of this constraint is found to produce 1/f-type noise, ubiquitous in nature, in systems that otherwise exhibit white noise. Simulations of various models using a similar constraint have been reported in previous publications [8][9][10][11][12]. Here, we constrain the classical Heisenberg spin model, with and without dipolar anisotropy, and focus on 1/f noise in the net alignment.…”

Low frequency Raman study of the Boson peak in a Tellurite-tungstate glass over temperature

“…By looking to the discussion in the literature, the models still being developed and tested [34,35,36] or considering that the better understanding of BP could result in the exploration of new phenomena [37] and even in improvements of glass transparency [38], we have performed the low frequency Raman study presented here. The sample investigated is a tellurite-tungstate glass (in %molar 71T eO 2 − 22.5W O 3 − 5N a 2 O − 1.5N b 2 O 5 , which we will name here as TWNN) produced by the melting quenching process under controlled atmosphere as described elsewhere [39].…”