TY - JOUR
T1 - Modified Bose-Einstein and Fermi-Dirac statistics if excitations are localized on an intermediate length scale
T2 - Applications to non-Debye specific heat
AU - Chamberlin, Ralph
AU - Davis, Bryce F.
PY - 2013/10/7
Y1 - 2013/10/7
N2 - 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 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 and Fermi-Dirac distributions, if excitations in the heat bath are localized on an intermediate length scale, this mismatch is independent of system size up to at least 106 particles. We use a model for correlations between quanta of energy to adjust the statistical distributions and yield a thermodynamically consistent temperature. The model includes a chemical potential for units of energy, as is often used for other types of particles that are quantized and conserved. Experimental evidence for this model comes from its ability to characterize the excess specific heat of imperfect crystals at low temperatures.
AB - 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 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 and Fermi-Dirac distributions, if excitations in the heat bath are localized on an intermediate length scale, this mismatch is independent of system size up to at least 106 particles. We use a model for correlations between quanta of energy to adjust the statistical distributions and yield a thermodynamically consistent temperature. The model includes a chemical potential for units of energy, as is often used for other types of particles that are quantized and conserved. Experimental evidence for this model comes from its ability to characterize the excess specific heat of imperfect crystals at low temperatures.
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U2 - 10.1103/PhysRevE.88.042108
DO - 10.1103/PhysRevE.88.042108
M3 - Article
AN - SCOPUS:84886052055
SN - 1539-3755
VL - 88
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 4
M1 - 042108
ER -