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Register a new userModified Bose-Einstein and Fermi-Dirac statistics if excitations are localized on an intermediate length scale: Application to non-Debye specific heat
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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 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 10^6 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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This paper presents an analytical study of the coexistence of different transport regimes in quasi-one-dimensional surface-disordered waveguides (or electron conductors). To elucidate main features of surface scattering, the case of two open modes (channels) is considered in great detail. Main attention is paid to the transmission in dependence on various parameters of the model with two types of rough-surface profiles (symmetric and antisymmetric). It is shown that depending on the symmetry, basic mechanisms of scattering can be either enhanced or suppressed. As a consequence, different transport regimes can be realized. Specifically, in the waveguide with symmetric rough boundaries, there are ballistic, localized and coexistence transport regimes. In the waveguide with antisymmetric roughness of lateral walls, another regime of the diffusive transport can arise. Our study allows to reveal the role of the so-called square-gradient scattering which is typically neglected in literature, however, can give a strong impact to the transmission.
The low-temperature thermal properties of dielectric crystals are governed by acoustic excitations with large wavelengths that are well described by plane waves. This is the Debye model, which rests on the assumption that the medium is an elastic continuum, holds true for acoustic wavelengths large on the microscopic scale fixed by the interatomic spacing, and gradually breaks down on approaching it. Glasses are characterized as well by universal low-temperature thermal properties, that are however anomalous with respect to those of the corresponding crystalline phases. Related universal anomalies also appear in the low-frequency vibrational density of states and, despite of a longstanding debate, still remain poorly understood. Using molecular dynamics simulations of a model monatomic glass of extremely large size, we show that in glasses the structural disorder undermines the Debye model in a subtle way: the elastic continuum approximation for the acoustic excitations breaks down abruptly on the mesoscopic, medium-range-order length-scale of about ten interatomic spacings, where it still works well for the corresponding crystalline systems. On this scale, the sound velocity shows a marked reduction with respect to the macroscopic value. This turns out to be closely related to the universal excess over the Debye model prediction found in glasses at frequencies of ~1 THz in the vibrational density of states or at temperatures of ~10 K in the specific heat.
The Anderson localization transition is one of the most well studied examples of a zero temperature quantum phase transition. On the other hand, many open questions remain about the phenomenology of disordered systems driven far out of equilibrium. Here we study the localization transition in the prototypical three-dimensional, noninteracting Anderson model when the system is driven at its boundaries to induce a current carrying non-equilibrium steady state. Recently we showed that the diffusive phase of this model exhibits extensive mutual information of its non-equilibrium steady-state density matrix. We show that that this extensive scaling persists in the entanglement and at the localization critical point, before crossing over to a short-range (area-law) scaling in the localized phase. We introduce an entanglement witness for fermionic states that we name the mutual coherence, which, for fermionic Gaussian states, is also a lower bound on the mutual information. Through a combination of analytical arguments and numerics, we determine the finite-size scaling of the mutual coherence across the transition. These results further develop the notion of entanglement phase transitions in open systems, with direct implications for driven many-body localized systems, as well as experimental studies of driven-disordered systems.
Recent theoretical advances offer an exact, first-principle theory of jamming criticality in infinite dimension as well as universal scaling relations between critical exponents in all dimensions. For packings of frictionless spheres near the jamming transition, these advances predict that nontrivial power-law exponents characterize the critical distribution of (i) small inter-particle gaps and (ii) weak contact forces, both of which are crucial for mechanical stability. The scaling of the inter-particle gaps is known to be constant in all spatial dimensions $d$ -- including the physically relevant $d=2$ and 3, but the value of the weak force exponent remains the object of debate and confusion. Here, we resolve this ambiguity by numerical simulations. We construct isostatic jammed packings with extremely high accuracy, and introduce a simple criterion to separate the contribution of particles that give rise to localized buckling excitations, i.e., bucklers, from the others. This analysis reveals the remarkable dimensional robustness of mean-field marginality and its associated criticality.
Despite the enormous interest in quantum spin liquids, their experimental existence still awaits broad consensus. In particular, quenched disorder may turn a specific system into a spin glass and possibly preclude the formation of a quantum spin liquid. Here, we demonstrate that the glass transition among geometrically frustrated magnets, a materials class in which spin liquids are expected, differs qualitatively from conventional spin glass. Whereas conventional systems have a glass temperature that increases with increasing disorder, geometrically frustrated systems have a glass temperature that increases with decreasing disorder, approaching, in the clean limit, a finite value. This behaviour implies the existence of a hidden energy scale (far smaller than the Weiss constant) which is independent of disorder and drives the glass transition in the presence of disorder. Motivated by these observations, we propose a scenario in which the interplay of interactions and entropy in the disorder-free system yields a temperature-dependent magnetic permeability with a crossover temperature that determines the hidden energy scale. The relevance of this scale for quantum spin liquids is discussed.
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