12,479 research outputs found
Stationary points approach to thermodynamic phase transitions
Nonanalyticities of thermodynamic functions are studied by adopting an
approach based on stationary points of the potential energy. For finite
systems, each stationary point is found to cause a nonanalyticity in the
microcanonical entropy, and the functional form of this nonanalytic term is
derived explicitly. With increasing system size, the order of the nonanalytic
term grows, leading to an increasing differentiability of the entropy. It is
found that only "asymptotically flat" stationary points may cause a
nonanalyticity that survives in the thermodynamic limit, and this property is
used to derive an analytic criterion establishing the existence or absence of
phase transitions. We sketch how this result can be employed to analytically
compute transition energies of classical spin models.Comment: 5 pages, 2 figures. Contribution to the proceedings of the 11th
Granada Seminar on Computational Physic
Nonequivalence of ensembles for long-range quantum spin systems in optical lattices
Motivated by the anisotropic long-range nature of the interactions between
cold dipolar atoms or molecules in an optical lattice, we study the anisotropic
quantum Heisenberg model with Curie-Weiss-type long-range interactions. Absence
of a heat bath in optical lattice experiments suggests a study of this model
within the microcanonical ensemble. The microcanonical entropy is calculated
analytically, and nonequivalence of microcanonical and canonical ensembles is
found for a range of anisotropy parameters. From the shape of the entropy it
follows that the Curie-Weiss Heisenberg model is indistinguishable from the
Curie-Weiss Ising model in canonical thermodynamics, although their
microcanonical thermodynamics differs. Qualitatively, the observed features of
nonequivalent ensembles are expected to be relevant for long-range quantum spin
systems realized in optical lattice experiments.Comment: 5 pages, 1 figur
Why Everettians Should Appreciate the Transactional Interpretation
The attractive feature of the Everett approach is its admirable spirit of approaching the quantum puzzle with a Zen-like "beginner’s mind" in order to try to envision what the pure formalism might be saying about quantum reality, even if that journey leads to a strange place. It is argued that the transactional interpretation of quantum mechanics (TI), appropriately interpreted, shares the same motivation and achieves much more, with far fewer conceptual perplexities, by taking into account heretofore overlooked features of the quantum formalism itself (i.e. advanced states). In particular, TI does not need to talk about brain states, consciousness, or observers (rational or otherwise). In its possibilist variant (“PTI”), it shares the realist virtues of treating state vector branches as genuine dynamical entities, without having to explain how or why all of their associated outcomes actually happen (they don’t), how to account for a plenitude of counterpart observers in some coherent notion of trans-temporal identity of the bifurcating observers (observers don’t bifurcate in TI), nor how the certainty of all outcomes could be consistent with any coherent theory of probability, let alone the Born probability (the Born probability emerges naturally in TI). In short, TI is precisely the one-world interpretation Kent is looking for in his (2010)
Entanglement-enhanced spreading of correlations
Starting from a product initial state, equal-time correlations in
nonrelativistic quantum lattice models propagate within a lightcone-like causal
region. The presence of entanglement in the initial state can modify this
behavior, enhancing and accelerating the growth of correlations. In this paper
we give a quantitative description, in the form of Lieb-Robinson-type bounds on
equal-time correlation functions, of the interplay of dynamics vs. initial
entanglement in quantum lattice models out of equilibrium. We test the bounds
against model calculations, and also discuss applications to quantum quenches,
quantum channels, and Kondo physics.Comment: 15 pages, 4 figure
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