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Probability in Orthodox Quantum Mechanics: Probability as a Postulate Versus Probability as an Emergent Phenomenon [PDF]
, 2000 The role of probability in quantum mechanics is reviewed, with a discussion of the ``orthodox'' versus the statistical interpretive frameworks, and of a number of related issues. After a brief summary of sources of unease with quantum mechanics, a survey
A. J. Leggett +14 more
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Axioms, 2023 This expository paper advocates an approach to physics in which “typicality” is identified with a suitable form of algorithmic randomness. To this end various theorems from mathematics and physics are reviewed.
Klaas Landsman
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Entropy, 2015 There is a well-known analogy between statistical and quantum mechanics. In statistical mechanics, Boltzmann realized that the probability for a system in thermal equilibrium to occupy a given state is proportional to \(\exp(-E/kT)\), where \(E\) is the ...
John C. Baez, Blake S. Pollard
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Correlations and Work Statistics in Critical Quantum Systems [PDF]
arXiv, 2022 In this dissertation, we analyze equilibrium and out-of-equilibrium quantum phase transitions present in quantum spin-$\frac{1}{2}$ models, using a quantum information approach through quantum correlations and phase space formalism, and a quantum thermodynamic approach through the work statistics formalism.
arxiv
Quantum statistical mechanics over function fields [PDF]
, 2006 In this paper we construct a noncommutative space of ``pointed Drinfeld modules'' that generalizes to the case of function fields the noncommutative spaces of commensurability classes of Q-lattices.
Consani, Caterina, Marcolli, Matilde
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A statistical-mechanical description of quantum entanglement [PDF]
Journal of Physics A: Mathematical and Theoretical, 2008 We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable states. We further study this system using statistical mechanical methods.
J. K. Korbicz +4 more
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Equilibration of quantum gases
New Journal of Physics, 2016 Finding equilibration times is a major unsolved problem in physics with few analytical results. Here we look at equilibration times for quantum gases of bosons and fermions in the regime of negligibly weak interactions, a setting which not only includes ...
Terry Farrelly
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Local normality in Quantum Statistical Mechanics [PDF]
Communications in Mathematical Physics, 1973 It is shown that K.M.S.-states are locally normal on a great number ofC*-algebras that may be of interest in Quantum Statistical Mechanics. The lattice structure and the Choquet-simplex structure of various sets of states are investigated. In this respect special attention is payed to the interplay of the K.M.S.-automorphism group with other ...
Takesaki, Masamichi, Winnink, Marinus
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Reworking Zubarev’s Approach to Nonequilibrium Quantum Statistical Mechanics
Particles, 2019 In this work, the nonequilibrium density operator approach introduced by Zubarev more than 50 years ago to describe quantum systems at a local thermodynamic equilibrium is revisited.
Francesco Becattini +2 more
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Many body localization and thermalization in quantum statistical mechanics
, 2014 We review some recent developments in the statistical mechanics of isolated quantum systems. We provide a brief introduction to quantum thermalization, paying particular attention to the `Eigenstate Thermalization Hypothesis' (ETH), and the resulting ...
Huse, David A., Nandkishore, Rahul
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