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Full-Text Articles in Physical Sciences and Mathematics
A Comparison Of Boltzmann And Gibbs Definitions Of Microcanonical Entropy For Small Systems, Randall B. Shirts
A Comparison Of Boltzmann And Gibbs Definitions Of Microcanonical Entropy For Small Systems, Randall B. Shirts
Faculty Publications
Two different definitions of entropy, S= klnW, in the microcanonical ensemble have been competing for over 100 years. The Boltzmann/Planck definition is that W is the number of states accessible to the system at its energy E (also called the surface entropy). The Gibbs/Hertz definition is that W is the number of states of the system up to the energy E (also called the volume entropy). These two definitions agree for large systems but differ by terms of order N-1 for small systems, where N is the number of particles in the system. For three analytical …
Disordered Bosons In One Dimension: From Weak- To Strong-Randomness Criticality, Fawaz Hrahsheh, Thomas Vojta
Disordered Bosons In One Dimension: From Weak- To Strong-Randomness Criticality, Fawaz Hrahsheh, Thomas Vojta
Physics Faculty Research & Creative Works
We investigate the superfluid-insulator quantum phase transition of one-dimensional bosons with off-diagonal disorder by means of large-scale Monte Carlo simulations. For weak disorder, we find the transition to be in the same universality class as the superfluid-Mott insulator transition of the clean system. The nature of the transition changes for stronger disorder. Beyond a critical disorder strength, we find nonuniversal, disorder-dependent critical behavior. We compare our results to recent perturbative and strong-disorder renormalization group predictions. We also discuss experimental implications as well as extensions of our results to other systems.
Information Content Of Spontaneous Symmetry Breaking, Marcelo Gleiser, Nikitas Stamatopoulos
Information Content Of Spontaneous Symmetry Breaking, Marcelo Gleiser, Nikitas Stamatopoulos
Dartmouth Scholarship
We propose a measure of order in the context of nonequilibrium field theory and argue that this measure, which we call relative configurational entropy (RCE), may be used to quantify the emergence of coherent low-entropy configurations, such as time-dependent or time-independent topological and nontopological spatially extended structures. As an illustration, we investigate the nonequilibrium dynamics of spontaneous symmetry breaking in three spatial dimensions. In particular, we focus on a model where a real scalar field, prepared initially in a symmetric thermal state, is quenched to a broken-symmetric state. For a certain range of initial temperatures, spatially localized, long-lived structures known …
Everything Is Entangled, Roman V. Buniy, Stephen D. H. Hsu
Everything Is Entangled, Roman V. Buniy, Stephen D. H. Hsu
Mathematics, Physics, and Computer Science Faculty Articles and Research
We show that big bang cosmology implies a high degree of entanglement of particles in the universe. In fact, a typical particle is entangled with many particles far outside our horizon. However, the entanglement is spread nearly uniformly so that two randomly chosen particles are unlikely to be directly entangled with each other - the reduced density matrix describing any pair is likely to be separable.