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"Statistical physics Mathematical models."
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Free energy computations
This monograph provides a general introduction to advanced computational methods for free energy calculations, from the systematic and rigorous point of view of applied mathematics. Free energy calculations in molecular dynamics have become an outstanding and increasingly broad computational field in physics, chemistry and molecular biology within the past few years, by making possible the analysis of complex molecular systems. This work proposes a new, general and rigorous presentation, intended both for practitioners interested in a mathematical treatment, and for applied mathematicians interested in molecular dynamics.
eBook
Exact methods in low-dimensional statistical physics and quantum computing : École d'été de physique des Houches, session LXXXIX, 30 June-1 August 2008 : École thématique du CNRS
Recent years have shown important and spectacular convergences between techniques traditionally used in theoretical physics and methods emerging from modern mathematics (combinatorics, probability theory, topology, algebraic geometry, etc). These techniques, and in particular those of low-dimensional statistical models, are instrumental in improving our understanding of emerging fields, such as quantum computing and cryptography, complex systems, and quantum fluids. This book sets these issues into a larger and more coherent theoretical context than is currently available. For instance, understanding the key concepts of quantum entanglement (a measure of information density) necessitates a thorough knowledge of quantum and topological field theory, and integrable models. To achieve this goal, the lectures were given by international leaders in the fields of exactly solvable models in low dimensional condensed matter and statistical physics.
eBook
The fiber bundle model : modeling failure in materials
Gathering research from physics, mechanical engineering, and statistics in a single resource for the first time, this text presents the background to the model, its theoretical basis, and applications ranging from materials science to earth science.
eBook
Conformal Invariance
Conformal invariance has been a spectacularly successful tool in advancing our understanding of the two-dimensional phase transitions found in classical systems at equilibrium. This volume sharpens our picture of the applications of conformal invariance, introducing non-local observables such as loops and interfaces before explaining how they arise in specific physical contexts. It then shows how to use conformal invariance to determine their properties. Moving on to cover key conceptual developments in conformal invariance, the book devotes much of its space to stochastic Loewner evolution (SLE), detailing SLE's conceptual foundations as well as extensive numerical tests. The chapters then elucidate SLE's use in geometric phase transitions such as percolation or polymer systems, paying particular attention to surface effects. As clear and accessible as it is authoritative, this publication is as suitable for non-specialist readers and graduate students alike.
eBook
Dissipative phase transitions
Phase transition phenomena arise in a variety of relevant real world situations, such as melting and freezing in a solid-liquid system, evaporation, solid-solid phase transitions in shape memory alloys, combustion, crystal growth, damage in elastic materials, glass formation, phase transitions in polymers, and plasticity. The practical interest of such phenomenology is evident and has deeply influenced the technological development of our society, stimulating intense mathematical research in this area. This book analyzes and approximates some models and related partial differential equation problems that involve phase transitions in different contexts and include dissipation effects.
eBook
Exact Methods in Low-Dimensional Statistical Physics and Quantum Computing
Low-dimensional statistical models are instrumental in improving our understanding of emerging fields, such as quantum computing and cryptography, complex systems, and quantum fluids. This book of lectures by international leaders in the field sets these issues into a larger and more coherent theoretical perspective than is currently available.
eBook
Direct observations of thermalization to a Rayleigh–Jeans distribution in multimode optical fibres
Nonlinear multimode optical systems support a host of intriguing effects that are impossible in single-mode settings. Although nonlinearity can provide a rich environment where the chaotic power exchange among thousands of modes can lead to novel behaviours, understanding and harnessing these processes to our advantage is challenging. Over the years, statistical models have been developed to macroscopically describe the response of these complex systems. One of the cornerstones of these theoretical formalisms is the prediction of a photon–photon-mediated thermalization process that leads to a Rayleigh–Jeans distribution of mode occupations. Here we report the use of mode-resolved measurement techniques to directly observe the thermalization to a Rayleigh–Jeans power distribution in a multimode optical fibre. We experimentally demonstrate that the underlying system Hamiltonian remains invariant during propagation, whereas power equipartition takes place among degenerate groups of modes—all in full accordance with theoretical predictions. Our results may pave the way towards a new generation of high-power optical sources whose brightness and modal content can be controlled using principles from thermodynamics and statistical mechanics.
Optical nonlinearities in multimodal systems lead to a complex behaviour that can be described as a thermalization process, which is expected to lead to a Rayleigh–Jeans distribution. This process has now been observed in graded-index fibres.
Journal Article
Brownian regularity for the Airy line ensemble, and multi-polymer watermelons in Brownian last passage percolation
The Airy line ensemble is a positive-integer indexed system of random continuous curves whose finite dimensional distributions are
given by the multi-line Airy process. It is a natural object in the KPZ universality class: for example, its highest curve, the
Airy
In this paper, we employ the Brownian Gibbs property to make a close
comparison between the Airy line ensemble’s curves after affine shift and Brownian bridge, proving the finiteness of a superpolynomially
growing moment bound on Radon-Nikodym derivatives.
We also determine the value of a natural exponent describing in Brownian last
passage percolation the decay in probability for the existence of several near geodesics that are disjoint except for their common
endpoints, where the notion of ‘near’ refers to a small deficit in scaled geodesic energy, with the parameter specifying this nearness
tending to zero.
To prove both results, we introduce a technique that may be useful elsewhere for finding upper bounds on
probabilities of events concerning random systems of curves enjoying the Brownian Gibbs property.
Several results in this article
play a fundamental role in a further study of Brownian last passage percolation in three companion papers (Hammond 2017a,b,c), in which
geodesic coalescence and geodesic energy profiles are investigated in scaled coordinates.
eBook