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Register a new userInversion of lattice models from the observations of microscopic degrees of freedom: parameter estimation with uncertainty quantification
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Added by
Sai Mani Prudhvi Valleti
Publication date
2019
fields
Physics
and research's language is
English
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Experimental advances in condensed matter physics and material science have enabled ready access to atomic-resolution images, with resolution of modern tools often sufficient to extract minute details of symmetry-breaking distortions such as polarization, octahedra tilts, or other structure-coupled order parameters. The patterns of observed distortions in turn contain the information on microscopic driving forces defining the development of materials microstructure and associated thermodynamics. However, the analysis of underpinning physical models from experimentally observed microscopic degrees of freedom remains a largely unresolved issue. Here, we explore such an approach using the paradigmatic Ising model on a square lattice. We show that the microscopic parameters of the Ising model both for ferromagnetic and antiferromagnetic case can be extracted from the spin configurations for temperatures an order of magnitude higher than the phase transition and perform uncertainty analysis for such reconstructions. This suggests that microscopic observations of materials with sufficiently high precision can provide information on generative physics at temperatures well above corresponding phase transition, opening new horizons for scientific exploration via high-resolution imaging.
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The emergence of scanning probe and electron beam imaging techniques have allowed quantitative studies of atomic structure and minute details of electronic and vibrational structure on the level of individual atomic units. These microscopic descriptors in turn can be associated with the local symmetry breaking phenomena, representing stochastic manifestation of underpinning generative physical model. Here, we explore the reconstruction of exchange integrals in the Hamiltonian for the lattice model with two competing interactions from the observations of the microscopic degrees of freedom and establish the uncertainties and reliability of such analysis in a broad parameter-temperature space. As an ancillary task, we develop a machine learning approach based on histogram clustering to predict phase diagrams efficiently using a reduced descriptor space. We further demonstrate that reconstruction is possible well above the phase transition and in the regions of the parameter space when the macroscopic ground state of the system is poorly defined due to frustrated interactions. This suggests that this approach can be applied to the traditionally complex problems of condensed matter physics such as ferroelectric relaxors and morphotropic phase boundary systems, spin and cluster glasses, quantum systems once the local descriptors linked to the relevant physical behaviors are known.
We present a theory of spinor superfluidity in a two-species heteronuclear ultracold fermionic atomic gas consisting of arbitrary half-integer spin and one-half spin atoms. In particular, we focus on the magnetism of the superfluid phase and determine the possible phases in the absence of a magnetic field. Our work demonstrates similarities between heteronuclear fermionic superfluids and spinor Bose-Einstein condensates at the mean-field level. Possible experimental situations are discussed.
We study the behavior of a moving wall in contact with a particle gas and subjected to an external force. We compare the fluctuations of the system observed in the microcanonical and canonical ensembles, at varying the number of particles. Static and dynamic correlations signal significant differences between the two ensembles. Furthermore, velocity-velocity correlations of the moving wall present a complex two-time relaxation which cannot be reproduced by a standard Langevin-like description. Quite remarkably, increasing the number of gas particles in an elongated geometry, we find a typical timescale, related to the interaction between the partitioning wall and the particles, which grows macroscopically.
Fusion cross-sections are computed for the $^{40}$Ca$+^{40}$Ca system over a wide energy range with two microscopic approaches where the only phenomenological input is the Skyrme energy density functional. The first method is based on the coupled-channels formalism, using the bare nucleus-nucleus potential calculated with the frozen Hartree-Fock technique and the deformation parameters of vibrational states computed with the time-dependent Hartree-Fock (TDHF) approach. The second method is based on the density-constrained TDHF method to generate nucleus-nucleus potentials from TDHF evolution. Both approaches incorporate the effect of couplings to internal degrees of freedoms in different ways. The predictions are in relatively good agreement with experimental data.
Systems with interacting degrees of freedom play a prominent role in stochastic thermodynamics. Our aim is to use the concept of detached path probabilities and detached entropy production for bipartite Markov processes and elaborate on a series of special cases including measurement-feedback systems, sensors and hidden Markov models. For these special cases we show that fluctuation theorems involving the detached entropy production recover known results which have been obtained separately before. Additionally, we show that the fluctuation relation for the detached entropy production can be used in model selection for data stemming from a hidden Markov model. We discuss the relation to previous approaches including those which use information flow or learning rate to quantify the influence of one subsystem on the other. In conclusion, we present a complete framework with which to find fluctuation relations for coupled systems.
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