In mathematical physics, the diagrammatic Monte Carlo method is based on stochastic summation of Feynman diagrams with controllable error bars. [1] [2] It was developed by Boris Svistunov and Nikolay Prokof'ev. It was proposed as a generic approach to overcome the numerical sign problem that precludes simulations of many-body fermionic problems. [3] Diagrammatic Monte Carlo works in the thermodynamic limit, and its computational complexity does not scale exponentially with system or cluster volume. [4]
A polaron is a quasiparticle used in condensed matter physics to understand the interactions between electrons and atoms in a solid material. The polaron concept was proposed by Lev Landau in 1933 and Solomon Pekar in 1946 to describe an electron moving in a dielectric crystal where the atoms displace from their equilibrium positions to effectively screen the charge of an electron, known as a phonon cloud. This lowers the electron mobility and increases the electron's effective mass.
In the interpretation of quantum mechanics, a local hidden-variable theory is a hidden-variable theory that satisfies the principle of locality. These models attempt to account for the probabilistic features of quantum mechanics via the mechanism of underlying, but inaccessible variables, with the additional requirement that distant events be statistically independent.
Parallel tempering, in physics and statistics, is a computer simulation method typically used to find the lowest energy state of a system of many interacting particles. It addresses the problem that at high temperatures, one may have a stable state different from low temperature, whereas simulations at low temperatures may become "stuck" in a metastable state. It does this by using the fact that the high temperature simulation may visit states typical of both stable and metastable low temperature states.
In physics, a Fano resonance is a type of resonant scattering phenomenon that gives rise to an asymmetric line-shape. Interference between a background and a resonant scattering process produces the asymmetric line-shape. It is named after Italian-American physicist Ugo Fano, who in 1961 gave a theoretical explanation for the scattering line-shape of inelastic scattering of electrons from helium; however, Ettore Majorana was the first to discover this phenomenon. Fano resonance is a weak coupling effect meaning that the decay rate is so high, that no hybridization occurs. The coupling modifies the resonance properties such as spectral position and width and its line-shape takes on the distinctive asymmetric Fano profile. Because it is a general wave phenomenon, examples can be found across many areas of physics and engineering.
Quantum Monte Carlo encompasses a large family of computational methods whose common aim is the study of complex quantum systems. One of the major goals of these approaches is to provide a reliable solution of the quantum many-body problem. The diverse flavors of quantum Monte Carlo approaches all share the common use of the Monte Carlo method to handle the multi-dimensional integrals that arise in the different formulations of the many-body problem.
In theoretical physics, thermal quantum field theory or finite temperature field theory is a set of methods to calculate expectation values of physical observables of a quantum field theory at finite temperature.
Extremal optimization (EO) is an optimization heuristic inspired by the Bak–Sneppen model of self-organized criticality from the field of statistical physics. This heuristic was designed initially to address combinatorial optimization problems such as the travelling salesman problem and spin glasses, although the technique has been demonstrated to function in optimization domains.
In computational physics, variational Monte Carlo (VMC) is a quantum Monte Carlo method that applies the variational method to approximate the ground state of a quantum system.
Gaussian Quantum Monte Carlo is a quantum Monte Carlo method that shows a potential solution to the fermion sign problem without the deficiencies of alternative approaches. Instead of the Hilbert space, this method works in the space of density matrices that can be spanned by an over-complete basis of gaussian operators using only positive coefficients. Containing only quadratic forms of the fermionic operators, no anti-commuting variables occur and any quantum state can be expressed as a real probability distribution.
Path integral Monte Carlo (PIMC) is a quantum Monte Carlo method used to solve quantum statistical mechanics problems numerically within the path integral formulation. The application of Monte Carlo methods to path integral simulations of condensed matter systems was first pursued in a key paper by John A. Barker.
In continuum mechanics, wave turbulence is a set of nonlinear waves deviated far from thermal equilibrium. Such a state is usually accompanied by dissipation. It is either decaying turbulence or requires an external source of energy to sustain it. Examples are waves on a fluid surface excited by winds or ships, and waves in plasma excited by electromagnetic waves etc.
In applied mathematics, the numerical sign problem is the problem of numerically evaluating the integral of a highly oscillatory function of a large number of variables. Numerical methods fail because of the near-cancellation of the positive and negative contributions to the integral. Each has to be integrated to very high precision in order for their difference to be obtained with useful accuracy.
Philippe Blanchard has been a Professor of Mathematical Physics at Faculty of Physics, Bielefeld University since 1980. He is both director of the Research Center BiBoS and deputy managing director of the Center for Interdisciplinary Research at Bielefeld University.
Matjaž Perc is Professor of Physics at the University of Maribor in Slovenia, and director of the Complex Systems Center Maribor. He is member of Academia Europaea and among top 1% most cited physicists according to Thomson Reuters Highly Cited Researchers. He is Outstanding Referee of the Physical Review and Physical Review Letters journals, and Distinguished Referee of EPL. He received the Young Scientist Award for Socio-and Econophysics in 2015. His research has been widely reported in the media and professional literature.
In computational solid state physics, Continuous-time quantum Monte Carlo (CT-QMC) is a family of stochastic algorithms for solving the Anderson impurity model at finite temperature. These methods first expand the full partition function as a series of Feynman diagrams, employ Wick's theorem to group diagrams into determinants, and finally use Markov chain Monte Carlo to stochastically sum up the resulting series.
Massimo Boninsegni is an Italian-Canadian theoretical condensed matter physicist. He graduated with a Bachelor's degree in physics at the Universita' degli Studi di Genova in 1986.
Boris Vladimirovich Svistunov is a Russian-American physicist specialised in the condensed matter physics. He received his MSc in physics in 1983 from Moscow Engineering Physics Institute, Moscow. In 1990, he received his PhD in theoretical physics from Kurchatov Institute (Moscow), where he worked from 1986 to 2003. In 2003, he joined the Physics Department of the University of Massachusetts, Amherst where he is currently full professor. He is currently also an affiliated faculty member of Wilczek Quantum Center in Shanghai at SJTU and is a participant of Simons collaboration on many electron systems.
Nikolay Victorovich Prokof'ev is a Russian-American physicist known for his works on supersolidity and strongly correlated systems and pioneering numerical approaches.
Quantum computational chemistry is an emerging field that exploits quantum computing to simulate chemical systems. Despite quantum mechanics' foundational role in understanding chemical behaviors, traditional computational approaches face significant challenges, largely due to the complexity and computational intensity of quantum mechanical equations. This complexity arises from the exponential growth of a quantum system's wave function with each added particle, making exact simulations on classical computers inefficient.