What is he best known for?
The fields of study he is best known for:
- Quantum mechanics
- Mathematical analysis
- Partial differential equation
His primary areas of investigation include Mathematical analysis, Schrödinger equation, Classical mechanics, Planck constant and Semiclassical physics.
His Mathematical analysis research incorporates themes from Applied mathematics and Nonlinear system.
Peter A. Markowich focuses mostly in the field of Nonlinear system, narrowing it down to topics relating to Numerical analysis and, in certain cases, Gross–Pitaevskii equation.
His work deals with themes such as Wigner distribution function, Quantum and Phase space, which intersect with Schrödinger equation.
His Planck constant research integrates issues from Invariant, Classical limit and Quantum hydrodynamics.
While the research belongs to areas of Semiclassical physics, Peter A. Markowich spends his time largely on the problem of Limit, intersecting his research to questions surrounding Boundary value problem, Scattering and Macroscopic quantum phenomena.
His most cited work include:
- Semiconductor equations (1405 citations)
- Homogenization limits and Wigner transforms (488 citations)
- Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation (397 citations)
What are the main themes of his work throughout his whole career to date?
His primary scientific interests are in Mathematical analysis, Nonlinear system, Classical mechanics, Boundary value problem and Schrödinger equation.
His Partial differential equation, Poisson's equation, Singular perturbation, Numerical analysis and Asymptotic expansion investigations are all subjects of Mathematical analysis research.
The Nonlinear system study combines topics in areas such as Bose–Einstein condensate, Spectral method, Statistical physics, Uniqueness and Applied mathematics.
The concepts of his Classical mechanics study are interwoven with issues in Quantum, Classical limit, Quantum hydrodynamics and Gross–Pitaevskii equation.
His Boundary value problem research is multidisciplinary, incorporating elements of Eigenvalues and eigenvectors and Ordinary differential equation, Differential equation.
His work carried out in the field of Schrödinger equation brings together such families of science as Mathematical physics and Semiclassical physics.
He most often published in these fields:
- Mathematical analysis (47.41%)
- Nonlinear system (18.10%)
- Classical mechanics (13.36%)
What were the highlights of his more recent work (between 2015-2020)?
- Mathematical analysis (47.41%)
- Applied mathematics (11.64%)
- Limit (9.05%)
In recent papers he was focusing on the following fields of study:
His main research concerns Mathematical analysis, Applied mathematics, Limit, Statistical physics and Partial differential equation.
His studies deal with areas such as Time evolution, Square and Relaxation as well as Mathematical analysis.
His work on Ode as part of general Applied mathematics research is frequently linked to Model parameters, bridging the gap between disciplines.
His Statistical physics study incorporates themes from Network formation and Boundary.
Peter A. Markowich has researched Dynamical systems theory in several fields, including Balanced flow and Classical mechanics.
His Schrödinger equation study frequently draws connections to adjacent fields such as Nonlinear system.
Between 2015 and 2020, his most popular works were:
- Continuous data assimilation for the three-dimensional Brinkman-Forchheimer-extended Darcy model (51 citations)
- Notes on a PDE System for Biological Network Formation (25 citations)
- Biological transportation networks: Modeling and simulation (21 citations)
In his most recent research, the most cited papers focused on:
- Quantum mechanics
- Mathematical analysis
- Partial differential equation
Mathematical analysis, Partial differential equation, Applied mathematics, Network formation and Discretization are his primary areas of study.
His Mathematical analysis study integrates concerns from other disciplines, such as Inverse and Square.
His Partial differential equation research includes elements of Isotropy, Dynamical systems theory and Classical mechanics.
Peter A. Markowich combines subjects such as State and Graph with his study of Applied mathematics.
His work in Network formation covers topics such as Statistical physics which are related to areas like Limit, Continuum and Function.
In Discretization, Peter A. Markowich works on issues like Finite element method, which are connected to Reaction–diffusion system.
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