Dr. ADRIAN MAURICIO ESCOBAR RUIZ

I am Adrián Mauricio Escobar Ruiz, currently at the Physics Department of Metropolitan Autonomous University Campus Iztapalapa. My research is in Mathematical Physics primarily focused on the use of symmetries in classical and quantum mechanics. This includes, among other things, perturbative and variational methods in Molecular and Atomic Physics; the classification of (super)integrable higher order Hamiltonian systems; the classical and quantum N-body problem; the semiclassical expansion in QM and QFT, and the phenomenology of Lorentz symmetry breaking.

“Las leyes físicas deben tener la simplicidad y belleza de las matemáticas”

Paul Dirac

PERSONAL INFORMATION

Born

  • Mexico city, Mexico, June 12, 1985

Citizenship

  • Mexican

RESEARCH INTERESTS

Mathematical Physics

  • Integrability and Superintegrability of classical and quantum Hamiltonian systems
  • Path Integral and Feynman diagrams (Instanton calculus)
  • Classical and Quantum many body-problem
  • Perturbative and variational methods in quantum mechanics (atomic and molecular systems in magnetic field)

EDUCATION

2014 | PhD, Physics

  • National Autonomous University of Mexico (UNAM), Mexico
  • Thesis (with Honors): Two charges on a plane in a constant magnetic field
  • Advisor: Alexander V. Turbiner

2010 | MS, Physics

  • National Autonomous University of Mexico (UNAM), Mexico
  • Thesis: Electrostatic models for hydrogen-like molecular chains of two electrons in strong magnetic fields
  • Advisor: Juan Carlos L. Vieyra

2008 | BS, Physics

  • Licentiate in Physics (with Honors) National Autonomous University of Mexico (UNAM), Mexico

MEMBERSHIPS

2017 – 2025

  • National System of Researchers, Mexico (SNI) Level I

TEACHING EXPERIENCE

Fall 2022 | Autonomous Metropolitan University-I | México

Lecturer

  • Mechanics and Chaos (Graduate)
  • Introduction to Continuum Mechanics

Summer 2022 | Autonomous Metropolitan University-I | México

Lecturer

  • Lab of Simulation
  • Introduction to Continuum Mechanics

Spring 2022 | Autonomous Metropolitan University-I | México

Lecturer

  • Advanced topics in Quantum Mechanics
  • Advanced topics in Classical Mechanics

Winter 2022 | Autonomous Metropolitan University-I | México

Lecturer

  • Quantum Mechanics (Graduate)
  • Lab of Simulation

Fall 2021 | Autonomous Metropolitan University-I | México

Lecturer

  • Introduction to QFT
  • Introduction to Continuum Mechanics

Spring 2021 | Autonomous Metropolitan University-I | México

Lecturer

  • Special Relativity
  • Advanced topics in Quantum Mechanics

Winter 2021 | Autonomous Metropolitan University-I | México

Lecturer

  • Quantum Mechanics II

Fall 2020 | Autonomous Metropolitan University-I | México

Lecturer

  • Quantum Mechanics I

Summer 2020 | Autonomous Metropolitan University-I | México

Lecturer

  • Mechanics and Chaos (Graduate)

Spring 2020 | Autonomous Metropolitan University-I | México

Lecturer

  • Classical Mechanics

Winter 2020 | Autonomous Metropolitan University-I | México

Lecturer

  • Elementary Mechanics

Fall 2014 | National Autonomous University of México | México

Teaching Assistant

  • Special Relativity

Spring 2014 | National Autonomous University of México | México

Teaching Assistant

  • Collective Phenomena

Fall 2011-Spring 2013 | National Autonomous University of México | México

Teaching Assistant

  • Selected themes in Theoretical and Mathematical Physics

Fall 2009 | National Autonomous University of México | México

Teaching Assistant

  • Electromagnetism II

Spring 2009 | National Autonomous University of México | México

Teaching Assistant

  • Electromagnetism I

SKILLS

Languages

  • Spanish
  • English
  • Basic French

Coding

  • Fortran
  • Python
  • Mathematica
  • Tex

AWARDS AND SCHOLARSHIPS

September 2016-July 2019

  • Postdoctoral Fellowship, CRM, Université de Montréal, Canadá

2014-August 2016

  • Postdoctoral Fellowship, University of Minnesota, USA

2008-2014

  • National Council of Science and Technology Scholarship, UNAM, México

2007

  • Highest Distinction in Undergraduate General Scholarship, UNAM, México

EDITORIAL WORK

Refereed for Communications in Mathematical Physics, Journal of Physics A, Physical Review D, Annals of Physics, Physics Letters A, Journal of Mathematical Physics, Physica Scripta, Journal of Mathematical Analysis and Applications, Modern Physics Letters B, European Physical Journal

RECENT CONFERENCE AND SEMINAR TALKS

Two-body Coulomb system and g(2) algebra

  • Talk at XII International Symposium on Quantum Theory and Symmetries, Czech Technical University in Prague, Czech Republic, July 2023

El sistema Coulombiano de 2 cargas y el álgebra escondida g^{(2)}

  • Plática en la XXXI Reunión Anual de la División de Gravitación y Física Matemática de la Sociedad Mexicana de Física, que se realizó en el Departamento de Física, CINVESTAV, el 27 y 28 de abril de 2023

Classical 4-body system in volume variables

  • Ponencia en la Sección México de la Sociedad para las Matemáticas Industriales y Aplicadas, 7 a 9 de junio de 2023 en el ITAM, CDMX

Pavel Winternitz and charming lessons in Superintegrability

  • Conferencia Méthodes de théorie des groupes en physique, CRM, Montréal 28 july 2021

Helium-like ions in d-dimensions: analyticity and generalized ground state Majorana solutions

  • Plática en el 11º Taller de Dinámica y Estructura de la Materia, UAM-I, CDMX, 23 june 2021

Two-body neutral system in a constant magnetic field: an approximate solution

  • Seminario de Estructura de la Materia, ICN, UNAM, 18 de febrero de 2021

El sistema clásico de 3 cuerpos

  • Seminario de Gravitación y Física Matemática, Cinvestav, 18 de marzo 2021

Towards instanton amplitudes in QFTs: instanton calculus in 1D quantum mechanics

  • Seminario Sandoval Vallarta, Instituto de Física, UNAM, 20 de noviembre 2020

RECENT PUBLICATIONS


EXPERIENCE