Absence of continuous symmetry-breaking in 2-dimensional quantum systems

• Grant number: 11/20133-0
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: March 19, 2012
• End date: December 24, 2012
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Anatoli Iambartsev
• Grantee: Anatoli Iambartsev
• Visiting researcher: Mark Kelbert
• Visiting researcher institution: Swansea University, Wales
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This project deals with the study of properties of new materials like graphene. The project is concentrated on mathematical problems which emerge in an analysis of properties of a continuous symmetry in two dimensional models of quantum statistical mechanics. Principal goal of the project is to prove that a continuous symmetry of the Hamiltonian is inherited in the Gibbs state, independently of whether the Gibbs state is unique or not. (AU)

Scientific publications

(7)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

KELBERT, MARK; LEONENKO, NIKOLAI; BELITSKY, VLADIMIR. On the Bartlett spectrum of randomized Hawkes processes. Mathematical Communications, v. 18, n. 2, p. 393-407, NOV 2013. (11/20133-0)

KELBERT, M.; SUHOV, YU; YAMBARTSEV, A.. A Mermin-Wagner Theorem for Gibbs States on Lorentzian Triangulations. Journal of Statistical Physics, v. 150, n. 4, p. 671-677, FEB 2013. (12/04372-7, 11/20133-0)

KELBERT, MARK; SUHOV, YURII. A Quantum Mermin-Wagner Theorem for a Generalized Hubbard Model. ADVANCES IN MATHEMATICAL PHYSICS, v. 2013, p. 20-pg., 2013-01-01. (11/20133-0, 12/04372-7)

KELBERT, MARK; SUHOV, YURII. A Quantum Mermin-Wagner Theorem for a Generalized Hubbard Model. ADVANCES IN MATHEMATICAL PHYSICS, 2013. (12/04372-7, 11/20133-0)

SUHOV, Y.; STUHL, I.. FK-DLR properties of a quantum multi-type Bose-gas with a repulsive interaction. Journal of Mathematical Physics, v. 55, n. 8, AUG 2014. (11/51845-5, 11/20133-0)

KELBERT, M.; SUHOV, YU.; YAMBARTSEV, A.. A Mermin-Wagner theorem on Lorentzian triangulations with quantum spins. BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS, v. 28, n. 4, p. 515-537, NOV 2014. (12/04372-7, 11/20133-0)

KELBERT, MARK; SUHOV, YURII. A quantum Mermin-Wagner theorem for quantum rotators on two-dimensional graphs. Journal of Mathematical Physics, v. 54, n. 3, MAR 2013. (12/04372-7, 11/20133-0)