Thermodynamic Properties and Correlation Functions of Low-Dimensional Ultracold Gases
Project PNII-RU-TE-2012-3-0196 (Contract No. 9 25/04/2013 financed by CNCS-UEFISCDI)
Summary
We propose to investigate the thermodynamics and static correlation functions of integrable multicomponent one-dimensional ultracold atomic gases using a new method based on the connection with anisotropic multicomponent spin chains and the quantum transfer matrix. This method has the advantage of deriving a finite number of integral equations characterizing the thermodynamics in stark contrast with the thermodynamic Bethe ansatz approach which produces an infinite number of equations. In addition we can also obtain exact analytical expressions for the correlation lengths of various Green’s functions. The main motivation behind the need for these results is the experimental realization of quasi-one-dimensional spinorial gases in optical lattices and atom chips and the search for new exotic phases.
Objectives
Derivation of efficient (finite number of integral equations) thermodynamic descriptions for multi-component 1D gases (two-component Fermi and Bose gases in 1D with delta-function interaction). Investigation of static correlation functions for various 1D models using the quantum transfer matrix formalism.
Team
Ovidiu I. Patu CS III (PI), Cecil Pompiliu Grunfeld CS I
Articles (ISI)
[PK1] Ovidiu I. Patu and Andreas Klumper, Correlation lengths of the repulsive one-dimensional Bose gas, Phys. Rev. A, 88 033623 (2013) [Impact factor (2012) 3.046 , Top 25% Optics]
[KP1] Andreas Klumper and Ovidiu Patu, Temperature-driven crossover in the Lieb-Liniger model, Phys. Rev. A, 90 053626 (2014) [Impact factor (2013) 2.991 , Top 25% Optics]
[P1] Ovidiu I. Patu, Correlation functions and momentum distribution of one-dimensional hard-core anyons in optical lattices, J. Stat. Mech. P01004 (2015) [Impact factor (2013) 2.056, Top 25% Mathematical Physics]
[PK2] Ovidiu I. Patu and Andreas Klumper, Thermodynamics, density profiles and correlation functions of the inhomogeneous one-dimensional spinor Bose gas, Phys. Rev. A, 92 043631 (2015) [Impact factor (2014) 2.808 , Top 25% Optics]
[PK3] Ovidiu I. Patu and Andreas Klumper, Thermodynamics, contact and density profiles of the repulsive Gaudin-Yang model, Phys. Rev. A, 93, 033616 (2016) [Impact factor (2015) 2.765 , Top 25% Optics]
Articles in preparation
[PK4] Ovidiu I. Patu and Andreas Klumper, Thermodynamics and local correlation functions of the Bose-Fermi mixture
Talks given at conferences and workshops
[C1] Ovidiu I. Patu and Andreas Klumper, Correlation lengths of the Lieb-Linger model, talk presented at „Correlation Functions of Quantum Integrable Models”, September 4-6, 2013 Dijon (France)
[C2] Ovidiu I. Patu and Andreas Klumper, Temperature driven crossover in the 1D Bose gas, talk presented at „Integrable Lattice Models and Quantum Field Theories”, 28 June- 2 July, 2014 Bad Honnef (Germany)
[C3] Ovidiu I. Patu and Andreas Klumper, Efficient thermodynamic description of the Gaudin-Yang model, talk presented at Recent Advances in Quantum Integrable Models (RAQIS 2016) , August 22-26, 2016 Geneve (Switzerland)
[C4] Ovidiu I. Patu and Andreas Klumper, Efficient thermodynamic description of the Gaudin-Yang model, talk presented at New Trends in Low-Dimensional Physics: Quantum Integrability and Aplications September 1-15, 2016 Beijing (China)
Participation at conferences
[CC1] Ovidiu I. Patu Recent Advances in Quantum Integrable Systems, 1-5 September, 2014 Dijon (France)
Scientific reports
Dissemination of results
[K1] Andreas Klumper and Ovidiu I. Patu, Large-distance asymptotic behavior of the temperature correlators in the one-dimensional Bose gas, talk given by A. Klumper at „Mathematical Statistical Physics” July 29-August 3, 2013 Kyoto, Japan
[K2] Andreas Klumper and Ovidiu I. Patu, Large-distance asymptotics of the temperature correlators in one-dimensional Bose gases, talk given by A. Klumper at „Quantum Integrable Systems”, December 2-6, 2013 Calcutta (India)
[K3] Andreas Klumper and Ovidiu I. Patu, Thermodynamics, contact and density profiles of the repulsive Gaudin-Yang model, talk given by A. Klumper at STATPHYS 26, July 18-22, 2016 Lyon (France)