# Quantum journal club

Seminar room, (about each 2 weeks) on Mondays @ 11:00am to 12:00am.

##### 11/26/18 : " Correlations of occupation numbers in the canonical ensemble " by Christophe Texier

The connection between the statistical physics of non-interaction indistinguishable particles in quantum mechanics and the theory of symmetric functions will be reviewed.Then, I will study the $p$-point correlation function $\overline{n_1\cdots n_p}$ of occupation numbers in the canonical ensemble ; in the grand canonical ensemble, they are trivially obtained from the independence of individual quantum states, however the constraint on the number of particles makes the problem non trivial in the canonical ensemble. I will show several representations of these correlation functions. I will illustrate the main formulae by revisiting the problem of Bose-Einstein condensation in a 1D harmonic trap in the canonical ensemble, for which we have obtained several analytical results. In particular, in the temperature regime dominated by quantum correlations, the distribution of the ground state occupancy is shown to be a truncated Gumbel law.

Reference :Olivier Giraud, AurÃ©lien Grabsch & Christophe Texier, Correlations of occupation numbers in the canonical ensemble and application to BEC in a 1D harmonic trap, Phys. Rev. A 97, 053615 (2018).

##### 10/29/18 : " Organising strong correlations: Schwinger-Shastry formalism " by Eoin Quinn

##### 10/15/18 : " Topological Transition in a Non-Hermitian Quantum Walk " by Leonardo Mazza

References: M. S. Rudner and L. S. Levitov, Phys. Rev. Lett. 102, 065703 (2009)(https://arxiv.org/abs/0807.2048)

##### 07/09/18 : " Out-of-time-order correlators in quantum mechanics" by Bradraj Pandey

References:1. Out-of-time-order correlators in quantum mechanics (https://arxiv.org/abs/1703.09435) 2. Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet (https://arxiv.org/abs/1608.08938).

##### 06/18/18 : Lieb-Robinson bounds " by Maurizio Fagotti :

##### 06/04/18 : **Quantum mechanics in multi-connected space and the origin of new statistics in low dimensional system** by Raoul santachiara

We recall how to define the problem of N indinstinguishible quantum particles and argue that the topology of the configuration space plays a crucial role. This observation, that has been put on solid grounds by Leinaas and Mirheim in the 1977, has provided the theoretical framework for the existence of anyonic statistics in two dimensions. Moreover, it inspired the connection between the Conformal field theory and topological phases in two dimensions: via this connection, the occurence of non-Abelian anyons in the fractional quantum Hall effect has been suggested.

##### 03/26/18 **Supersolids: a short overview** by Giovanni Martone

References: " Colloquium: Supersolids: What and where are they"by M. Boninsegni and N. V. Prokof'ev, " , "Quantum Tricriticality and Phase Transitions in Spin-Orbit Coupled Bose-Einstein Condensates" by Y. Li, L. P. Pitaevskii, and S. Stringari and "A stripe phase with supersolid properties in spin-orbit-coupled Bose-Einstein condensates" by J. Li, J. Lee, W. Huang, S. Burchesky, B. Shteynas, F. Ç. Top, A. O. Jamison, and W. Ketterle

##### 03/12/18 **Dynamical Quantum phase transition** by Guillaume Roux

References: *Dynamical quantum phase transitions: a review* by M. Heyl and *Dynamical quantum phase transitions* by A.A. Zvyagin