Joan Claramunt

Joan Claramunt
University of Leipzig · Institute of Mathematics

Doctor of Philosophy

About

14
Publications
576
Reads
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46
Citations
Additional affiliations
August 2020 - present
Lancaster University
Position
  • Research Associate
February 2020 - July 2020
Federal University of Santa Catarina
Position
  • PostDoc Position
December 2018 - January 2020
Autonomous University of Barcelona
Position
  • PostDoc Position
Education
July 2014 - April 2015
Imperial College London
Field of study
  • Mathematics and Physics
August 2009 - June 2014
Autonomous University of Barcelona
Field of study
  • Mathematics and Physics

Publications

Publications (14)
Article
In this paper, we introduce a new technique in the study of the * -regular closure of some specific group algebras KG inside 𝒰 ⁢ ( G ) , the * -algebra of unbounded operators affiliated to the group von Neumann algebra 𝒩 ⁢ ( G ) . The main tool we use for this study is a general approximation result for a class of crossed product algebras of the fo...
Article
Full-text available
We apply a construction developed in a previous paper by the authors in order to obtain a formula which enables us to compute $$\ell ^2$$ ℓ 2 -Betti numbers coming from a family of group algebras representable as crossed product algebras. As an application, we obtain a whole family of irrational $$\ell ^2$$ ℓ 2 -Betti numbers arising from the lampl...
Article
In spinor Bose-Einstein condensates, spin-changing collisions are a remarkable proxy to coherently realize macroscopic many-body quantum states. These processes have been, e.g., exploited to generate entanglement, to study dynamical quantum phase transitions, and proposed for realizing nematic phases in atomic condensates. In the same systems dress...
Preprint
In spinor Bose-Einstein condensates, spin-changing collisions are a remarkable proxy to coherently realize macroscopic many-body quantum states. These processes have been, e.g., exploited to generate entanglement, to study dynamical quantum phase transitions, and proposed for realizing nematic phases in atomic condensates. In the same systems dress...
Article
In this paper we consider the algebraic crossed product ${\mathcal{A}}:=C_{K}(X)\rtimes _{T}\mathbb{Z}$ induced by a homeomorphism $T$ on the Cantor set $X$ , where $K$ is an arbitrary field with involution and $C_{K}(X)$ denotes the $K$ -algebra of locally constant $K$ -valued functions on $X$ . We investigate the possible Sylvester matrix rank fu...
Article
Light-induced spin-orbit coupling is a flexible tool to study quantum magnetism with ultracold atoms. In this work we show that spin-orbit coupled Bose gases in a one-dimensional optical lattice can be mapped into a two-leg triangular ladder with staggered flux following a lowest-band truncation of the Hamiltonian. The effective flux and the ratio...
Preprint
Full-text available
We apply a construction developed in a previous paper by the authors in order to obtain a formula which enables us to compute $\ell^2$-Betti numbers coming from a family of group algebras representable as crossed product algebras. As an application, we obtain a whole family of irrational $\ell^2$-Betti numbers arising from the lamplighter group alg...
Preprint
Full-text available
In this paper, we introduce a new technique in the study of the $*$-regular closure of some specific group algebras $KG$ inside $\mathcal{U}(G)$, the $*$-algebra of unbounded operators affiliated to the group von Neumann algebra $\mathcal{N}(G)$. The main tool we use for this study is a general approximation result for a class of crossed product al...
Preprint
Light-induced spin-orbit coupling is a flexible tool to study quantum magnetism with ultracold atoms. In this work we show that spin-orbit coupled Bose gases in a one-dimensional optical lattice can be mapped into a two-leg triangular ladder with staggered flux following a lowest-band truncation of the Hamiltonian. The effective flux and the ratio...
Article
We study beyond-mean-field properties of interacting spin-1 Bose gases with synthetic Rashba-Dresselhaus spin-orbit coupling at low energies. We derive a many-body Hamiltonian following a tight-binding approximation in quasimomentum space, where the effective spin dependence of the collisions that emerge from spin-orbit coupling leads to dominant c...
Preprint
We study beyond-mean-field properties of interacting spin-1 Bose gases with synthetic Rashba-Dresselhaus spin-orbit coupling at low energies. We derive a many-body Hamiltonian following a tight-binding approximation in quasi-momentum space, where the effective spin dependence of the collisions that emerges from spin-orbit coupling leads to dominant...
Preprint
Full-text available
In this paper we consider the algebraic crossed product $\mathcal A := C_K(X) \rtimes_T \mathbb{Z}$ induced by a homeomorphism $T$ on the Cantor set $X$, where $K$ is an arbitrary field and $C_K(X)$ denotes the $K$-algebra of locally constant $K$-valued functions on $X$. We investigate the possible Sylvester matrix rank functions that one can const...
Article
Full-text available
Recent results of Laca, Raeburn, Ramagge and Whittaker show that any self-similar action of a groupoid on a graph determines a 1-parameter family of self-mappings of the trace space of the groupoid C*-algebra. We investigate the fixed points for these self-mappings, under the same hypotheses that Laca et al. used to prove that the C*-algebra of the...
Article
Full-text available
For a division ring $D$, denote by $\mathcal M_D$ the $D$-ring obtained as the completion of the direct limit $\varinjlim_n M_{2^n}(D)$ with respect to the metric induced by its unique rank function. We prove that, for any ultramatricial $D$-ring $\mathcal B$ and any non-discrete extremal pseudo-rank function $N$ on $\mathcal B$, there is an isomor...

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