Postdoc at Caltech 
Supervisor: Gil Refael
Email: [justin@jhwilson.com](mailto:justin@jhwilson.com)

## Interests
- Non-equilibrium effects in topological phases.
- MBL (beyond exact diagonalization)
- Weyl and Dirac metals
- Spin-$S>0$ BECs dynamics and structure.
- Casimir and optical phenomena

## Ongoing projects
- [Persistent Hall response in a quantum quench](http://knowen.org/nodes/1177)
- Phases of a Spin-1 BEC in synthetic dimension experiments with interactions.
	- Charge density waves develop (with ferromagnetic and anti-ferromagnetic interactions) in addition to spin density waves.
    - First order transition into a uniform phase occurs for anti-ferromagnetic interactions.
- Disorder induced phases in a 3D $p+ip$ superconductor
	- Thermal insulator, semi-metal, and diffusive metal found and characterized with critical exponents.
    - Peak in DOS (See Eq. (37) of [Senthil and Fisher](http://arxiv.org/abs/cond-mat/9906290)) observed for strong enough disorder associated with thermally diffusive behavior.
    - Anderson insulating transition observed numerically.
    - Rare region effects destroy the semi-metallic *phase* for infinitesimal disorder.

## Papers 
- J. H. Wilson, J. C. W. Song, and G. Refael, [Persistent Hall response in a quantum quench](https://arxiv.org/abs/1603.01621), arXiv:1603.01621.
- A. A. Allocca, J. H. Wilson, and V. M. Galitski, [Quantum interference phenomena in the Casimir effect](http://dx.doi.org/10.1103/PhysRevA.91.062512), _Phys. Rev. A_ **91**, 062512 (2015). [arXiv:1501.06096](http://arxiv.org/abs/1501.06096)
- J. H. Wilson, A. A. Allocca, and  V. M. Galitski, [Repulsive Casimir force between Weyl semimetals](http://dx.doi.org/10.1103/PhysRevB.91.235115), _Phys. Rev. B_ **91**, 235115 (2015). [arXiv:1501.07659](http://arxiv.org/abs/1501.07659)
- J. H. Wilson, D. K. Efimkin, and V. M. Galitski, [Resonant Faraday and Kerr effects due to in-gap states on the surface of topological insulator](http://dx.doi.org/10.1103/PhysRevB.90.205432), _Phys. Rev. B_ **90**, 205432 (2014). [arXiv:1408.5139](https://arxiv.org/abs/1408.5139)
- A. A. Allocca, J. H. Wilson, and V. M. Galitski, [Non-analytic behavior of the Casimir force across a Lifshitz transition in a spin-orbit coupled material](http://dx.doi.org/10.1103/PhysRevB.90.075420), _Phys. Rev. B_ **90**, 075420 (2014). [arXiv:1312.6754](http://arxiv.org/pdf/1312.6754)
- J. H. Wilson, J. Mitchell, and V. M. Galitski, [Probing the structure of entanglement with entanglement moments](), Solid State Comm. **195**, 43-48 (2014). [arXiv.1305.2005](http://arxiv.org/pdf/1305.2005)
- J. H. Wilson, B. M. Fregoso, and V. M. Galitski, [Entanglement dynamics in a non-Markovian environment: an exactly solvable model](http://prb.aps.org/abstract/PRB/v85/i17/e174304), Phys. Rev. B **85**, 174304 (2012). [arXiv:1202.1614](http://arxiv.org/pdf/1202.1614)
- J. H. Wilson and V. Galitski, [Breakdown of the coherent state path integral: two simple examples](http://link.aps.org/doi/10.1103/PhysRevLett.106.110401), Phys. Rev. Lett. **106**, 110401 (2011). [arXiv:1012.1328](http://arxiv.org/pdf/1012.1328)
- G. Berkolaiko, J. Harrison, and J. H. Wilson, [Mathematical aspects of vacuum energy in quantum graphs](http://iopscience.iop.org/1751-8121/42/2/025204), J. Phys. A: Math. Theor. **42**, 025204 (2009). [arXiv:0711.2707v3](http://arxiv.org/pdf/0711.2707)
- S. A. Fulling, P. Kuchment, and J. H. Wilson, [Index theorems for quantum graphs](http://iopscience.iop.org/1751-8121/40/47/009), J. Phys. A: Math. Theor. **40**, 14165–14180 (2007). [arXiv:0708.3456](http://arxiv.org/pdf/0708.3456)
- S. A. Fulling, L. Kaplan, and J. H. Wilson, [Vacuum energy and repulsive Casimir forces in quantum star graphs](http://pra.aps.org/abstract/PRA/v76/i1/e012118), Phys. Rev. A 76, 012118 (2007). [arXiv:quant-ph/0703248](http://arxiv.org/pdf/quant-ph/0703248)
- S. A. Fulling and J. H. Wilson, [Vacuum energy and closed orbits in quantum graphs](https://www.math.tamu.edu/~stephen.fulling/fulaga.pdf), Proc. Symp. Pure Math. 77, 673–689 (2008) (volume associated with the program Analysis on Graphs and its applications, Newton Institute, 2007).

## Theses
- Optical and Casimir Effects in Topological Materials, Ph. D. Dissertation in condensed matter physics, University of Maryland at College Park, 2015. [http://hdl.handle.net/1903/16633](http://hdl.handle.net/1903/16633)
- Vacuum Energy in Quantum Graphs, University Undergraduate Research Fellows Thesis, Texas A&M University, 2007. [http://handle.tamu.edu/1969.1/5682](http://handle.tamu.edu/1969.1/5682)