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Lars Onsager and Richard Feynman envisioned that the three-dimensional (3D) superfluid-to-normal $\lambda$ transition in $^{4}$He occurs through the proliferation of vortices. This process should hold for every phase transition in the same…
In the present work the Chern-Simons(C-S) gauge field theory developed by Jackiw and Pi [1] and widely used to explain the fractional quantum Hall effects, was applied to describe the two-dimensional (2D) electron-hole (e-h) system in a…
A continuum version of the vortex-boson duality in (3+1) dimensions is formulated and its implications studied in the context of a pair Wigner crystal in underdoped cuprate superconductors. The dual theory to a phase fluctuating…
The description of a system of vortices in terms of dual fields provides a window to new phases of the system. It was found recently that dualizing a 3+1-d boson-fermion system leads to a system of fermions and vortices interacting via a…
We present a simple scheme for implementing a one-dimensional (1D) magnetic-flux lattice of ultracold fermionic spin-$1/2$ atoms. The resulting tight-binding model supports gapped and gapless topological phases, and chiral currents for…
We consider a rotating Bose-Einstein condensate confined in combined harmonic and quartic traps, following recent experiments [V. Bretin, S. Stock, Y. Seurin and J. Dalibard, cond-mat/0307464]. We investigate numerically the behavior of the…
A Bose-Einstein condensate of atoms, trapped in an axially symmetric harmonic potential, is considered. By averaging the spatial density along the symmetry direction over a length that preserves the aspect ratio, the system may be mapped on…
Motivated by recent experimental works, we investigate a system of vortex dynamics in an atomic Bose-Einstein condensate (BEC), consisting of three vortices, two of which have the same charge. These vortices are modeled as a system of point…
Full quantum-mechanical description of electrons moving in 3D structures with unidirectional periodic modulation subject to tilted magnetic fields requires an extensive numerical calculation. To understand magneto-oscillations in such…
For a constant density of spinless fermions in strongly disordered two dimensional clusters, the energy level spacing between the ground state and the first excitation is studied for increasing system sizes. The average indicates a smooth…
We proposed a formally exact, probabilistic method to assess the validity of the Thomas-Fermi potential for three-dimensional condensed matter systems where electron dynamics is constrained to the Fermi surface. Our method, which relies on…
We show that in (3+1)-D space-time dimensions, the O(6) non-linear sigma model, with a level-1 Wess-Zumino-Witten term, exhibits the electromagnetic duality. If we name the six components of the sigma field as the Neel and…
We start from a Lorentz non-invariant Abelian-Higgs model in 1+3 dimensions, and carry out its dimensional reduction to $D=1+2$. The planar model resulting thereof is composed by a Maxwell-Chern-Simons-Proca gauge sector, a massive scalar…
We leverage random phase approximation and unbiased auxiliary-field quantum Monte Carlo methods to compute dynamical correlations for a dilute homogeneous two-dimensional attractive Fermi gas. Our main purpose is to quantitatively study the…
The noncommutativity of a four-dimensional phase space is introduced from a purely symplectic point of view. We show that there is always a coordinate map to locally eliminate the gauge fluctuations inducing the deformation of the…
Quantum electrodynamics in three spacetime dimensions, with one massless fermion species, is studied using a non-perturbative variational approach. Quantization of the theory follows Dirac's Hamiltonian procedure, with a gauge invariant…
We report on a theoreticl study of the electronic structure of quasiperiodic, quasi-one-dimensional systems where fully three dimensional interaction potentials are taken into account. In our approach, the actual physical potential acting…
We investigate probe limit vortex solutions of a charged scalar field in Einstein-Maxwell theory in 3+1 dimensions, for an asymptotically AdS Schwarzschild black hole metric with the addition of an axionic coupling to the Maxwell field. We…
Three dimensional continuous and discrete Fourier-like transforms, based on the three simple and four semisimple compact Lie groups of rank 3, are presented. For each simple Lie group, there are three families of special functions ($C$-,…
Gauge invariance requires physical states to be composite, even in the weak sector of the Standard Model (SM). The Fr\"ohlich-Morchio-Strocchi (FMS) mechanism resolves this subtlety and predicts additional Higgs contributions in SM…