Related papers: Doubly Periodic Instanton Zero Modes
We obtain multi-soliton solutions of the time-dependent Bogoliubov-de Gennes equations or, equivalently, Gorkov equations that describe the dynamics of a fermionic condensate in the dissipationless regime. There are two kinds of solitons -…
We find the full spectrum of fermion bound states on a Z_2 kink. In addition to the zero mode, there are int[2 m_f/m_s] bound states, where m_f is the fermion and m_s the scalar mass. We also study fermion modes on the background of a…
Pairing between fermions that attract each other, reveal itself to the macroscopic world in the form of superfluidity. Since the discovery of fermionic superfluidity, intense search has been going on to find various unconventional forms of…
Recently the anomalous behaviour of Fermions below the Fermi temperature was analysed in detail from different viewpoints. In the present communication we obtain a justification for this anomalous semionic behaviour and also obtain the…
Noninteracting fermions, placed in a system with a continuous density of states, may have zeros in the $N$-fermion canonical partition function on the positive real $\beta$ axis (or very close to it), even for a small number of particles.…
In this chapter the recent theoretical work on phase transition in imbalanced fermion superfluids is reviewed. The imbalanced systems are those in which the two fermionic species candidate to form pairing have different Fermi surfaces or…
We study Landau-Zener transitions in a fermionic dissipative environment where a two-level (up and down states) system is coupled to two metallic leads kept with different chemical potentials at zero temperature. The dynamics of the system…
It is known that a non-local complex fermion can be written in terms of two Majorana fermions. We exploit this fact to explain the system of two Majorana zero modes bound to a vortex and an anti-vortex, on the surface of a topological…
We consider two types of "dimension bubbles", which are viewed as 4d nontopological solitons that emerge from a 5d theory with a compact extra dimension. The size of the extra dimension varies rapidly within the domain wall of the soliton.…
We propose one possible mechanism for deconfinement based on an SU(2) slave-boson theory. Resorting to an effective field theory approach, we show that introduction of an isospin interaction potential gives rise to a fermion zero mode in an…
We clarify certain aspects of instanton operators in five-dimensional supersymmetric gauge theories. In particular, we show how, in the pointlike limit, they become supersymmetric and provide the natural bridge with the instantonic states…
We derive analytic formulas for the zero-modes of the Dirac equation in the adjoint representation in the background field of Q=1 SU(N) calorons. Solutions with various boundary conditions are obtained, including the physically most…
We analyze the zero-modes of the Dirac operator in quenched SU(3) gauge configurations at non-zero temperature and compare periodic and anti-periodic temporal boundary conditions for the fermions. It is demonstrated that for the different…
We investigate some properties of a system of Dirac fermions in 2+1 dimensions, with a space dependent mass having domain wall like defects.These defects are defined by the loci of the points where the mass changes sign. In general, they…
A sign of topological order in a gapped one-dimensional quantum chain is the existence of edge zero modes. These occur in the Z_2-invariant Ising/Majorana chain, where they can be understood using free-fermion techniques. Here I discuss…
We look for minimal chiral sets of fermions beyond the standard model that are anomaly free and, simultaneously, vectorlike particles with respect to colour SU(3) and electromagnetic U(1). We then study whether the addition of such…
Candidate homogeneous, isotropic superfluid or superconducting states of paired fermion species with different chemical potentials, can lead to quasiparticle excitation energies that vanish at either zero, one, or two spheres in momentum…
We initiate the systematic study of $G_2$-instantons with $SU(2)^2$-symmetry. As well as developing foundational theory, we give existence, non-existence and classification results for these instantons. We particularly focus on…
Electron fractionalization is intimately related to topology. In one-dimensional systems, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall…
We construct a five-parameter family of gauge-nonequivalent SU(2) instantons on a noncommutative four sphere $S_\theta^4$ and of topological charge equal to -1. These instantons are critical points of a gauge functional and satisfy…